{ "schema_version": 1, "generated_from": "data/events/*.yaml", "events": [ { "schema_version": 1, "id": "evt-2026-openai-math-release", "slug": "openai-722-manuscript-mathematics-release", "title": { "en": "OpenAI releases 722 AI-generated mathematics manuscripts across 372 result families", "zh-CN": "OpenAI 发布 722 篇 AI 生成数学手稿，覆盖 372 个成果族" }, "dates": { "event": "2026-10-06", "first_public_claim": "2026-10-06", "paper_release": "2026-10-06", "artifact_release": "2026-10-06", "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "discovery", "proof", "formalization" ], "significance": { "tier": "H1", "rationale": { "en": "This release is a Historical Milestone because it moves AI-generated research mathematics from isolated flagship results to a public corpus at unprecedented scale. OpenAI released 722 manuscripts grouped into 372 result families, together with a substantial Lean formalization programme, reasoning summaries, compute and process disclosures, persistent public artifacts and revision commitments. The historical significance lies in the scale and public scholarly interface of the release, not in treating every mathematical claim in the collection as correct.", "zh-CN": "该发布被列为 Historical Milestone，因为它把 AI 生成研究数学从少量旗舰成果推进到 前所未有规模的公开成果库。OpenAI 一次性公开 722 篇手稿、372 个成果族，并配套 大规模 Lean 形式化计划、推理摘要、算力与流程披露、持久化公开产物及版本修订承诺。 其历史意义来自发布规模和面向学术共同体的公开接口，而不是把库内每一项数学主张都 视为已经正确验证。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "On 6 October 2026, OpenAI released a public collection of mathematical manuscripts and proof artifacts produced by an unreleased internal model. The repository reports 722 manuscripts organized into 372 result families, selected from roughly 4,000 posed research problems. OpenAI says that the vast majority were produced with a common procedure averaging about three hours of ChatGPT Pro thinking compute per result. The collection includes claimed resolutions and advances across multiple areas of mathematics and theoretical computer science, with many but not all manuscripts accompanied by Lean formalizations.", "zh-CN": "2026 年 10 月 6 日，OpenAI 公开发布由未公开内部模型产生的数学手稿与证明产物集合。 仓库记录共有 722 篇手稿、372 个成果族，来源于约 4,000 个被提出的研究问题。 OpenAI 表示绝大多数结果使用统一流程产生，平均每项结果消耗约三小时 ChatGPT Pro thinking compute。集合覆盖数学与理论计算机科学多个方向中的开放问题解决或推进， 其中许多但并非全部手稿配有 Lean 形式化。" }, "summary": { "en": "The public repository includes an overview, a manuscript map, PDFs and sources, a Lean library and formalization catalogue, ten selected reasoning summaries and release-history commitments. OpenAI explicitly warns that some unformalized results may contain issues and says revisions will remain accessible. The release followed consultation with the independent Advisory Group on Mathematics and Artificial Intelligence. AGMAI publicly stated that its advice does not endorse the mathematics or OpenAI's process and characterized the release as the beginning of broader human understanding and community assessment.", "zh-CN": "公开仓库包含总览、手稿索引、PDF 与源码、Lean 库与形式化目录、十个精选 reasoning summaries，以及保存公开版本历史的承诺。OpenAI 明确提醒部分未形式化结果可能存在问题， 并表示后续修订将保留历史版本。此次发布此前与独立的 Advisory Group on Mathematics and Artificial Intelligence 进行了沟通；AGMAI 随后公开声明，其建议不构成对数学结果 或 OpenAI 流程的背书，并把本次发布视为更广泛人类理解与共同体评估的开始。" }, "why_it_matters": { "en": "The event changes the scale at which frontier AI-generated mathematics enters the public research ecosystem. It combines bulk research generation, formal verification infrastructure, provenance disclosure, citation and revision mechanisms and governance consultation in one release. It also creates a new editorial challenge: aggregate historical importance can be high even while individual results occupy very different verification states and require separate specialist review.", "zh-CN": "本事件改变了前沿 AI 生成数学进入公共研究生态的规模，把批量研究生成、形式验证基础设施、 provenance 披露、引用与修订机制以及治理咨询集中到一次发布中。它同时带来新的编辑问题： 整体事件可以具有很高历史重要性，但其中各个结果的验证状态可能差异巨大，仍需分别接受 专业审查。" }, "ai_role": { "level": "unclear", "description": { "en": "OpenAI describes the unreleased internal model as the primary producer of the collection and says the vast majority of results were obtained through a common evaluation procedure. However, the exact human contribution, editing, checking and formalization process varies across the 372 families. Chronicle therefore records strong AI authorship at the aggregate level without assigning one uniform per-result model-human division of labour.", "zh-CN": "OpenAI 将未公开内部模型描述为该成果集的主要产生者，并表示绝大多数结果来自统一评测流程。 但 372 个成果族中的人类贡献、编辑、检查与形式化流程并不完全一致，因此 Chronicle 只在整体层面记录强 AI 生成属性，不为每项结果统一指定同一套模型—人类分工。" } }, "human_contribution": { "description": { "en": "Humans selected and posed research problems, curated results into families and manuscripts, prepared the release infrastructure, performed varying levels of editing and verification, and coordinated formalization and external consultation. The repository identifies exceptions to the otherwise common production procedure.", "zh-CN": "人类负责选择和提出研究问题、把结果整理成成果族和手稿、准备发布基础设施、进行不同程度 的编辑与验证，并协调形式化和外部咨询。公开仓库也明确标记了少数偏离统一生成流程的例外。" } }, "systems": [ "openai-internal-math-model", "lean", "comparator" ], "organizations": [ "openai", "advisory-group-on-mathematics-and-artificial-intelligence" ], "people": [], "problems": [], "methods": [ "large-scale-mathematical-discovery", "research-problem-evaluation", "formal-verification", "provenance-disclosure", "responsible-release" ], "verification": { "evidence_level": "E3", "status": "under_verification", "formal_assurance": "artifact_available", "history": [ { "date": "2026-10-06", "status": "under_verification", "evidence_level": "E3", "note": { "en": "OpenAI released the manuscripts, source files and a substantial public formalization library. The repository explicitly states that verification stages differ across results, that not all manuscripts have Lean formalizations and that some unformalized results may contain issues.", "zh-CN": "OpenAI 公开发布手稿、源码以及大规模形式化库。仓库明确说明不同成果处于不同验证阶段， 并非全部手稿都有 Lean 形式化，而且部分未形式化结果可能存在问题。" } }, { "date": "2026-10-06", "status": "under_verification", "evidence_level": "E3", "note": { "en": "AGMAI independently confirmed its consultation role and the importance of public scrutiny while explicitly declining to endorse the mathematical claims or certify OpenAI's compliance with its recommendations. Aggregate release significance is therefore kept separate from per-result mathematical verification.", "zh-CN": "AGMAI 独立确认了其咨询角色以及公开审查的重要性，同时明确不对数学主张背书，也不认证 OpenAI 已完全遵守其建议。因此 Chronicle 将整体发布的历史意义与逐项数学验证严格分离。" } } ] }, "sources": [ { "id": "openai-sharing-ai-progress-math-2026", "tier": "S2", "type": "official_announcement", "title": "Sharing AI progress in mathematics", "url": "https://openai.com/index/sharing-ai-progress-in-mathematics/", "primary": true, "published_date": "2026-10-06", "accessed_at": "2026-10-07" }, { "id": "openai-math-repository-2026", "tier": "S1", "type": "repository", "title": "OpenAI mathematics manuscript collection", "url": "https://github.com/openai/math", "primary": true, "published_date": "2026-10-06", "accessed_at": "2026-10-07" }, { "id": "agmai-openai-release-2026", "tier": "S2", "type": "official_announcement", "title": "On OpenAI's Release of Mathematical Results", "url": "https://agmai.org/", "primary": false, "published_date": "2026-10-06", "accessed_at": "2026-10-07" }, { "id": "agmai-responsible-release-2026", "tier": "S2", "type": "official_announcement", "title": "Responsible Release of AI-Generated Mathematics", "url": "https://agmai.org/general-sep29/", "primary": false, "published_date": "2026-09-29", "accessed_at": "2026-10-07" } ], "artifacts": [ { "id": "openai-math-corpus", "kind": "code", "title": "OpenAI public mathematics collection", "url": "https://github.com/openai/math" } ], "relationships": { "predecessors": [ "evt-2026-agmai-responsible-release" ], "successors": [], "related": [ "evt-2026-openai-prime-gaps-186", "evt-2026-openai-ten-advances" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "openai", "ai-generated-mathematics", "mathematical-discovery", "formalization", "lean", "responsible-release", "research-corpus" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-claude-3sum-apsp", "slug": "claude-3sum-apsp-polynomial-speedup", "title": { "en": "Claude is credited with discovering truly subquadratic 3SUM and truly subcubic APSP algorithms", "zh-CN": "Claude 被归因于发现真正次二次 3SUM 与真正次三次 APSP 算法" }, "dates": { "event": "2026-10-05", "first_public_claim": "2026-10-05", "paper_release": "2026-10-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "discovery", "proof", "formalization" ], "significance": { "tier": "H1", "rationale": { "en": "This result is a Historical Milestone because it reports the first polynomial exponent improvements for 3SUM and APSP, two problems whose conjectured near-quadratic and near-cubic barriers structured fine-grained complexity for decades. The paper attributes the core algorithmic discovery to an Anthropic research model operating in a long session without human input, after which Josh Alman and Virginia Vassilevska Williams independently understood, simplified, strengthened and extended the method. Anthropic subsequently released a substantial Lean formalization of the principal deterministic claims.", "zh-CN": "该结果被列为 Historical Milestone，因为它报告了 3SUM 与 APSP 的首次多项式级 指数改进，而这两个问题长期以来的近二次与近三次复杂度假设塑造了 fine-grained complexity 的研究框架。论文把核心算法发现归因于一个 Anthropic 研究模型在无人类 输入的长程 session 中完成；随后 Josh Alman 与 Virginia Vassilevska Williams 独立理解、简化、强化并扩展该方法。Anthropic 又公开了主要 deterministic claims 的大规模 Lean 形式化。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "Alman and Vassilevska Williams report deterministic algorithms solving 3SUM on polynomial-size integer inputs in O(n^1.9992) time and APSP with polynomially bounded integer weights in O(n^2.99942) time in their word-RAM formulation, together with related improvements for Exact Triangle, min-plus product and zero-weight k-Clique. The paper states that these are the first truly subquadratic and truly subcubic algorithms in the corresponding settings and that they refute the standard 3SUM and APSP hypotheses used in fine-grained complexity.", "zh-CN": "Alman 与 Vassilevska Williams 报告 deterministic algorithms：在其 word-RAM 模型中，对多项式大小整数输入的 3SUM 达到 O(n^1.9992)，对多项式有界整数权重的 APSP 达到 O(n^2.99942)，并同时改进 Exact Triangle、min-plus product 与 zero-weight k-Clique。论文称这些是在相应设定下首次真正次二次与真正次三次算法， 并由此推翻 fine-grained complexity 中常用的 3SUM 与 APSP hypotheses。" }, "summary": { "en": "The paper's methodology section says an Anthropic employee initially asked an internal research model to study a cryptographic question based on average-case Zero-k-Clique. Claude unexpectedly developed a new algorithm, first for the average-case setting and then for the worst case, during a session producing about 16 million output tokens with no human input. Anthropic shared the result with Alman and Vassilevska Williams, who reconstructed the argument, simplified it, improved constants and exponents, derived additional consequences and wrote the research paper. After the paper was complete, Anthropic used a research model to formalize major deterministic claims in Lean.", "zh-CN": "论文的方法部分说明，Anthropic 员工最初让内部研究模型研究一个基于 average-case Zero-k-Clique 的密码学问题。Claude 在约 1,600 万 output tokens、无人类输入的 session 中意外发展出新算法，先处理平均情形，再推广到最坏情形。Anthropic 将结果 提供给 Alman 与 Vassilevska Williams；两位作者随后重新理解论证、简化方法、 改进常数与指数、推出更多后果并撰写论文。论文完成后，Anthropic 又使用研究模型 把主要 deterministic claims 形式化到 Lean 中。" }, "why_it_matters": { "en": "This event provides unusually explicit provenance for a frontier mathematical algorithm originating in a long autonomous model run and then surviving expert human reconstruction. The result does not merely improve a benchmark: it changes the conjectural landscape of fine-grained complexity and forces reconsideration of reductions and hardness assumptions built on 3SUM and APSP. The accompanying Lean artifact further makes a subset of the headline claims mechanically inspectable.", "zh-CN": "本事件为“前沿数学算法由长程自主模型运行产生、随后经专家重新理解”的过程提供了罕见的 明确 provenance。它不是 benchmark 提升，而是改变 fine-grained complexity 的 猜想格局，并迫使研究者重新审视建立在 3SUM 与 APSP 假设上的归约和困难性框架。 配套 Lean artifact 还使部分 headline claims 可以接受机械检查。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The paper attributes the core algorithmic discovery to an Anthropic research model in a 16-million-output-token session with no human input. Human authors then independently understood the method, simplified and strengthened it, derived new consequences and took responsibility for the final paper. This classification applies to the reported discovery workflow, not to every theorem and exposition choice in the final manuscript.", "zh-CN": "论文把核心算法发现归因于 Anthropic 研究模型在约 1,600 万 output tokens 且 无人类输入的 session 中完成。人类作者随后独立理解该方法、简化并强化论证、 推出新的后果，并对最终论文负责。该分类描述的是公开披露的发现流程，并不表示 最终论文中的每个定理和阐释选择都由模型完成。" } }, "human_contribution": { "description": { "en": "Josh Alman and Virginia Vassilevska Williams reconstructed the model's algorithm, simplified and strengthened it, improved quantitative bounds, developed further consequences and wrote the paper. Anthropic researchers supplied the model run and later formalization infrastructure.", "zh-CN": "Josh Alman 与 Virginia Vassilevska Williams 重新构建模型算法、简化并强化方法、 改进定量界、发展进一步后果并撰写论文；Anthropic 研究人员提供模型运行以及后续 形式化基础设施。" } }, "systems": [ "claude", "lean", "comparator", "nanoda" ], "organizations": [ "anthropic" ], "people": [ "josh-alman", "virginia-vassilevska-williams" ], "problems": [ "three-sum", "all-pairs-shortest-paths" ], "methods": [ "fine-grained-algorithms", "sparse-lopsided-triangles", "word-ram", "formal-verification" ], "verification": { "evidence_level": "E3", "status": "under_verification", "formal_assurance": "machine_checked", "history": [ { "date": "2026-10-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The research paper publicly states the algorithmic results and gives an explicit account of the AI discovery workflow and subsequent human reconstruction.", "zh-CN": "研究论文公开陈述算法结果，并明确记录 AI 发现流程及随后的人类重建过程。" } }, { "date": "2026-10-07", "status": "under_verification", "evidence_level": "E3", "note": { "en": "Anthropic's public Lean project proves five headline deterministic claims, including the 3SUM and APSP word-RAM bounds, and documents Comparator/Nanoda checking procedures. The repository also explicitly lists paper claims that are not formalized in the same machine model. Chronicle has not located an independent external replay or specialist review sufficient for independently_verified status.", "zh-CN": "Anthropic 的公开 Lean 项目证明五项 headline deterministic claims，其中包括 3SUM 与 APSP 的 word-RAM 界，并记录 Comparator/Nanoda 检查流程。仓库也明确 列出未在同一机器模型中形式化的论文主张。Chronicle 尚未找到足以支持 independently_verified 状态的外部独立重放或专业审查。" } } ] }, "sources": [ { "id": "alman-vw-3sum-apsp-2026", "tier": "S1", "type": "paper", "title": "Truly Subquadratic 3SUM and Truly Subcubic APSP via Triangles in Sparse Lopsided Graphs", "url": "https://arxiv.org/abs/2610.06783", "primary": true, "published_date": "2026-10-05", "accessed_at": "2026-10-07" }, { "id": "anthropic-3sum-apsp-formalization", "tier": "S1", "type": "formal_artifact", "title": "Truly Subquadratic 3SUM and Truly Subcubic APSP — Lean 4 formalization", "url": "https://github.com/anthropics/formal-math/tree/main/3sum-apsp", "primary": true, "published_date": null, "accessed_at": "2026-10-07" } ], "artifacts": [ { "id": "anthropic-3sum-apsp-lean", "kind": "proof", "title": "Lean formalization of the principal deterministic 3SUM and APSP claims", "url": "https://github.com/anthropics/formal-math/tree/main/3sum-apsp" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "claude", "3sum", "apsp", "fine-grained-complexity", "algorithms", "lean", "ai-generated-mathematics" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-chatgpt-kls-proof", "slug": "chatgpt-assisted-kls-proof", "title": { "en": "Bizeul, Klartag and Lehec release a ChatGPT-assisted proof of the KLS conjecture", "zh-CN": "Bizeul、Klartag 与 Lehec 发布由 ChatGPT 深度参与的 KLS 猜想证明" }, "dates": { "event": "2026-10-04", "first_public_claim": "2026-10-04", "paper_release": "2026-10-04", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "discovery", "proof" ], "significance": { "tier": "H1", "rationale": { "en": "This Event is a Historical Milestone because the paper claims a complete proof of the Kannan–Lovász–Simonovits conjecture, a central long-standing problem in asymptotic convex geometry and high-dimensional probability, and the authors explicitly credit ChatGPT with finding most proofs and mathematical ideas in the manuscript. If the result withstands specialist scrutiny, it is a direct example of a general-purpose conversational AI making primary intellectual contributions to the resolution of a major open conjecture.", "zh-CN": "本事件被列为 Historical Milestone，因为论文声称完整证明 Kannan–Lovász–Simonovits 猜想——渐近凸几何与高维概率中的长期核心问题——并且作者明确将论文中大多数证明与 数学思想归因于 ChatGPT。如果该结果经受专业审查，它将成为通用对话式 AI 对重大开放 猜想解决作出主要智力贡献的直接案例。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Pierre Bizeul, Boaz Klartag and Joseph Lehec claim a dimension-free Poincaré bound for isotropic log-concave probability measures, thereby proving the Kannan–Lovász–Simonovits conjecture. Their paper builds on very recent work of Song and Zhang that reduced the remaining dimension dependence to a slowly growing factor and claims to remove that dependence completely.", "zh-CN": "Pierre Bizeul、Boaz Klartag 与 Joseph Lehec 声称对 isotropic log-concave probability measures 建立与维数无关的 Poincaré bound，从而证明 Kannan–Lovász–Simonovits 猜想。论文建立在 Song 与 Zhang 极近期工作之上； 后者已把剩余维数依赖降到缓慢增长因子，而新论文声称进一步完全去除该依赖。" }, "summary": { "en": "In the acknowledgements, the authors state that most proofs and mathematical ideas in the paper were found by ChatGPT. They identify the suspension idea as a notable human contribution and describe their role as understanding the model's proofs, checking and organizing the mathematics and improving the exposition. The paper is currently a very recent preprint; Chronicle has not located a public proof-assistant artifact or independent specialist review sufficient to move the event beyond a paper-released verification state.", "zh-CN": "作者在致谢中明确表示，论文中的大多数证明与数学思想由 ChatGPT 找到；其中 suspension idea 被特别指出为人类作者提出的重要贡献。作者把自己的主要作用描述为理解模型给出的 证明、检查和组织数学内容并改善阐释。目前该成果仍是一篇非常新的预印本；Chronicle 尚未找到公开 proof-assistant artifact 或足以把事件提升到更高验证状态的独立专业审查。" }, "why_it_matters": { "en": "KLS connects convex geometry, concentration of measure, Markov-chain mixing and high-dimensional algorithms. A correct dimension-free proof would close a major research programme with broad consequences. The explicit attribution to ChatGPT is historically significant because the model is described not merely as a calculator, proof checker or drafting assistant, but as the source of most of the mathematical ideas and proofs later understood and presented by expert human authors.", "zh-CN": "KLS 连接凸几何、测度集中、Markov chain mixing 与高维算法。若 dimension-free 证明正确，将结束一条重要研究路线并产生广泛后果。作者对 ChatGPT 的明确归因具有特殊 历史意义：模型并非仅作为计算器、证明检查器或写作助手，而被描述为后来由专家作者理解 和呈现的大多数数学思想与证明的来源。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The authors explicitly state that ChatGPT found most proofs and mathematical ideas in the paper. Human authors supplied important ideas of their own, including the suspension idea, and were responsible for understanding, checking, organizing and presenting the final proof. This classification records the authors' own account and does not imply independent reconstruction of every model interaction.", "zh-CN": "作者明确表示 ChatGPT 找到了论文中的大多数证明与数学思想。人类作者也提供了重要原创 思想，包括 suspension idea，并负责理解、检查、组织和呈现最终证明。该分类记录作者 自己的叙述，并不表示 Chronicle 已独立重建每一次模型交互。" } }, "human_contribution": { "description": { "en": "Pierre Bizeul, Boaz Klartag and Joseph Lehec selected and developed the research direction, contributed original ideas, understood and checked the model-produced arguments, integrated them with the recent literature and wrote the final mathematical exposition.", "zh-CN": "Pierre Bizeul、Boaz Klartag 与 Joseph Lehec 负责选择和发展研究方向，贡献原创 思想，理解并检查模型生成的论证，把结果与最新文献整合，并完成最终数学阐释。" } }, "systems": [ "chatgpt" ], "organizations": [], "people": [ "pierre-bizeul", "boaz-klartag", "joseph-lehec" ], "problems": [ "kannan-lovasz-simonovits-conjecture" ], "methods": [ "convex-geometry", "localization", "stochastic-localization", "poincare-inequality", "human-ai-collaboration" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2026-10-04", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The authors released a public preprint containing the claimed KLS proof and an explicit first-party description of ChatGPT's role. The Event records that publication and attribution; it does not independently certify the mathematical correctness or historical priority of the proof.", "zh-CN": "作者公开发布包含 KLS 证明主张的预印本，并直接说明 ChatGPT 的作用。该 Event 记录的是论文发布与归因，不代表 Chronicle 独立认证证明的数学正确性或历史优先权。" } } ] }, "sources": [ { "id": "bizeul-klartag-lehec-kls-2026", "tier": "S1", "type": "paper", "title": "A proof of the Kannan–Lovász–Simonovits conjecture", "url": "https://arxiv.org/abs/2610.05474", "primary": true, "published_date": "2026-10-04", "accessed_at": "2026-10-07" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "kls-conjecture", "chatgpt", "convex-geometry", "high-dimensional-probability", "mathematical-discovery", "ai-generated-mathematics" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-meta-muse-spark-open-research", "slug": "meta-muse-spark-open-research", "title": { "en": "Meta publishes six Muse Spark–mathematician research papers, five answering open questions", "zh-CN": "Meta 发布六篇 Muse Spark 与数学家合作论文，其中五篇回答开放研究问题" }, "dates": { "event": "2026-10-02", "first_public_claim": "2026-10-02", "paper_release": "2026-10-02", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "discovery", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "Meta's six-paper release is a field milestone because expert mathematicians used Muse Spark 1.1 and 1.2 through the ordinary meta.ai chat interface, without a bespoke research scaffold, to make substantive contributions across several areas of mathematics. Five papers answer previously open research questions according to Meta, and the release documents materially different AI roles including proof exploration, counterexample search, GAP code generation, cross-field connection finding and drafting technical arguments. The work is explicitly human-guided and reviewed, and several results have concurrent independent solutions, so it is better characterized as an H2 collaboration milestone than an autonomous H1 event.", "zh-CN": "Meta 的六篇论文发布构成领域级里程碑，因为专业数学家使用 Muse Spark 1.1 与 1.2， 直接通过普通 meta.ai 聊天界面、无需专门研究脚手架，在多个数学领域作出实质贡献。 Meta 表示其中五篇回答此前开放的研究问题；公开材料还记录了多种不同 AI 角色，包括 探索证明、搜索反例、生成 GAP 程序、发现跨领域联系以及起草技术论证。由于工作明确由 人类引导并经第二组数学家审查，且若干结果存在同期独立解，本事件更适合定位为 H2 人机协作里程碑，而非自主型 H1 事件。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "On 2 October 2026, Meta released six research papers produced by mathematicians working with Muse Spark 1.1 and 1.2 in Thinking Mode through the standard meta.ai chat interface. Meta states that five papers answer previously open research questions. The results include a finite-time blow-up theorem for the mass-critical biharmonic nonlinear Schrödinger equation, counterexamples in group theory and evolution algebras, an exactness characterization in optimization, a Gaussian ellipsoid-fitting threshold result, and a new arithmetic-physics connection.", "zh-CN": "2026 年 10 月 2 日，Meta 发布六篇由数学家与 Muse Spark 1.1、1.2 在 Thinking Mode 下通过普通 meta.ai 聊天界面合作完成的研究论文。Meta 表示其中五篇回答此前开放的 研究问题。成果包括质量临界双调和非线性薛定谔方程的有限时间爆破解、群论与 evolution algebra 中的反例、优化问题中的精确性刻画、高斯椭球拟合阈值结果，以及新的算术物理联系。" }, "summary": { "en": "Meta says human mathematicians selected and guided the research, a separate group of mathematicians reviewed the work, each paper marks passages primarily drafted by researchers versus AI, and prior or concurrent work is credited. Muse Spark's role varied by project: it helped test and revise calculations, generated a GAP search program that found a 384-element group counterexample, proposed counterexamples and proof strategies, and generated candidate proofs and technical sections. Meta also acknowledges that several questions were independently resolved by other teams, including one semiabelian-group counterexample reported by the Nilradical AI agent before Meta's publication.", "zh-CN": "Meta 表示，人类数学家负责选题并引导研究，另有一组数学家对工作进行审查；每篇论文标记 哪些段落主要由研究者或 AI 起草，并明确引用已有及同期工作。Muse Spark 在不同项目中的 作用并不相同：它协助测试与修订计算，生成 GAP 搜索程序并找到一个 384 阶群反例， 提出反例与证明策略，还生成候选证明并起草技术章节。Meta 同时承认若干问题被其他团队 独立解决，其中包括 Nilradical AI agent 在 Meta 发布前报告的另一 semiabelian-group 反例。" }, "why_it_matters": { "en": "The release shows a different AI4Math research mode from autonomous lab-scale search: expert mathematicians can use a generally available frontier chat model as an active research collaborator on genuine open questions while retaining explicit human authorship, review and passage-level attribution. The combination of ordinary user interface, heterogeneous mathematical contributions and transparent division of labour makes the batch a useful reference point for human–AI mathematical research practice even where individual priority is shared or concurrent.", "zh-CN": "该发布展示了一种不同于实验室自主搜索的 AI4Math 研究模式：专业数学家可以把面向普通 用户的前沿聊天模型作为开放问题研究中的活跃协作者，同时保留明确的人类署名、审查与 段落级贡献标注。普通用户界面、多样化数学贡献以及透明分工的组合，使这批工作即使在 部分成果存在同期或共享优先权的情况下，仍成为人机数学研究实践的重要参照。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Muse Spark made substantive but project-dependent contributions under human direction. Meta documents roles ranging from calculations and proof exploration to code-generated counterexample search, candidate proofs, proof strategies and technical drafting. Human mathematicians selected the problems, steered the work, checked and corrected arguments, and a second group reviewed the papers.", "zh-CN": "Muse Spark 在人类引导下承担实质但因项目而异的贡献。Meta 记录的作用包括计算与证明 探索、通过代码搜索反例、生成候选证明与证明策略以及技术写作。人类数学家负责选题、 引导研究、检查和修正论证，并由第二组数学家进行审查。" } }, "human_contribution": { "description": { "en": "Human researchers supplied the research questions and mathematical direction, evaluated model suggestions, completed or corrected arguments, wrote substantial parts of the papers and accepted responsibility for the final results. Separate mathematicians reviewed the work before release.", "zh-CN": "人类研究者提供研究问题与数学方向，评估模型建议，完成或修正论证，撰写论文中的 实质内容并对最终成果负责；另有独立数学家在发布前进行审查。" } }, "systems": [ "muse-spark-1-1", "muse-spark-1-2" ], "organizations": [ "meta" ], "people": [ "aykut-arslan", "leonard-dinh", "joseph-phillip-brennan", "milana-golich", "anindya-dey", "gabriel-herczeg", "an-huang", "nicolas-jaramillo-torres", "jacob-h-swenberg", "andres-barei" ], "problems": [], "methods": [ "human-ai-collaboration", "natural-language-mathematical-reasoning", "counterexample-search", "gap-computation", "proof-development" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2026-10-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Meta released six public research papers and a detailed account of the collaboration and review workflow. Chronicle records Meta's claim that five papers answer previously open questions while preserving the stated concurrent independent results and without treating internal review as independent community verification.", "zh-CN": "Meta 发布六篇公开研究论文，并详细说明协作与审查流程。Chronicle 记录 Meta 关于 “其中五篇回答此前开放问题”的主张，同时保留其披露的同期独立结果，不把 Meta 内部或合作审查直接等同于数学共同体的独立验证。" } } ] }, "sources": [ { "id": "meta-muse-open-research-2026", "tier": "S2", "type": "official_announcement", "title": "Solving Open Research Problems Together", "url": "https://research.meta.ai/blog/solving-open-research-problems-together", "primary": true, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-gaussian-ellipsoid-paper-2026", "tier": "S1", "type": "paper", "title": "The Strict Threshold for Gaussian Ellipsoid Fitting", "url": "https://ai.meta.com/research/publications/the-strict-threshold-for-gaussian-ellipsoid-fitting/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-biharmonic-nls-paper-2026", "tier": "S1", "type": "paper", "title": "Finite-Time Blow-Up of Radial Negative-Energy Solutions for the Mass-Critical Biharmonic Nonlinear Schrödinger Equation", "url": "https://ai.meta.com/research/publications/finite-time-blow-up-of-radial-negative-energy-solutions-for-the-mass-critical-biharmonic-nonlinear-schrodinger-equation/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-semiabelian-paper-2026", "tier": "S1", "type": "paper", "title": "Semiabelian Groups Need Not Be Monomial", "url": "https://ai.meta.com/research/publications/semiabelian-groups-need-not-be-monomial/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-cycle-relaxation-paper-2026", "tier": "S1", "type": "paper", "title": "Tightness of the Cycle-Based Relaxation for Completed Length-Three Alpha-Cycles", "url": "https://ai.meta.com/research/publications/tightness-of-the-cycle-based-relaxation-for-completed-length-three-alpha-cycles/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-string-height-paper-2026", "tier": "S1", "type": "paper", "title": "String Two-Point Function = Height Function on a Curve", "url": "https://ai.meta.com/research/publications/string-two-point-function-height-function-on-a-curve/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" }, { "id": "meta-evolution-algebra-paper-2026", "tier": "S1", "type": "paper", "title": "On Solvable Evolution Algebras and a Conjecture by García-Martínez and Pérez-Rodríguez", "url": "https://ai.meta.com/research/publications/on-solvable-evolution-algebras-and-a-conjecture-by-garcia-martinez-and-perez-rodriguez/", "primary": false, "published_date": "2026-10-02", "accessed_at": "2026-10-07" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "muse-spark", "open-research", "human-ai-collaboration", "mathematical-discovery", "counterexamples", "proof-development", "meta" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-agmai-responsible-release", "slug": "agmai-responsible-release-ai-generated-mathematics", "title": { "en": "AGMAI publishes responsible-release norms for AI-generated mathematics", "zh-CN": "AGMAI 发布 AI 生成数学成果的负责任发布规范" }, "dates": { "event": "2026-09-29", "first_public_claim": "2026-09-29", "paper_release": null, "artifact_release": "2026-09-29", "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "AGMAI's responsible-release recommendations are a field-building milestone because they translate the 2026 debate over AI-generated mathematics into a concrete, public set of norms for frontier AI labs. The recommendations address human understanding, publication channels, citations, provenance, model and prompt disclosure, compute reporting, formalization standards, failure disclosure, community-led assimilation and equitable access. They were informed by more than six hundred community responses and were subsequently discussed with OpenAI before its large October mathematics release.", "zh-CN": "AGMAI 的负责任发布建议构成领域建构里程碑，因为它把 2026 年围绕 AI 生成数学成果的 争论转化为一套面向前沿 AI 实验室的公开、具体规范。建议覆盖人类理解、发布渠道、 引用、provenance、模型与 prompt 披露、算力报告、形式化标准、失败样本披露、 共同体主导的成果吸收以及公平访问。该规范吸收了六百余份共同体反馈，并在 OpenAI 10 月大规模数学成果发布前与其进行了讨论。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "On 29 September 2026, the Advisory Group on Mathematics and Artificial Intelligence published recommendations for the responsible release of AI-generated mathematics. The group asks frontier labs to stop testing advanced mathematical problems on proprietary models as its preferred long-term norm, while also specifying how significant results should be released when such work occurs. For results not yet understood by humans, the recommendations call for improved citations and exposition, persistent community-oriented repositories, disclosure of the model, prompts, summarized reasoning, time and compute, documentation of AI use and problem selection, comparable failure statistics for batch releases, formalization where possible, and material support for community-led human understanding.", "zh-CN": "2026 年 9 月 29 日，Advisory Group on Mathematics and Artificial Intelligence 发布 AI 生成数学成果的负责任发布建议。该组织把“停止使用不可公开的专有模型测试前沿 数学问题”作为理想的长期规范，同时也规定当此类研究已经发生时，重要结果应如何发布。 对尚无人类完整理解的成果，建议要求改进引用与阐释、使用面向共同体的持久化仓库、 披露模型、prompts、摘要式推理、时间与算力、说明 AI 使用与选题过程、对批量发布给出 可比较的失败统计、尽可能进行形式化，并为共同体主导的人类理解投入实质支持。" }, "summary": { "en": "AGMAI says the recommendations were informed by more than 600 responses from the mathematical community. The document distinguishes ordinary papers that a responsible mathematician fully understands from AI outputs that nobody yet understands. In the latter case it proposes technical release norms and a parallel obligation for labs to fund independent, community-led workshops, conferences, expository work and other activities needed to assimilate the mathematics. It also warns that unequal access to frontier systems could create a multi-tier mathematical community.", "zh-CN": "AGMAI 表示该建议吸收了数学共同体超过 600 份反馈。文件区分两类情形：由负责的数学家 完整理解的普通论文，以及尚无人类完整理解的 AI 输出。针对后一类，文件既提出技术发布 规范，也要求实验室为独立、共同体主导的研讨会、会议、阐释工作及其他理解和吸收数学 所需活动提供支持；同时警告前沿系统访问不平等可能制造多层级的数学共同体。" }, "why_it_matters": { "en": "Earlier 2026 statements identified problems in attribution, incentives, access and research dissemination. This document converts those concerns into an operational checklist that can be compared against actual releases. OpenAI's 6 October release explicitly says it drew on AGMAI's advice, and AGMAI subsequently stated that it had discussed the recommendations with OpenAI while leaving assessment of compliance and mathematical merit to the wider community.", "zh-CN": "2026 年此前的共同体声明主要指出归属、激励、访问和研究发布方面的问题；这份文件则把 这些问题转化为可以与真实发布行为逐项对照的操作规范。OpenAI 10 月 6 日的发布明确表示 参考了 AGMAI 建议；AGMAI 随后也说明已与 OpenAI 讨论这些规范，同时把是否充分遵循规范 以及成果数学价值的判断留给更广泛的共同体。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records human-authored scholarly-governance norms for AI-generated mathematics rather than an AI system performing mathematical research.", "zh-CN": "本事件记录的是人类制定的 AI 生成数学成果学术治理规范，而不是 AI 系统执行具体数学研究。" } }, "human_contribution": { "description": { "en": "AGMAI members synthesized community feedback into public recommendations for frontier AI labs and committed to independent, transparent engagement with the mathematical community and AI companies.", "zh-CN": "AGMAI 成员把共同体反馈整理为面向前沿 AI 实验室的公开建议，并承诺以独立、透明的方式 持续与数学共同体及 AI 企业互动。" } }, "systems": [], "organizations": [ "advisory-group-on-mathematics-and-artificial-intelligence", "institute-for-advanced-study" ], "people": [], "problems": [], "methods": [ "scholarly-governance", "responsible-release", "provenance-disclosure", "formalization-standards", "community-led-review", "equitable-access" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2026-09-29", "status": "claimed", "evidence_level": "E2", "note": { "en": "AGMAI's public recommendations establish the document, its scope and its stated basis in more than 600 community responses.", "zh-CN": "AGMAI 的公开建议确认了文件本身、规范范围以及其基于六百余份共同体反馈的说明。" } }, { "date": "2026-10-06", "status": "claimed", "evidence_level": "E2", "note": { "en": "AGMAI's statement on OpenAI's large mathematics release says the group discussed its recommendations with OpenAI and reaffirms them, while explicitly declining to endorse the released mathematics or certify that the recommendations were followed successfully.", "zh-CN": "AGMAI 针对 OpenAI 大规模数学成果发布的声明表示其已与 OpenAI 讨论这些建议并再次 重申规范，同时明确不对发布的数学成果背书，也不自行认证 OpenAI 已成功遵循全部建议。" } } ] }, "sources": [ { "id": "agmai-responsible-release-2026", "tier": "S2", "type": "official_announcement", "title": "Responsible Release of AI-Generated Mathematics", "url": "https://agmai.org/general-sep29/", "primary": true, "published_date": "2026-09-29", "accessed_at": "2026-10-07" }, { "id": "agmai-openai-release-statement-2026", "tier": "S2", "type": "official_announcement", "title": "On OpenAI's Release of Mathematical Results", "url": "https://agmai.org/", "primary": false, "published_date": "2026-10-06", "accessed_at": "2026-10-07" }, { "id": "openai-sharing-math-2026", "tier": "S2", "type": "official_announcement", "title": "Sharing AI progress in mathematics", "url": "https://openai.com/index/sharing-ai-progress-in-mathematics/", "primary": false, "published_date": "2026-10-06", "accessed_at": "2026-10-07" } ], "artifacts": [ { "id": "agmai-responsible-release-document", "kind": "other", "title": "Responsible Release of AI-Generated Mathematics", "url": "https://agmai.org/general-sep29/" } ], "relationships": { "predecessors": [ "evt-2026-agmai-advisory-group" ], "successors": [ "evt-2026-openai-math-release" ], "related": [ "evt-2026-severe-misalignment-ai-mathematics" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "field-building", "ai-governance", "responsible-release", "research-integrity", "provenance", "formalization", "mathematical-community" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-frenzymath-poincare-formalization", "slug": "frenzymath-poincare-formalization", "title": { "en": "FrenzyMath releases a Comparator-checked AI-assisted Lean formalization of the Poincaré conjecture", "zh-CN": "FrenzyMath 发布经 Comparator 检查的 AI 辅助庞加莱猜想 Lean 形式化" }, "dates": { "event": "2026-09-28", "first_public_claim": "2026-09-28", "paper_release": null, "artifact_release": "2026-09-28", "independently_verified": null, "added_to_chronicle": "2026-10-07", "last_updated": "2026-10-07" }, "event_types": [ "formalization", "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "FrenzyMath's Poincaré development is a field milestone in AI-assisted formalization because it packages a complete smooth/topological Poincaré proof route into a multi-million-line Lean project and reports completion of most of the work within roughly half a month using agentic pipelines and publicly available commercial language models. The project exposes a Mathlib-facing statement, full-build evidence and Comparator/Nanoda verification. A separate team released another complete Lean development essentially concurrently, showing that research-scale geometric-analysis formalization had moved from an isolated demonstration to a reproducible frontier. Because the mathematical theorem was already known and the exact agent/human division is not reconstructed theorem by theorem, H2 is more appropriate than H1.", "zh-CN": "FrenzyMath 的庞加莱猜想形式化构成 AI 辅助形式化方向的领域级里程碑：该项目把完整的 smooth/topological Poincaré 证明路线组织成数百万行 Lean 工程，并报告主要工作在约 半个月内通过 agentic pipelines 与公开商用大语言模型完成。项目公开了面向 Mathlib 的独立 statement、全量构建证据以及 Comparator/Nanoda 验证。几乎同期，另一支团队 也发布了独立完整 Lean 开发，表明研究级几何分析形式化已经从孤立演示走向可重复的 前沿实践。由于数学定理本身早已解决，且逐定理的人机分工并未被完整重建，因此 H2 比 H1 更合适。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal" ], "claim": { "en": "On 28 September 2026, FrenzyMath announced a complete Lean 4 formalization of the smooth and topological three-dimensional Poincaré conjecture, primarily following Morgan and Tian's exposition of the Hamilton–Perelman proof. The team reports a full Lean build and Comparator verification of two public endpoint statements using Lean's kernel and Nanoda with only the standard axioms propext, Classical.choice and Quot.sound. FrenzyMath reports that three AI developers with mathematical backgrounds and several volunteer mathematicians completed most of the work within half a month using publicly available commercial LLMs.", "zh-CN": "2026 年 9 月 28 日，FrenzyMath 宣布完成三维 smooth 与 topological 庞加莱猜想的 Lean 4 形式化，证明路线主要跟随 Morgan–Tian 对 Hamilton–Perelman 证明的阐释。 团队报告全量 Lean build 已通过，并使用 Comparator 对两个公开 endpoint statement 进行验证，同时由 Lean kernel 与 Nanoda 检查，允许的公理仅为 propext、 Classical.choice 与 Quot.sound。FrenzyMath 表示，三名具有数学背景的 AI 开发者与 数名志愿数学家使用公开商用 LLM，在约半个月内完成了大部分工作。" }, "summary": { "en": "FrenzyMath reports about 3.2 million lines of Lean and less than USD 30,000 in LLM and compute costs for the project. The repository separates the Mathlib-only endpoint statements from the proof library and preserves Comparator configuration, verifier revisions, logs and source-provenance records. The announcement also notes that an independent team led by Ziyang Qin, Yuan Liao, Ayush Khaitan and Bennett Chow released another complete Poincaré Lean development earlier the same day; that separate arXiv paper records a full public build and says automated assistance was used for proofs and prose.", "zh-CN": "FrenzyMath 报告该项目约包含 320 万行 Lean，LLM 与计算服务器总成本低于 3 万美元。 仓库将仅依赖 Mathlib 的 endpoint statements 与证明库分离，并保存 Comparator 配置、 verifier 版本、日志和源码 provenance 记录。公告同时指出，Ziyang Qin、Yuan Liao、 Ayush Khaitan 与 Bennett Chow 等组成的独立团队在同一天稍早也发布了另一套完整 庞加莱 Lean 开发；该独立 arXiv 论文记录了公开全量构建，并说明证明与文字工作中使用了 自动化辅助。" }, "why_it_matters": { "en": "Poincaré is a foundational modern theorem whose standard proof uses a large stack of geometric analysis, topology, partial differential equations and Ricci-flow machinery. Compressing a project of this scope into weeks of AI-assisted formalization demonstrates that frontier formal-mathematics agents can now operate over extensive prerequisite libraries rather than only isolated olympiad theorems or short research arguments. The near-simultaneous second formalization reinforces the historical signal while also discouraging a simplistic single-project priority claim.", "zh-CN": "庞加莱猜想是现代数学的基础性定理，其标准证明依赖庞大的几何分析、拓扑、偏微分方程与 Ricci flow 理论体系。把这种规模的项目压缩到数周 AI 辅助形式化，说明前沿形式数学 Agent 已能处理广泛前置理论库，而不再局限于孤立奥赛定理或短篇研究论证。近乎同期出现的第二套 独立形式化进一步强化了这一历史信号，同时也提醒 Chronicle 不应把里程碑简单归为单一项目 的优先权。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "FrenzyMath describes the project as a collaboration among AI developers with mathematical backgrounds, volunteer mathematicians and publicly available commercial LLMs coordinated through agentic pipelines. The public announcement establishes substantial AI assistance but does not give a theorem-by-theorem reconstruction of model versus human intellectual contributions.", "zh-CN": "FrenzyMath 将该项目描述为具有数学背景的 AI 开发者、志愿数学家与公开商用 LLM 在 agentic pipelines 中协作完成。公开材料足以确认 AI 的实质参与，但没有逐定理重建 模型与人类的具体智力贡献。" } }, "human_contribution": { "description": { "en": "Human developers and mathematicians designed and operated the pipelines, selected the proof route and sources, reviewed integration and provenance, and maintained the public verification surface and mathematical blueprint.", "zh-CN": "人类开发者与数学家负责设计和运行 pipeline、选择证明路线与文献来源、审查集成与 provenance，并维护公开验证界面及数学 blueprint。" } }, "systems": [ "lean", "comparator", "nanoda" ], "organizations": [ "frenzymath", "pku-ai4math" ], "people": [], "problems": [ "poincare-conjecture" ], "methods": [ "agentic-formalization", "blueprint-guided-formalization", "formal-verification", "independent-kernel-checking" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "machine_checked", "history": [ { "date": "2026-09-28", "status": "claimed", "evidence_level": "E3", "note": { "en": "FrenzyMath's announcement and repositories expose the endpoint statements, proof library, full-build instructions and Comparator/Nanoda verification records. Chronicle has not independently replayed the artifact in this maintenance pass, so machine_checked records the released verification surface rather than an independently_replayed status.", "zh-CN": "FrenzyMath 的公告与公开仓库提供 endpoint statements、证明库、全量构建说明以及 Comparator/Nanoda 验证记录。本轮 Chronicle 没有自行独立重放该 artifact，因此 machine_checked 表示公开的机器检查证据，而不是 independently_replayed 状态。" } } ] }, "sources": [ { "id": "frenzymath-poincare-announcement-2026", "tier": "S2", "type": "official_announcement", "title": "Formalization of the Poincaré Conjecture", "url": "https://frenzymath.com/news/poincare-formalization/", "primary": true, "published_date": "2026-09-28", "accessed_at": "2026-10-07" }, { "id": "frenzymath-poincare-repository", "tier": "S1", "type": "formal_artifact", "title": "Poincare Conjecture Lean formalization", "url": "https://github.com/frenzymath/Poincare-Conjecture", "primary": true, "published_date": null, "accessed_at": "2026-10-07" }, { "id": "qin-liao-khaitan-chow-poincare-2026", "tier": "S1", "type": "paper", "title": "A Lean Formalization of the Hamilton--Perelman Proof of the Three-Dimensional Poincaré Conjecture", "url": "https://arxiv.org/abs/2609.33842", "primary": false, "published_date": "2026-09-27", "accessed_at": "2026-10-07" } ], "artifacts": [ { "id": "frenzymath-poincare-lean", "kind": "proof", "title": "FrenzyMath Poincaré Lean project", "url": "https://github.com/frenzymath/Poincare-Conjecture" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2026-claude-flt-formalization", "evt-2026-formalflow-mipstarre" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "poincare-conjecture", "lean", "formalization", "comparator", "nanoda", "geometric-analysis", "ricci-flow", "ai-agents" ], "editorial": { "created_at": "2026-10-07", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-agmai-advisory-group", "slug": "agmai-advisory-group", "title": { "en": "Independent Advisory Group on Mathematics and Artificial Intelligence launches at IAS", "zh-CN": "独立的数学与人工智能顾问组在 IAS 成立" }, "dates": { "event": "2026-09-21", "first_public_claim": "2026-09-21", "paper_release": null, "artifact_release": "2026-09-21", "independently_verified": null, "added_to_chronicle": "2026-09-22", "last_updated": "2026-10-07" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The Advisory Group on Mathematics and Artificial Intelligence is a field-building milestone because it creates a standing, institutionally hosted channel between mathematicians and AI companies for the review, presentation and dissemination of AI-generated mathematical results. Its independence rules, public-recommendation commitment, ability to advise any AI company with substantial mathematical impact, IAS hosting and open community-input mechanism make it more durable than a one-off company panel or petition. The group also represents a concrete institutional response to the September 2026 debate over research incentives, attribution and the release of AI-generated mathematics.", "zh-CN": "Advisory Group on Mathematics and Artificial Intelligence 构成领域建构里程碑， 因为它建立了一个由学术机构承载、连接数学家与 AI 企业的持续性机制，用于讨论 AI 生成数学成果的审查、呈现与发布。该组织明确规定独立运作、公开发布建议、 可面向任何对数学产生重大影响的 AI 企业提供意见，并由 IAS 承载且开放共同体 意见入口，因此其制度持续性明显高于一次性的企业顾问委员会或联署声明。 它同时也是 2026 年 9 月围绕研究激励、归属与 AI 数学成果发布方式争论后出现的 具体制度回应。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "On 21 September 2026, the Advisory Group on Mathematics and Artificial Intelligence announced its creation, hosted at the Institute for Advanced Study. The group states that it operates independently of AI companies, its members accept no payment for this work, it will publish recommendations to AI companies, and it may advise any company whose models are likely to have a significant impact on mathematics. It has no decision-making power at AI companies. OpenAI states that the group will advise on reviewing and communicating emerging mathematical results, coordinating dissemination, academic and professional standards, and tools for mathematical research and learning; OpenAI also states that the group will not advise on the pace of its internal mathematical progress.", "zh-CN": "2026 年 9 月 21 日，Advisory Group on Mathematics and Artificial Intelligence 宣布成立，并由 Institute for Advanced Study 承载。该组织声明其独立于 AI 企业 运作，成员不因这项工作接受 AI 企业付款，将公开向 AI 企业提出的建议，并可为任何 其模型可能对数学产生重大影响的企业提供意见；该组织不拥有 AI 企业内部决策权。 OpenAI 表示，该组织将就新数学成果的审查与沟通、发布协调、数学研究的学术与职业 规范，以及支持数学研究和学习的工具提供建议；同时，OpenAI 明确表示该组织不负责 就其内部数学研究进展的速度提出建议。" }, "summary": { "en": "The group says it formed after OpenAI approached some future members about creating an external advisory board; in agreement with OpenAI, those mathematicians instead formed an independent group and invited additional members. Its initial membership consists of François Charles, Camillo De Lellis, Timothy Gowers, Martin Hairer, Nikhil Srivastava, Ulrike Tillmann, Ravi Vakil, Edward Witten and Melanie Matchett Wood. The group's first stated task is to advise OpenAI on coordinating the release of a large number of significant mathematical results that OpenAI reports were produced by an internal model. OpenAI's announcement explicitly cites A Severe Misalignment of AI in Mathematics as part of the context for creating this bridge to the mathematical community.", "zh-CN": "该组织说明，其形成始于 OpenAI 接触部分后来的成员，希望建立外部顾问委员会； 在与 OpenAI 沟通后，这些数学家决定改为成立一个独立组织并邀请其他成员加入。 首批成员包括 François Charles、Camillo De Lellis、Timothy Gowers、Martin Hairer、 Nikhil Srivastava、Ulrike Tillmann、Ravi Vakil、Edward Witten 与 Melanie Matchett Wood。该组织当前明确的首项任务，是就 OpenAI 所称由内部模型 产生的大量重要数学成果如何协调发布向其提供建议。OpenAI 的公告同时明确引用 《A Severe Misalignment of AI in Mathematics》，将其列为建立这一数学共同体 沟通渠道的直接背景之一。" }, "why_it_matters": { "en": "Earlier AI-and-mathematics governance efforts largely took the form of professional society committees, declarations or publication policies. This event adds a different institutional layer: an independent group of research mathematicians positioned specifically between frontier AI companies and the mathematical community, with a public-accountability commitment and a remit extending beyond one company. It turns the 2026 governance debate from statements of principle into an operating interface for reviewing and releasing AI-associated mathematical research.", "zh-CN": "此前 AI 与数学治理工作主要表现为专业学会委员会、共同体声明或出版政策。 本事件增加了另一种制度层：一个由研究数学家组成、明确位于前沿 AI 企业与数学 共同体之间的独立组织，并承诺公开建议且职责范围不限于单一企业。它把 2026 年 围绕 AI4Math 的治理争论，从原则性声明进一步推进为处理 AI 参与数学研究审查与 发布问题的实际运作接口。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records a human-created governance institution concerning AI and mathematical research rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是人类建立的 AI 与数学研究治理机制，而不是某个 AI 系统执行具体 数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "The founding mathematicians established the independent group, defined its independence and transparency principles, accepted institutional hosting at IAS, opened a channel for community input and undertook to formulate public advice for AI companies. OpenAI initiated contact with some members and is the group's first stated advisee, while responsibility for company decisions remains with OpenAI.", "zh-CN": "创始数学家建立独立组织、制定独立性与透明度原则、接受 IAS 的机构承载、开放 共同体意见渠道，并承诺形成面向 AI 企业的公开建议。OpenAI 最初接触了部分成员， 也是该组织当前首个明确的建议对象；企业决策责任仍由 OpenAI 自身承担。" } }, "systems": [], "organizations": [ "advisory-group-on-mathematics-and-artificial-intelligence", "institute-for-advanced-study", "openai" ], "people": [ "francois-charles", "camillo-de-lellis", "timothy-gowers", "martin-hairer", "nikhil-srivastava", "ulrike-tillmann", "ravi-vakil", "edward-witten", "melanie-matchett-wood" ], "problems": [], "methods": [ "scholarly-governance", "community-industry-interface", "research-dissemination", "academic-standards", "public-accountability" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2026-09-21", "status": "claimed", "evidence_level": "E2", "note": { "en": "The advisory group's own site and direct guest announcement establish its purpose, independence rules, membership, OpenAI origin story and current task. OpenAI's announcement independently records the collaboration and the limits of the group's role inside the company.", "zh-CN": "顾问组官网及其直接发布的客座公告确认了组织目的、独立性规则、成员构成、 与 OpenAI 接触的形成过程以及当前任务；OpenAI 的公告另行记录了双方合作关系 与该组织在公司内部职责的边界。" } }, { "date": "2026-09-22", "status": "claimed", "evidence_level": "E2", "note": { "en": "The Institute for Advanced Study lists the advisory group as an FY26 Spring Award project of its Nelson Center for Collaborative Research, naming Camillo De Lellis and Edward Witten as principal investigators and reproducing the group's field-facing purpose and membership. This corroborates institutional hosting and durability without implying endorsement of any AI company's mathematical claims.", "zh-CN": "Institute for Advanced Study 将该顾问组列为 Nelson Center for Collaborative Research 的 FY26 Spring Award 项目，列出 Camillo De Lellis 与 Edward Witten 为 principal investigators，并记录该组织面向数学共同体的目的与成员构成。 这为其机构承载与持续性提供佐证，但不表示 IAS 对任何 AI 企业的数学成果主张 作出背书。" } } ] }, "sources": [ { "id": "agmai-official", "tier": "S2", "type": "official_announcement", "title": "Advisory Group on Mathematics and Artificial Intelligence", "url": "https://agmai.org/", "primary": true, "published_date": null, "accessed_at": "2026-09-22" }, { "id": "openai-agmai-announcement", "tier": "S2", "type": "official_announcement", "title": "Advisory Group on Mathematics and Artificial Intelligence", "url": "https://openai.com/index/advisory-group-on-mathematics-and-ai/", "primary": true, "published_date": "2026-09-21", "accessed_at": "2026-09-22" }, { "id": "ias-agmai-project", "tier": "S2", "type": "official_announcement", "title": "Advisory Group on Mathematics and Artificial Intelligence — IAS Nelson Center project", "url": "https://www.ias.edu/nccr/projects", "primary": false, "published_date": null, "accessed_at": "2026-09-22" }, { "id": "tao-agmai-guest-announcement", "tier": "S2", "type": "community", "title": "Announcing the Advisory Group on Mathematics and Artificial Intelligence", "url": "https://terrytao.wordpress.com/2026/09/21/advisory-group-on-mathematics-and-artificial-intelligence/", "primary": false, "published_date": "2026-09-21", "accessed_at": "2026-09-22" } ], "artifacts": [ { "id": "agmai-public-site", "kind": "other", "title": "Advisory Group on Mathematics and Artificial Intelligence public site", "url": "https://agmai.org/" } ], "relationships": { "predecessors": [ "evt-2026-severe-misalignment-ai-mathematics" ], "successors": [ "evt-2026-agmai-responsible-release" ], "related": [ "evt-2023-ams-ai-advisory", "evt-2026-leiden-declaration" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "advisory-group", "field-building", "ai-governance", "mathematical-community", "research-integrity", "research-dissemination", "academic-standards", "institute-for-advanced-study" ], "editorial": { "created_at": "2026-09-22", "last_reviewed": "2026-10-07", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-lean-pool", "slug": "lean-pool-ai-maintained-archive", "title": { "en": "Lean Pool publishes an AI-maintained archive for large-scale formalized mathematics", "zh-CN": "Lean Pool 发布面向大规模形式化数学的 AI 维护档案库" }, "dates": { "event": "2026-09-21", "first_public_claim": "2026-09-21", "paper_release": "2026-09-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-27", "last_updated": "2026-09-27" }, "event_types": [ "infrastructure", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Lean Pool is a field milestone in AI-maintained formal-mathematics infrastructure because it turns a large collection of independent Lean developments into an actively maintained archive with deterministic quality gates, LLM-assisted admission review, documentation, semantic search and a kernel-checked challenge workflow. Its significance is the operating model for maintaining formalized mathematics at scale with AI agents rather than a claim that every archived project was discovered or authored by AI.", "zh-CN": "Lean Pool 构成 AI 维护形式数学基础设施方向的领域级里程碑：它把大量独立 Lean 开发组织为持续维护的档案库，并配套确定性质量门禁、LLM 辅助准入审查、文档、 语义检索以及由 kernel 检查的 challenge 工作流。其历史意义在于展示 AI Agent 如何参与大规模形式化数学维护，而不是声称库内每个项目都由 AI 发现或编写。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal" ], "claim": { "en": "Lean Pool presents a repository of formalized mathematics that is grown, maintained and optimized with AI agents. The project accepts completed Lean developments that pass repository-wide build, linter, style and proof-integrity gates, supplements deterministic checks with LLM review, and maintains accepted projects against evolving Lean and Mathlib versions. Its separate challenge workflow uses Comparator to compare problem and solution statements and replay proofs through Lean's kernel.", "zh-CN": "Lean Pool 将自身定位为由 AI Agent 扩展、维护和优化的形式化数学仓库。项目接收已完成 的 Lean 开发，并要求通过全库构建、linter、风格和证明完整性门禁；确定性检查之外 还加入 LLM 审查，并持续把已收录项目迁移到新的 Lean 与 Mathlib 版本。其独立 challenge 工作流使用 Comparator 对照题目与解答陈述，并通过 Lean kernel 重放证明。" }, "summary": { "en": "The archive occupies a deliberately different position from Mathlib: it accepts independent completed formalization projects that may not fit Mathlib's tightly integrated library scope, while imposing automated maintenance and quality checks. The public repository reports that project imports are still selected by humans, while AI systems participate materially in review, maintenance and optimization. The corpus size changes continuously and is therefore not treated as a frozen historical claim in this Event.", "zh-CN": "该档案库有意采用不同于 Mathlib 的定位：它接收可能不适合 Mathlib 高度整合式库结构 的独立完整形式化项目，同时施加自动化维护与质量检查。公开仓库说明，目前项目导入 仍由人类选择，而 AI 系统实质参与审查、维护与优化。由于库规模持续变化，本 Event 不把某一时点的项目数或代码行数作为冻结的历史主张。" }, "why_it_matters": { "en": "As AI-generated and AI-assisted Lean projects proliferate, preservation and maintenance become bottlenecks distinct from proving individual theorems. Lean Pool supplies an AI-assisted archival layer between highly curated integrated libraries and loose standalone repositories, making maintenance, search, quality gates and challenge verification part of the AI4Math infrastructure problem.", "zh-CN": "随着 AI 生成和 AI 辅助的 Lean 项目增多，保存与维护开始成为不同于“证明单个定理” 的新瓶颈。Lean Pool 在高度精选的一体化数学库与松散独立仓库之间提供 AI 辅助档案层， 把版本维护、检索、质量门禁与 challenge 验证都纳入 AI4Math 基础设施问题。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "AI agents materially support repository growth, maintenance, optimization and admission review. The repository explicitly states that projects have so far been selected and added by humans, and many archived formalizations are human-authored, so the archive should not be described as wholly AI-authored mathematics.", "zh-CN": "AI Agent 实质参与仓库扩展、维护、优化与准入审查。仓库同时明确说明，目前项目仍由 人类选择并加入，而且其中许多形式化本身由人类编写，因此不能把整个档案库描述为 完全由 AI 创作的数学。" } }, "human_contribution": { "description": { "en": "Human maintainers created the archive, choose candidate projects, define review and quality policies, maintain governance and can intervene in integration work; the project was created at the UW Lean Hackathon by Vasily Ilin and Justin Asher.", "zh-CN": "人类维护者建立档案库、选择候选项目、制定审查与质量政策、维护治理并可参与集成工作； 项目由 Vasily Ilin 与 Justin Asher 在 UW Lean Hackathon 期间创建。" } }, "systems": [ "lean-pool", "lean", "gpt-6-astra", "comparator" ], "organizations": [], "people": [ "vasily-ilin", "justin-asher" ], "problems": [], "methods": [ "ai-assisted-maintenance", "formal-mathematics-archiving", "llm-review", "semantic-search", "proof-integrity-checking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2026-09-21", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The arXiv record and public repository establish the archive's stated AI-maintained operating model and expose its CI, review and challenge-verification machinery. Reservoir independently indexes the Lean package and reports build results for repository revisions. These sources corroborate the existence and operation of the infrastructure but do not certify the mathematical semantics or novelty of every project contained in the evolving archive.", "zh-CN": "arXiv 记录与公开仓库确认了该档案库所述 AI 维护运作模式，并公开其 CI、审查和 challenge 验证机制。Reservoir 独立索引该 Lean package，并报告仓库版本的构建 结果。这些证据佐证基础设施的存在与运行，但并不认证持续变化的档案中每个项目 的数学语义或新颖性。" } } ] }, "sources": [ { "id": "lean-pool-arxiv-2026", "tier": "S1", "type": "paper", "title": "Lean Pool: An AI-Maintained Archive of Formalized Mathematics", "url": "https://arxiv.org/abs/2609.25199", "primary": true, "published_date": "2026-09-21", "accessed_at": "2026-09-27" }, { "id": "lean-pool-github", "tier": "S1", "type": "repository", "title": "Lean Pool", "url": "https://github.com/Vilin97/lean-pool", "primary": true, "published_date": null, "accessed_at": "2026-09-27" }, { "id": "lean-pool-reservoir", "tier": "S3", "type": "independent_analysis", "title": "lean-pool package record on Reservoir", "url": "https://reservoir.lean-lang.org/@Vilin97/lean-pool", "primary": false, "published_date": null, "accessed_at": "2026-09-27" } ], "artifacts": [ { "id": "lean-pool-repository", "kind": "code", "title": "Lean Pool repository", "url": "https://github.com/Vilin97/lean-pool" } ], "relationships": { "predecessors": [ "evt-2017-mathlib3" ], "successors": [], "related": [ "evt-2026-palomar-registry" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean-pool", "lean", "formalized-mathematics", "infrastructure", "ai-maintenance", "proof-archive", "comparator" ], "editorial": { "created_at": "2026-09-27", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-formalflow-mipstarre", "slug": "formalflow-mipstarre", "title": { "en": "FormalFlow completes a 126,000-line Lean formalization of a core theorem underlying MIP* = RE", "zh-CN": "FormalFlow 完成支撑 MIP* = RE 核心定理的 12.6 万行 Lean 形式化" }, "dates": { "event": "2026-09-17", "first_public_claim": "2026-09-17", "paper_release": "2026-09-17", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-27", "last_updated": "2026-09-27" }, "event_types": [ "formalization", "system", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "FormalFlow is a field milestone in long-horizon AI-assisted formalization because it reports completion of a machine-checked Lean development for the quantum soundness theorem of the classical low individual-degree test, a technically central ingredient underlying MIP* = RE. The project required 63 days and produced 126,367 lines of Lean code generated by proving agents under human supervision, demonstrating sustained proof planning, composition and review far beyond isolated theorem-hole solving while stopping short of a new mathematical theorem.", "zh-CN": "FormalFlow 构成长程 AI 辅助形式化方向的领域级里程碑：它报告完成了经典低个体次数 测试 quantum soundness 定理的 Lean 机器检查形式化，而该定理是 MIP* = RE 证明 体系中的核心技术组成。项目历时 63 天，形成 126,367 行由证明 Agent 生成、在人类 监督下完成的 Lean 代码，体现了远超单个 proof hole 求解的持续规划、组合与审查能力； 但其核心贡献是已知研究证明的形式化，而不是新的数学定理。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "hybrid" ], "claim": { "en": "The FormalFlow team reported a complete machine-checked Lean 4 proof of the quantum soundness of the classical low individual-degree test, a core theorem used in the MIP* = RE line of work. The paper reports that the development took 63 days, contains 126,367 lines of Lean code generated by AI proving agents, and corrected several side conditions and intermediate errors while preserving the published final error bound under corrected assumptions.", "zh-CN": "FormalFlow 团队报告完成经典低个体次数测试 quantum soundness 定理的完整 Lean 4 机器检查证明；该定理是 MIP* = RE 研究路线中的核心定理之一。论文报告该开发历时 63 天，包含 126,367 行由 AI 证明 Agent 生成的 Lean 代码，并在保持修正后假设下 最终误差界不变的同时，纠正了若干边界条件与中间错误。" }, "summary": { "en": "FormalFlow organizes long formalization projects around a shared blueprint and nested planning, proving and review loops. AI agents implement and review proof tasks while humans supervise the project, compare the formal development with the source mathematics and resolve semantic discrepancies. The public MIPStarRE repository preserves Lean sources, the active blueprint, source-paper material and CI-oriented proof-integrity infrastructure.", "zh-CN": "FormalFlow 以共享 blueprint 为核心，将长程形式化组织为嵌套的规划、证明与审查循环。 AI Agent 负责实现和审查证明任务，人类则监督整体项目、对照形式化开发与原始数学文本， 并处理语义偏差。公开的 MIPStarRE 仓库保存 Lean 源码、活动 blueprint、源论文材料 以及面向 CI 的证明完整性基础设施。" }, "why_it_matters": { "en": "Large research proofs expose failure modes that short theorem-proving benchmarks do not: statement drift, dependency management, incompatible local lemmas and review debt. FormalFlow provides evidence that agentic workflows can sustain a research-scale formalization over months while using the Lean kernel as a final syntactic proof checker and additional project processes to audit semantic fidelity.", "zh-CN": "大型研究证明会暴露短题 benchmark 难以体现的问题，包括 statement drift、依赖管理、 局部 lemma 不兼容与长期审查债务。FormalFlow 表明，Agent 工作流可以在数月尺度上 持续推进研究级形式化，并把 Lean kernel 作为最终形式证明检查层，同时通过额外项目 流程审查形式陈述与原始数学之间的语义忠实度。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "The paper states that the Lean library was generated by AI proving agents coordinated through FormalFlow, while humans supervised the project and intervened in planning, source-faithfulness review and resolution of proof or statement gaps.", "zh-CN": "论文表示 Lean 代码库由 FormalFlow 协调的 AI 证明 Agent 生成；人类负责项目监督， 并参与规划、源数学忠实度审查以及证明或陈述缺口的处理。" } }, "human_contribution": { "description": { "en": "Human researchers designed and supervised the workflow, selected and interpreted the source theorem, maintained the blueprint and review process, and adjudicated semantic discrepancies between the paper and the formal development.", "zh-CN": "人类研究者设计并监督工作流、选择和解释目标定理、维护 blueprint 与审查流程， 并处理论文与形式化开发之间的语义差异。" } }, "systems": [ "formalflow", "lean" ], "organizations": [], "people": [ "sirui-lu", "ruixuan-deng", "yanqiao-zhu", "zhengfeng-ji" ], "problems": [ "mip-star-equals-re", "low-individual-degree-test" ], "methods": [ "long-horizon-autoformalization", "multi-agent-proof-development", "blueprint-guided-formalization", "formal-verification" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2026-09-17", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The arXiv paper reports a completed machine-checked Lean 4 formalization and the public MIPStarRE repository exposes the corresponding Lean project and proof development infrastructure. Chronicle has not located an independent replay of the release artifact in this maintenance pass.", "zh-CN": "arXiv 论文报告已完成 Lean 4 机器检查形式化，公开 MIPStarRE 仓库提供相应 Lean 工程及证明开发基础设施。本轮维护尚未发现针对该发布成果的独立重放记录。" } } ] }, "sources": [ { "id": "formalflow-arxiv-2026", "tier": "S1", "type": "paper", "title": "Long-horizon autoformalization of a core theorem underlying MIP* = RE", "url": "https://arxiv.org/abs/2609.19814", "primary": true, "published_date": "2026-09-17", "accessed_at": "2026-09-27" }, { "id": "mipstarre-github", "tier": "S1", "type": "formal_artifact", "title": "MIPStarRE Lean formalization repository", "url": "https://github.com/LionSR/MIPStarRE", "primary": true, "published_date": null, "accessed_at": "2026-09-27" } ], "artifacts": [ { "id": "mipstarre-lean-artifact", "kind": "proof", "title": "MIPStarRE Lean 4 development", "url": "https://github.com/LionSR/MIPStarRE" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "formalflow", "mip-star-re", "lean", "autoformalization", "multi-agent", "quantum-complexity", "formal-verification" ], "editorial": { "created_at": "2026-09-27", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-astra-liouville-goldbach", "slug": "astra-liouville-goldbach", "title": { "en": "Captain Sude credits GPT-6 Astra with an unconditional proof of the Liouville–Goldbach problem", "zh-CN": "Captain Sude 将 Liouville–Goldbach 问题的无条件证明归因于 GPT-6 Astra" }, "dates": { "event": "2026-09-16", "first_public_claim": "2026-09-16", "paper_release": "2026-09-16", "artifact_release": "2026-09-16", "independently_verified": null, "added_to_chronicle": "2026-09-21", "last_updated": "2026-09-27" }, "event_types": [ "discovery", "proof", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "The release addresses a named open Liouville–Goldbach problem by giving an unconditional all-even theorem where the closest direct predecessor required GRH and sufficiently large even inputs. The result is accompanied by a complete Lean formalization and an independent technical replay, making it a substantive AI-associated research milestone while remaining distinct from the classical binary Goldbach conjecture and below the Chronicle's H1 historical threshold.", "zh-CN": "该成果针对一个已有明确记录的 Liouville–Goldbach 开放问题，给出覆盖全部偶数的 无条件定理，而最直接的前驱结果仍依赖 GRH 且只适用于充分大的偶数。公开成果同时 提供完整 Lean 形式化，并已有独立技术重放，因此足以构成实质性的 AI 参与研究里程碑； 但它不同于经典二元哥德巴赫猜想，且目前尚不足以达到 Chronicle 的 H1 历史级门槛。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "Captain Sude publicly attributed to GPT-6 Astra an unconditional proof that every even integer N > 2 can be written as N = a + b with positive integers a and b satisfying lambda(a) = lambda(b) = -1. The released paper and Lean theorem state this all-even result without GRH or a sufficiently-large restriction. This is a Liouville analogue of binary Goldbach, not a proof of the classical Goldbach conjecture.", "zh-CN": "Captain Sude 公开将一项无条件证明归因于 GPT-6 Astra：对每个大于 2 的偶数 N， 都存在正整数 a、b，使 N = a + b 且 lambda(a) = lambda(b) = -1。公开论文与 Lean 定理均陈述这一覆盖全部偶数的结论，不依赖 GRH，也没有“充分大”限制。 这是二元哥德巴赫问题的 Liouville 类比，并非经典哥德巴赫猜想的证明。" }, "summary": { "en": "The public project supplies an authorless mathematical paper, a complete Lean 4 formalization against mathlib's Liouville function, pinned toolchain metadata, build and axiom audits, and proof-route checks. A separate audit repository independently rebuilt the frozen v1.0.0 artifact on Linux, matched the source hashes, repeated the axiom and route audits, and reported no sorry, custom theorem axiom, or native_decide. The public paper and repository do not preserve a detailed model–human derivation trace, so the precise division of intellectual labor remains source-attributed rather than independently reconstructed by the Chronicle.", "zh-CN": "公开项目提供一篇未署名数学论文、基于 mathlib Liouville 函数的完整 Lean 4 形式化、固定工具链元数据、构建与公理审计以及证明路线检查。另一个独立审计仓库 在 Linux 上重新构建冻结的 v1.0.0 产物，对照源码哈希并重复公理与路线审计， 报告未发现 sorry、自定义定理公理或 native_decide。由于公开论文和仓库没有保存 详细的模型—人类推导轨迹，Chronicle 对具体智力分工只做来源归因，不作独立重建。" }, "why_it_matters": { "en": "Mangerel's 2024 Shusterman paper obtained the same (-1,-1) sign-pattern conclusion only under GRH and for sufficiently large even N. The new release claims to remove both restrictions and packages the argument as a reproducible formal artifact. If the mathematical novelty and reported Astra provenance continue to withstand specialist scrutiny, it is evidence of AI participation in resolving a concrete open research problem rather than merely improving a benchmark.", "zh-CN": "Mangerel 2024 年关于 Shusterman 问题的论文，只在 GRH 假设下并对充分大的偶数 N 得到相同的 (-1,-1) 符号模式结论。此次发布声称同时去掉这两个限制，并把论证 封装为可复现的形式化产物。如果其数学新颖性与 Astra 来源归因继续经受专业审查， 该事件将体现 AI 参与解决具体开放研究问题，而不是仅仅提升基准成绩。" }, "ai_role": { "level": "unclear", "description": { "en": "Captain Sude publicly attributes the proof discovery to GPT-6 Astra, including a first multiples-of-four argument followed by a new route covering every even integer greater than two. The released paper and repository do not document enough interaction provenance to independently separate model-generated ideas from human problem selection, prompting, editing, proof repair, or formalization work.", "zh-CN": "Captain Sude 公开将证明发现归因于 GPT-6 Astra，包括先得到 4 的倍数情形， 随后找到覆盖全部大于 2 偶数的新路线。但公开论文与仓库没有记录足够详细的 交互 provenance，无法独立区分模型生成思想与人类的问题选择、提示、编辑、 证明修复或形式化工作。" } }, "human_contribution": { "description": { "en": "Captain Sude maintained and released the public project materials and publicly described the Astra attribution. The released record does not document the exact human contribution to target selection, prompting, manuscript editing, Lean proof repair, or verification, so those roles are not inferred more specifically here.", "zh-CN": "Captain Sude 维护并发布公开项目材料，同时公开说明 Astra 的归因。现有记录没有 具体说明人类在目标选择、提示、论文编辑、Lean 证明修复或验证中的精确贡献， 因此本记录不对这些角色作进一步推断。" } }, "systems": [ "gpt-6-astra", "lean" ], "organizations": [], "people": [], "problems": [ "liouville-goldbach-problem" ], "methods": [ "multiplicative-functions", "finite-field-symmetry", "descent", "quadratic-reciprocity", "formalization" ], "verification": { "evidence_level": "E4", "status": "partially_verified", "formal_assurance": "independently_replayed", "history": [ { "date": "2026-09-16", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public repository released the mathematical paper and a complete Lean formalization whose final theorem matches the stated all-even Liouville–Goldbach claim. The project records successful local build, axiom, and proof-route audits.", "zh-CN": "公开仓库发布数学论文与完整 Lean 形式化，最终定理与所述覆盖全部偶数的 Liouville–Goldbach 主张一致；项目同时记录了成功的本地构建、公理审计和 证明路线审计。" } }, { "date": "2026-09-17", "status": "partially_verified", "evidence_level": "E4", "note": { "en": "An independent audit repository reports a Linux rebuild of the frozen v1.0.0 release, zero source-hash mismatches, a fresh axiom audit, a successful route audit, and no sorry, custom theorem axiom, or native_decide. This supports independently_replayed formal assurance but is explicitly a technical reproduction rather than independent mathematical peer review or priority adjudication.", "zh-CN": "一个独立审计仓库报告对冻结的 v1.0.0 版本完成 Linux 重建，源码哈希零差异， 重新执行公理审计和证明路线审计，并未发现 sorry、自定义定理公理或 native_decide。 这些证据支持 independently_replayed 的形式保障，但该审计明确属于技术复现， 并非独立数学同行评议或历史优先权裁决。" } } ] }, "sources": [ { "id": "captain-sude-liouville-goldbach-repository", "tier": "S1", "type": "repository", "title": "A Goldbach theorem for the Liouville function", "url": "https://github.com/CaptainSude/Liouville-Goldbach", "primary": true, "published_date": "2026-09-16", "accessed_at": "2026-09-21" }, { "id": "captain-sude-liouville-goldbach-paper", "tier": "S1", "type": "paper", "title": "A Goldbach theorem for the Liouville function", "url": "https://github.com/CaptainSude/Liouville-Goldbach/blob/main/paper/liouville-goldbach.pdf", "primary": true, "published_date": "2026-09-16", "accessed_at": "2026-09-21" }, { "id": "captain-sude-astra-liouville-goldbach-announcement", "tier": "S2", "type": "official_announcement", "title": "Captain Sude announcement attributing the Liouville–Goldbach proof to GPT-6 Astra", "url": "https://x.com/captain_sude/status/2100277626120163664", "primary": true, "published_date": "2026-09-16", "accessed_at": "2026-09-21" }, { "id": "sunnyspot-liouville-goldbach-independent-audit", "tier": "S3", "type": "independent_analysis", "title": "Liouville–Goldbach Independent Audit Bundle", "url": "https://github.com/sunnyspot114514/Liouville-Goldbach-audit", "primary": false, "published_date": "2026-09-17", "accessed_at": "2026-09-21" }, { "id": "mangerel-shusterman-liouville-goldbach", "tier": "S1", "type": "paper", "title": "On Shusterman's Goldbach-type problem for sign patterns of the Liouville function", "url": "https://arxiv.org/abs/2412.17199", "primary": false, "published_date": "2024-12-23", "accessed_at": "2026-09-21" }, { "id": "mangerel-goldbach-liouville-correlation", "tier": "S1", "type": "paper", "title": "On a Goldbach-type problem for the Liouville function", "url": "https://arxiv.org/abs/2404.12117", "primary": false, "published_date": "2024-04-18", "accessed_at": "2026-09-21" }, { "id": "mathoverflow-liouville-goldbach-2018", "tier": "S5", "type": "community", "title": "Goldbach's conjecture for the Liouville function", "url": "https://mathoverflow.net/questions/307479/goldbachs-conjecture-for-the-liouville-function", "primary": false, "published_date": "2018-08-03", "accessed_at": "2026-09-21" } ], "artifacts": [ { "id": "liouville-goldbach-lean-proof", "kind": "proof", "title": "Complete Lean 4 formalization of the Liouville–Goldbach theorem", "url": "https://github.com/CaptainSude/Liouville-Goldbach/tree/main/lean" }, { "id": "liouville-goldbach-final-theorem", "kind": "proof", "title": "LiouvilleGoldbach.liouville_goldbach", "url": "https://github.com/CaptainSude/Liouville-Goldbach/blob/main/lean/LiouvilleGoldbach/Main.lean" }, { "id": "liouville-goldbach-independent-replay", "kind": "supplement", "title": "Independent Linux replay and audit bundle", "url": "https://github.com/sunnyspot114514/Liouville-Goldbach-audit" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2026-openai-ten-advances", "evt-2026-openai-prime-gaps-186" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "liouville-function", "goldbach-type-problem", "number-theory", "gpt-6-astra", "lean", "ai-generated-mathematics" ], "editorial": { "created_at": "2026-09-21", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-severe-misalignment-ai-mathematics", "slug": "severe-misalignment-ai-mathematics", "title": { "en": "Twenty-five Fields Medallists publish A Severe Misalignment of AI in Mathematics", "zh-CN": "25 位菲尔兹奖得主发布《A Severe Misalignment of AI in Mathematics》声明" }, "dates": { "event": "2026-09-11", "first_public_claim": "2026-09-11", "paper_release": null, "artifact_release": "2026-09-11", "independently_verified": null, "added_to_chronicle": "2026-09-17", "last_updated": "2026-09-22" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The statement became more than a short-lived petition because it articulated an AI4Math-specific position on research incentives, mathematical understanding, attribution, unpublished work and the role of human mathematicians, then entered institutional discussion within days. The French Mathematical Society board explicitly cited it in an official position on the OpenAI Navier–Stokes controversy, while IMPA republished the statement for its community. These cross-institutional responses satisfy the Chronicle's field-building publication gate without treating signatory prestige or media attention alone as sufficient evidence.", "zh-CN": "这份声明并非仅凭签名人数或短期媒体热度获得收录。它针对 AI4Math 的研究激励、数学理解、归属、未公开工作以及人类数学家的角色提出明确共同体立场，并在数日内进入机构层面的持续讨论。法国数学会理事会在针对 OpenAI Navier–Stokes 争议的正式立场中直接引用该声明，IMPA 也面向其共同体公开转载。由此形成的跨机构响应满足 Chronicle 的领域建构收录门槛。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "On 11 September 2026, a declaration titled A Severe Misalignment of AI in Mathematics was published with 25 initial signatories, all Fields Medallists according to Terence Tao's direct account. The statement argued that using the solution of prominent mathematical problems as an AI-company benchmark can conflict with the goals and norms of mathematical research, and raised concerns about understanding, communication, attribution, research incentives and the stewardship of mathematical knowledge. It invited additional signatures and quickly became a reference point in institutional responses to the September 2026 AI-and-mathematics controversies.", "zh-CN": "2026 年 9 月 11 日，《A Severe Misalignment of AI in Mathematics》公开发布。Terence Tao 的直接说明表明，首批共有 25 位签署者且均为菲尔兹奖得主。声明主张，把攻克知名数学问题作为 AI 企业 benchmark 的做法可能与数学研究的目标和规范发生冲突，并讨论数学理解与表达、归属、研究激励以及数学知识传承等问题。声明同时开放后续签署，并迅速成为 2026 年 9 月 AI 与数学争议中机构回应所引用的共同体文本。" }, "summary": { "en": "The declaration emerged from discussions among its initial signatories during a week of intense debate over rapidly improving AI systems and high-profile mathematical problem solving. It framed the central concern as a misalignment between benchmark-driven corporate incentives and the mathematical community's emphasis on understanding, communication, attribution, mentorship and durable knowledge. On 14 September, IMPA published the statement on its institutional news surface. On 15 September, the board of the French Mathematical Society cited it in an official position responding to the OpenAI Navier–Stokes announcement and its associated ethical controversy.", "zh-CN": "该声明形成于一周内围绕 AI 数学能力快速提升和高关注度数学问题求解展开的密集讨论。其核心框架是：企业以 benchmark 和竞赛式突破为导向的激励，可能与数学共同体重视理解、交流、归属、人才培养和长期知识积累的价值发生错位。9 月 14 日，IMPA 在机构新闻页面转载声明；9 月 15 日，法国数学会理事会在回应 OpenAI Navier–Stokes 公告及相关伦理争议的正式立场中直接引用该声明。" }, "why_it_matters": { "en": "The event records a shift from isolated reactions to an explicit, field-specific critique of how advanced AI should interact with mathematical research. In relation to the earlier Leiden Declaration, it sharpened the governance debate around incentives, competition, credit, unpublished work and the preservation of human mathematical culture. Its significance lies in becoming an institutional reference point during a live AI4Math governance dispute, not in the prestige or number of signatories by itself.", "zh-CN": "这一事件记录了数学共同体从零散反应转向针对先进 AI 如何参与数学研究的明确领域级批评。相较此前的 Leiden Declaration，它进一步把治理讨论聚焦到研究激励、竞赛式突破、署名与归属、未公开工作以及人类数学文化的保存。其历史意义来自它在正在发生的 AI4Math 治理争议中成为机构引用的参照文本，而非签署者数量或声望本身。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records a human-authored community statement about the governance and social effects of AI in mathematics rather than an AI system performing mathematical work.", "zh-CN": "本事件记录的是人类数学共同体围绕 AI 在数学研究中的治理与社会影响发布的声明，而不是 AI 系统执行具体数学工作，因此 AI role 不适用。" } }, "human_contribution": { "description": { "en": "The initial signatories discussed, drafted and published the statement, invited broader community endorsement, and mathematical institutions subsequently incorporated it into public discussion of research norms and governance.", "zh-CN": "首批签署者讨论、起草并发布声明，邀请更广泛的共同体参与；随后数学机构将该文本纳入关于研究规范与治理的公开讨论。" } }, "systems": [], "organizations": [], "people": [], "problems": [], "methods": [ "community-governance", "research-integrity", "attribution", "research-incentives" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2026-09-11", "status": "claimed", "evidence_level": "E2", "note": { "en": "The declaration website and Terence Tao's direct post establish the publication, date, initial-signatory count and the stated governance concerns.", "zh-CN": "声明官网与 Terence Tao 的直接文章确认了公开发布、日期、首批签署者数量以及声明提出的治理议题。" } }, { "date": "2026-09-17", "status": "claimed", "evidence_level": "E2", "note": { "en": "Institutional responses from IMPA and the French Mathematical Society show that the statement entered field-level discussion beyond its originating signatories. Chronicle records this as significance evidence, not as endorsement of every normative claim in the declaration.", "zh-CN": "IMPA 与法国数学会的机构级公开回应表明，该声明已经进入超越首批签署者范围的领域讨论。Chronicle 将其作为历史重要性证据，而不将其解释为对声明中全部规范性主张的背书。" } }, { "date": "2026-09-22", "status": "claimed", "evidence_level": "E2", "note": { "en": "OpenAI's 21 September announcement explicitly cited A Severe Misalignment of AI in Mathematics when explaining the need for a new bridge to the mathematical community, and the independently organized Advisory Group on Mathematics and Artificial Intelligence subsequently identified advising OpenAI on release coordination as its first task. This is recorded as downstream institutional impact, not as endorsement of every normative claim in the declaration.", "zh-CN": "OpenAI 在 9 月 21 日的公告中明确引用《A Severe Misalignment of AI in Mathematics》， 用以说明建立数学共同体沟通渠道的必要性；随后独立组建的 Advisory Group on Mathematics and Artificial Intelligence 又把就 OpenAI 的成果发布协调提供建议 列为首项任务。Chronicle 将其记录为该声明产生的后续制度影响，而不是对声明中 全部规范性主张的背书。" } } ] }, "sources": [ { "id": "severe-misalignment-official", "tier": "S2", "type": "community", "title": "A Severe Misalignment of AI in Mathematics", "url": "https://mathandai.org/", "primary": true, "published_date": "2026-09-11", "accessed_at": "2026-09-17" }, { "id": "tao-severe-misalignment", "tier": "S2", "type": "community", "title": "A Severe Misalignment of AI in Mathematics — Terence Tao", "url": "https://terrytao.wordpress.com/2026/09/11/a-severe-misalignment-of-ai-in-mathematics/", "primary": false, "published_date": "2026-09-11", "accessed_at": "2026-09-17" }, { "id": "impa-severe-misalignment", "tier": "S2", "type": "official_announcement", "title": "A Severe Misalignment of AI in Mathematics — IMPA", "url": "https://impa.br/notices/a-severe-misalignment-of-ai-in-mathematics/?lang=en", "primary": false, "published_date": "2026-09-14", "accessed_at": "2026-09-17" }, { "id": "smf-openai-position", "tier": "S2", "type": "official_announcement", "title": "Position of the SMF board on the recent announcements of OpenAI", "url": "https://smf.emath.fr/index.php/actualites-smf/position-bureau-smf-navier-stokes-et-openai", "primary": false, "published_date": "2026-09-15", "accessed_at": "2026-09-17" }, { "id": "openai-agmai-response", "tier": "S2", "type": "official_announcement", "title": "Advisory Group on Mathematics and Artificial Intelligence", "url": "https://openai.com/index/advisory-group-on-mathematics-and-ai/", "primary": false, "published_date": "2026-09-21", "accessed_at": "2026-09-22" } ], "artifacts": [ { "id": "severe-misalignment-declaration", "kind": "other", "title": "A Severe Misalignment of AI in Mathematics", "url": "https://mathandai.org/" } ], "relationships": { "predecessors": [ "evt-2026-leiden-declaration" ], "successors": [ "evt-2026-agmai-advisory-group" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "severe-misalignment", "field-building", "community-governance", "research-integrity", "attribution", "research-incentives", "ai-and-mathematics" ], "editorial": { "created_at": "2026-09-17", "last_reviewed": "2026-09-22", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-magenta", "slug": "magenta-lean-verification-loop", "title": { "en": "Magenta closes the loop between informal mathematical reasoning and Lean verification", "zh-CN": "Magenta 打通非形式数学推理与 Lean 验证闭环" }, "dates": { "event": "2026-09-10", "first_public_claim": "2026-09-10", "paper_release": "2026-09-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "system", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "Magenta is a field-level milestone in verifier-guided mathematical agents because it integrates informal problem solving, Lean statement construction, statement-faithfulness judging, proof search and error attribution into one feedback loop instead of treating formalization and proving as isolated stages.", "zh-CN": "Magenta 是验证器引导数学 Agent 路线上的领域级里程碑：它把非形式解题、Lean 命题构造、命题忠实性判断、证明搜索与错误归因整合为同一反馈闭环，而不是把形式化和证明视为彼此孤立的阶段。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "The Magenta paper introduced a training-free agentic pipeline that starts from a natural-language problem, derives an answer, formalizes the statement in Lean 4 and constructs a machine-checked proof; the authors report 100% accuracy on their evaluated Olympiad benchmarks and, with K2-Horizon-7B as the reasoner, successful proofs for all six IMO 2026 problems.", "zh-CN": "Magenta 论文提出一个无需额外训练的 Agent 管线：从自然语言问题出发，先得到答案，再将命题形式化为 Lean 4，并构造机器检查证明；作者报告该系统在其评测的奥赛基准上达到 100% 准确率，并在使用 K2-Horizon-7B 作为推理模型时完成 IMO 2026 全部 6 道题的证明。" }, "summary": { "en": "Magenta uses a statement judge to check whether a generated Lean statement preserves the original informal problem and an error-attribution judge to decide whether a failed attempt should return to mathematical re-derivation or local Lean repair. The paper reports that this feedback-guided correction loop outperforms independent resampling on difficult problems.", "zh-CN": "Magenta 使用 statement judge 检查生成的 Lean 命题是否保持原始非形式问题的含义，并使用 error-attribution judge 判断失败尝试应回到数学推导还是进行局部 Lean 修复。论文报告称，这种基于反馈的纠错闭环在困难问题上优于独立重采样。" }, "why_it_matters": { "en": "The work makes formal verification an active part of mathematical reasoning rather than only a final certificate. In particular, it addresses a central failure mode of end-to-end autoformalization systems: a prover can certify the wrong formal statement unless the pipeline also checks whether that statement faithfully represents the human problem.", "zh-CN": "该工作把形式验证变成数学推理过程中的主动反馈，而不只是最终证书。尤其是，它直接处理端到端自动形式化的核心失效模式：如果系统不检查形式命题是否忠实表达原始人类问题，那么证明器可能只是正确证明了错误的形式化目标。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Language-model agents perform the mathematical derivation, translate the result into Lean, construct proofs, judge statement fidelity and route failures between mathematical re-reasoning and Lean repair inside the evaluated pipeline.", "zh-CN": "在评测管线中，语言模型 Agent 承担数学推导、Lean 形式化、证明构造、命题忠实性判断，并在失败时决定进入重新数学推理还是 Lean 修复。" } }, "human_contribution": { "description": { "en": "Researchers designed the multi-stage pipeline, judges, routing logic and evaluation protocol, selected the underlying reasoners and benchmarks, and analyzed the failure and correction behavior.", "zh-CN": "研究者设计多阶段管线、判断器、错误路由逻辑与评测协议，选择底层推理模型和基准，并分析系统的失败与纠错行为。" } }, "systems": [ "magenta", "lean", "k2-horizon-7b" ], "organizations": [], "people": [], "problems": [ "olympiad-mathematics", "imo-2026" ], "methods": [ "agentic-theorem-proving", "autoformalization", "statement-verification", "error-attribution", "lean-feedback" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2026-09-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record describes the Magenta pipeline and reports the benchmark and IMO 2026 results. The paper states that successful outputs are checked in Lean 4; no independent replay or public proof artifact is recorded by the Chronicle at this stage.", "zh-CN": "arXiv 研究记录描述了 Magenta 管线，并报告其基准与 IMO 2026 结果。论文称成功输出由 Lean 4 检查；Chronicle 当前尚未记录独立重放或公开证明产物。" } } ] }, "sources": [ { "id": "arxiv-magenta-2609.11319", "tier": "S1", "type": "paper", "title": "Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification", "url": "https://arxiv.org/abs/2609.11319", "primary": true, "published_date": "2026-09-10", "accessed_at": "2026-09-14" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2025-mathesis" ], "successors": [], "related": [ "evt-2026-aimo-proof-pilot" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "magenta", "lean", "autoformalization", "theorem-proving", "agent", "olympiad", "imo-2026" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-buckmaster-alpoge-fluid-blowup", "slug": "buckmaster-alpoge-fluid-blowup", "title": { "en": "Buckmaster and Alpöge release AI-assisted smooth-forcing blowup results for Euler, Boussinesq and IPM", "zh-CN": "Buckmaster 与 Alpöge 发布 AI 辅助的 Euler、Boussinesq 与 IPM 光滑外力爆破结果" }, "dates": { "event": "2026-09-08", "first_public_claim": "2026-09-08", "paper_release": "2026-09-08", "artifact_release": "2026-09-08", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "proof", "formalization" ], "significance": { "tier": "H1", "rationale": { "en": "The release combines three new smooth-forcing blowup results in major fluid equations with documented substantive LLM-assisted proof development and public Lean formalizations for the Euler and Boussinesq results. If accepted as H1, its historical significance comes from demonstrating human-led AI collaboration on frontier mathematical research, not from an AI originating the underlying research program.", "zh-CN": "该发布把三个重要流体方程中的光滑外力爆破新结果，与有明确记录的 LLM 实质性证明辅助，以及 Euler、Boussinesq 结果的公开 Lean 形式化结合在一起。若被接受为 H1，其历史意义来自前沿数学研究中的人类主导 AI 协作，而不是 AI 从零提出了底层研究路线。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "Tristan Buckmaster and Levent Alpöge report finite-time blowup results with smooth forcing for the three-dimensional incompressible Euler equations, the planar inviscid Boussinesq equations and incompressible porous media, developed with substantial help from Claude and Codex; public Lean artifacts formalize the Euler and Boussinesq results.", "zh-CN": "Tristan Buckmaster 与 Levent Alpöge 报告了三维不可压 Euler 方程、二维无粘 Boussinesq 方程以及不可压多孔介质方程在光滑外力下的有限时间爆破结果；研究过程中 Claude 与 Codex 提供了大量实质性帮助，公开 Lean 产物则形式化了 Euler 与 Boussinesq 两项结果。" }, "summary": { "en": "The researchers explicitly credit Diego Córdoba and Luis Martínez-Zoroa for the underlying forced-blowup research program and describe using LLMs to push that program from rougher forcing toward smooth forcing and related fluid equations. The public `fluid_lean` repository contains complete Lean developments for the Euler and Boussinesq theorems, with its documentation attributing the Lean code to Claude under Alpöge's direction.", "zh-CN": "两位研究者明确将底层强迫爆破研究路线归功于 Diego Córdoba 与 Luis Martínez-Zoroa，并描述其使用 LLM 将该路线从较粗糙的外力条件推进到光滑外力及相关流体方程。公开的 `fluid_lean` 仓库包含 Euler 与 Boussinesq 定理的完整 Lean 开发，其文档将 Lean 代码归因于在 Alpöge 指导下工作的 Claude。" }, "why_it_matters": { "en": "The event is an unusually inspectable example of AI contributing substantively to frontier mathematical research while humans retain the research program, judgment and responsibility for the claims. The results also became immediate historical context for the contemporaneous OpenAI Navier–Stokes claim, making precise attribution and separation of the distinct mathematical statements important to the Chronicle.", "zh-CN": "该事件是一个少见且可检查度较高的案例：AI 对前沿数学研究作出实质性贡献，而研究路线、判断与主张责任仍由人类掌握。这些结果还立即成为同期 OpenAI Navier–Stokes 主张的重要历史背景，因此准确区分不同数学命题及其归属对 Chronicle 尤其重要。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Buckmaster's public account describes Claude and Codex as being used throughout the project with substantial help from LLMs in extending the existing program. The public Euler and Boussinesq Lean repositories state that all Lean code, including the trusted statement files, was written by Claude under Alpöge's direction. The authors explicitly state that the underlying research program was not originated by an LLM.", "zh-CN": "Buckmaster 的公开说明称项目全过程使用了 Claude 与 Codex，并由 LLM 在推进既有研究路线时提供大量帮助。公开的 Euler 与 Boussinesq Lean 仓库说明，包括可信 statement 文件在内的全部 Lean 代码均由 Claude 在 Alpöge 指导下编写。作者同时明确说明，底层研究路线并非由 LLM 原创提出。" } }, "human_contribution": { "description": { "en": "Buckmaster and Alpöge selected and developed the research direction, evaluated and organized the mathematical arguments, authored the released manuscripts and remained responsible for the claims. They credit Córdoba and Martínez-Zoroa with the foundational forced-blowup program; Alpöge directed and reviewed the public Lean formalization workflow.", "zh-CN": "Buckmaster 与 Alpöge 选择并推进研究方向、评估与组织数学论证、撰写公开稿件，并对最终主张负责。他们将基础性的强迫爆破研究路线归功于 Córdoba 与 Martínez-Zoroa；Alpöge 还指导并审阅了公开 Lean 形式化流程。" } }, "systems": [ "claude", "codex", "lean", "mathlib" ], "organizations": [], "people": [ "tristan-buckmaster", "levent-alpoge", "diego-cordoba", "luis-martinez-zoroa" ], "problems": [ "forced-euler-blowup", "forced-boussinesq-blowup", "forced-ipm-blowup" ], "methods": [ "human-ai-collaboration", "proof-development", "formal-theorem-proving", "lean" ], "verification": { "evidence_level": "E3", "status": "partially_verified", "formal_assurance": "artifact_available", "history": [ { "date": "2026-09-08", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Three manuscripts and a public Lean repository were released. The repository contains dedicated formalization projects for Euler and Boussinesq, while no corresponding IPM Lean project is present in the public repository tree.", "zh-CN": "三份稿件与一个公开 Lean 仓库同期发布。该仓库包含 Euler 与 Boussinesq 的专门形式化项目，而公开仓库目录中没有对应的 IPM Lean 项目。" } }, { "date": "2026-09-11", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "Terence Tao independently discussed the mathematical work and its relationship to the Córdoba–Martínez-Zoroa program, and OpenAI independently acknowledged Buckmaster and Alpöge's priority on the forced Euler result. These sources corroborate the event and its historical context but are not treated here as independent verification of all three underlying theorems or as an independent replay of the Lean artifacts.", "zh-CN": "Terence Tao 独立讨论了这项数学工作及其与 Córdoba–Martínez-Zoroa 研究路线的关系；OpenAI 也独立承认 Buckmaster 与 Alpöge 在 forced Euler 结果上的优先权。这些来源佐证了事件及其历史背景，但 Chronicle 不据此认定三个底层定理均已得到独立验证，也不视为对 Lean 产物的独立重放。" } } ] }, "sources": [ { "id": "buckmaster-alpoge-statement-2026", "tier": "S2", "type": "official_announcement", "title": "Tristan Buckmaster statement on the joint fluid blowup work with Levent Alpöge", "url": "https://cims.nyu.edu/~tristanb/statement.pdf", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "buckmaster-alpoge-euler-2026", "tier": "S1", "type": "paper", "title": "Finite-time blow-up for the three-dimensional incompressible Euler equations with smooth force", "url": "https://cims.nyu.edu/~tristanb/euler.pdf", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "buckmaster-alpoge-boussinesq-2026", "tier": "S1", "type": "paper", "title": "Finite-time blow-up for the planar inviscid Boussinesq equations with smooth force", "url": "https://cims.nyu.edu/~tristanb/boussinesq.pdf", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "buckmaster-alpoge-ipm-2026", "tier": "S1", "type": "paper", "title": "Extending the Córdoba–Martínez-Zoroa IPM blow-up to uniformly space-time smooth forcing", "url": "https://cims.nyu.edu/~tristanb/ipm.pdf", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "github-buckmaster-fluid-lean", "tier": "S1", "type": "formal_artifact", "title": "Lean formalizations for the Buckmaster–Alpöge fluid blowup results", "url": "https://github.com/tristanbuckmaster/fluid_lean", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "tao-fluid-blowup-2026", "tier": "S3", "type": "independent_analysis", "title": "Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations", "url": "https://terrytao.wordpress.com/2026/09/07/finite-time-blowup-with-smooth-forcing-term-for-the-incompressible-porous-medium-boussinesq-and-incompressible-euler-equations/", "primary": false, "published_date": "2026-09-07", "accessed_at": "2026-09-11" }, { "id": "openai-navier-stokes-2026-related", "tier": "S2", "type": "official_announcement", "title": "On the Navier–Stokes Millennium Prize Problem", "url": "https://openai.com/index/navier-stokes-solution/", "primary": false, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "techcrunch-buckmaster-alpoge-2026", "tier": "S4", "type": "media", "title": "OpenAI fought dirty on career-making math problem, says NYU mathematician", "url": "https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician/", "primary": false, "published_date": "2026-09-08", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "buckmaster-alpoge-fluid-lean-repository", "kind": "proof", "title": "Lean 4 formalizations for Euler and Boussinesq blowup results", "url": "https://github.com/tristanbuckmaster/fluid_lean" }, { "id": "buckmaster-alpoge-euler-paper", "kind": "proof", "title": "Euler smooth-forcing blowup manuscript", "url": "https://cims.nyu.edu/~tristanb/euler.pdf" }, { "id": "buckmaster-alpoge-boussinesq-paper", "kind": "proof", "title": "Boussinesq smooth-forcing blowup manuscript", "url": "https://cims.nyu.edu/~tristanb/boussinesq.pdf" }, { "id": "buckmaster-alpoge-ipm-paper", "kind": "proof", "title": "IPM smooth-forcing blowup manuscript", "url": "https://cims.nyu.edu/~tristanb/ipm.pdf" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2026-openai-navier-stokes" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "fluid-dynamics", "euler", "boussinesq", "ipm", "blowup", "human-ai-collaboration", "claude", "codex", "lean" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-openai-navier-stokes", "slug": "openai-navier-stokes-solution-claim", "title": { "en": "OpenAI publishes an AI-generated claimed solution to the Navier–Stokes Millennium Problem with Lean formalization", "zh-CN": "OpenAI 发布 AI 生成的 Navier–Stokes 千禧年问题解答主张及 Lean 形式化" }, "dates": { "event": "2026-09-08", "first_public_claim": "2026-09-08", "paper_release": "2026-09-08", "artifact_release": "2026-09-08", "independently_verified": "2026-09-08", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-17" }, "event_types": [ "discovery", "proof", "formalization", "system", "controversy" ], "significance": { "tier": "H1", "rationale": { "en": "A publicly released AI-generated claimed solution to a Millennium Prize Problem is intrinsically a historical AI4Math event regardless of whether the underlying mathematical claim ultimately survives review. H1 records the magnitude of the event; verification separately records independent corroboration, dispute and later changes in the historical record.", "zh-CN": "公开发布的 AI 生成千禧年难题解答主张本身就是历史级 AI4Math 事件，无论其底层数学结论最终能否经受住审查。H1 记录事件的重要程度；verification 则另行记录独立佐证、争议以及后续历史变化。" } }, "mathematical_novelty": { "type": "new_proof" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "OpenAI reports that a large coordinated-agent system produced a finite-time singularity construction resolving statements C and D of the Navier–Stokes Millennium Prize formulation, together with a Lean formalization.", "zh-CN": "OpenAI 报告一个大规模协同 Agent 系统构造了有限时间奇点，声称解决 Navier–Stokes 千禧年问题官方表述中的 C 与 D，并提供 Lean 形式化。" }, "summary": { "en": "OpenAI says roughly 10,000 concurrent agents worked for about 88 hours on the successful search, followed by additional Lean formalization and verification. Independent reporting corroborated the publication event while also documenting disputes over attribution, provenance and priority involving contemporaneous work by Tristan Buckmaster and Levent Alpöge. OpenAI now says that, following an investigation, Buckmaster's Codex prompts during the two months before the 8 September release could not have influenced the system in any way, including through training. That direct statement narrows one provenance concern, while separate disputes over attribution, priority and the collaboration process remain part of the public record.", "zh-CN": "OpenAI 表示成功搜索约使用 10,000 个并发 Agent 工作约 88 小时，随后继续进行 Lean 形式化与验证。独立报道确认了这一发布事件，同时也记录了围绕 Tristan Buckmaster 与 Levent Alpöge 同期工作的归属、来源与优先权争议。OpenAI 现表示，经调查确认，Buckmaster 在 9 月 8 日发布前两个月内提交给 Codex 的 prompts 不可能以任何方式影响该系统，包括通过训练产生影响。这一直接声明缩小了 provenance 争议中的一个子问题，但围绕归属、优先权和合作过程的其他争议仍然存在于公开记录中。" }, "why_it_matters": { "en": "Because the claim concerns a Millennium Prize Problem and immediately triggered broad independent scrutiny and controversy, the event is historically significant regardless of the claim's eventual mathematical disposition. The proof, priority, attribution and community reception remain subjects for external mathematical and historical assessment.", "zh-CN": "由于该主张涉及千禧年难题，并立即引发广泛独立审视与争议，无论其数学结论最终如何，该事件本身都具有历史重要性。证明本身、优先权、归属与共同体接受度仍应由外部数学与历史证据持续评估。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "OpenAI attributes the construction to a coordinated multi-agent system powered by an internal model, with GPT-6 Astra used for formalization and verification.", "zh-CN": "OpenAI 将核心构造归因于由内部模型驱动的多 Agent 协同系统，并使用 GPT-6 Astra 完成形式化与验证。" } }, "human_contribution": { "description": { "en": "OpenAI researchers selected target formulations, orchestrated the evaluation and released the proof. Tristan Buckmaster and Levent Alpöge were conducting separate contemporaneous fluid-dynamics research rather than contributing to OpenAI's proof; their work, use of frontier AI tools and subsequent public accounts became central to the attribution, provenance and priority dispute. External mathematicians, mathematical institutions and journalists continue to scrutinize the claim and its historical context.", "zh-CN": "OpenAI 研究者选择目标表述、组织评测并发布证明。Tristan Buckmaster 与 Levent Alpöge 当时正独立开展同期流体动力学研究，并非 OpenAI 证明的贡献者；他们的研究、对前沿 AI 工具的使用以及后续公开说明成为归属、来源与优先权争议的核心背景。外部数学家、数学机构与记者仍在持续审视该主张及其历史语境。" } }, "systems": [ "openai-internal-model", "gpt-6-astra", "lean" ], "organizations": [ "openai" ], "people": [ "tristan-buckmaster", "levent-alpoge" ], "problems": [ "navier-stokes-existence-and-smoothness" ], "methods": [ "multi-agent", "autonomous-research", "formalization", "lean" ], "verification": { "evidence_level": "E3", "status": "disputed", "formal_assurance": "machine_checked", "history": [ { "date": "2026-09-08", "status": "under_verification", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-08", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "Independent reporting corroborated the core event facts that OpenAI publicly announced the claimed Millennium Problem solution, released a proof manuscript and Lean formalization, and described the large multi-agent search. This event-level corroboration does not certify the underlying mathematical claim.", "zh-CN": "独立报道确认了该事件的核心事实：OpenAI 公开宣布这一千禧年问题解答主张，发布证明稿与 Lean 形式化，并披露大规模多 Agent 搜索过程。这一事件级佐证并不认证底层数学主张的最终正确性。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "The Chronicle confirmed the public 166-page proof manuscript and Lean 4 repository formalizing the Navier–Stokes and Euler results. These primary artifacts strengthen the evidence record and support machine-checked formal assurance; independent mathematical assessment of the underlying claim remains a separate question from event-level corroboration.", "zh-CN": "Chronicle 已确认公开的 166 页证明稿，以及形式化 Navier–Stokes 与 Euler 结果的 Lean 4 仓库。这些一手产物加强了证据记录并支持 machine-checked formal assurance；对底层数学主张的独立数学评估与事件级佐证属于不同问题。" } }, { "date": "2026-09-10", "status": "disputed", "evidence_level": "E3", "note": { "en": "Reliable independent reporting also documented material disputes over attribution, provenance and priority involving contemporaneous work by Tristan Buckmaster and Levent Alpöge. The Chronicle therefore records the event as `disputed` while preserving that the publication event itself is independently corroborated.", "zh-CN": "可靠独立报道同时记录了围绕 Tristan Buckmaster 与 Levent Alpöge 同期工作的归属、来源与优先权争议。因此 Chronicle 将当前事件状态记为 `disputed`，同时保留“发布事件本身已获独立佐证”这一事实。" } }, { "date": "2026-09-11", "status": "disputed", "evidence_level": "E3", "note": { "en": "Axios independently documented Buckmaster and Alpöge's provenance and credit concerns and reported OpenAI's then-public boundary: the company said it did not access their specific user data for the proof, while acknowledging uncertainty about whether de-identified product-usage data could have indirectly improved its models. This sharpened the provenance record without establishing that such indirect use occurred.", "zh-CN": "Axios 独立记录了 Buckmaster 与 Alpöge 对来源和署名的担忧，并报道了 OpenAI 当时公开给出的边界：公司称证明过程中没有访问两人的特定用户数据，同时对去标识化产品使用数据是否曾间接改善模型保留不确定性。这一证据进一步明确了 provenance 记录，但并不能证明这种间接使用确实发生。" } }, { "date": "2026-09-17", "status": "disputed", "evidence_level": "E3", "note": { "en": "OpenAI's current public account states that, after an investigation, Buckmaster's Codex prompts during the two months before the 8 September announcement could not have influenced the system in any way, including through training. This materially narrows the previously recorded prompt-training provenance uncertainty. The event remains `disputed` because the broader public record still contains separate attribution, priority and collaboration-process disputes. The French Mathematical Society's 15 September position also documents continuing institutional concern around the episode without independently adjudicating the underlying proof.", "zh-CN": "OpenAI 当前公开说明称，经调查确认，Buckmaster 在 9 月 8 日公告前两个月内提交给 Codex 的 prompts 不可能以任何方式影响该系统，包括通过训练产生影响。这一声明实质性缩小了此前记录的 prompt-training provenance 不确定性。事件仍保持 `disputed`，因为公开记录中仍存在相互独立的归属、优先权与合作过程争议。法国数学会 9 月 15 日发布的正式立场也表明该事件仍持续引发机构层面的关注，但并未对底层证明作独立数学裁决。" } } ] }, "sources": [ { "id": "openai-navier-stokes-2026", "tier": "S2", "type": "official_announcement", "title": "On the Navier–Stokes Millennium Prize Problem", "url": "https://openai.com/index/navier-stokes-solution/", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-17" }, { "id": "openai-navier-stokes-paper-2026", "tier": "S1", "type": "paper", "title": "Finite Time Blowup for Navier–Stokes", "url": "https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-10" }, { "id": "github-openai-navier-stokes-euler-lean", "tier": "S1", "type": "formal_artifact", "title": "Lean certificates accompanying Navier–Stokes and Euler results", "url": "https://github.com/openai/NavierStokesAndEuler", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-10" }, { "id": "guardian-openai-navier-stokes-2026", "tier": "S4", "type": "media", "title": "OpenAI claims to have solved maths problem that stumped humans for decades", "url": "https://www.theguardian.com/science/2026/sep/08/openai-claims-to-have-solved-maths-problem-that-stumped-humans-for-decades", "primary": false, "published_date": "2026-09-08", "accessed_at": "2026-09-10" }, { "id": "axios-openai-navier-stokes-credit-2026", "tier": "S4", "type": "media", "title": "OpenAI's historic math solution overshadowed by credit controversy", "url": "https://www.axios.com/2026/09/08/openai-math-solution-navier-stokes-credit", "primary": false, "published_date": "2026-09-08", "accessed_at": "2026-09-11" }, { "id": "smf-openai-navier-stokes-position-2026", "tier": "S2", "type": "official_announcement", "title": "Position of the SMF board on the recent announcements of OpenAI", "url": "https://smf.emath.fr/index.php/actualites-smf/position-bureau-smf-navier-stokes-et-openai", "primary": false, "published_date": "2026-09-15", "accessed_at": "2026-09-17" } ], "artifacts": [ { "id": "openai-navier-stokes-proof-pdf", "kind": "proof", "title": "Finite Time Blowup for Navier–Stokes proof manuscript", "url": "https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf" }, { "id": "openai-navier-stokes-lean-repository", "kind": "proof", "title": "Lean 4 formalization and proof-checking tooling", "url": "https://github.com/openai/NavierStokesAndEuler" } ], "relationships": { "predecessors": [ "evt-2026-unit-distance-disproof", "evt-2026-openai-ten-advances", "evt-2026-claude-flt-formalization" ], "successors": [], "related": [ "evt-2026-buckmaster-alpoge-fluid-blowup" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "navier-stokes", "millennium-prize", "multi-agent", "lean", "controversy", "provenance", "attribution", "priority" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-17", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [ { "date": "2026-09-10", "summary": { "en": "Clarified the title to describe OpenAI's publication as a claimed solution rather than as the Chronicle's own adjudication, and recorded the independently reported attribution/provenance dispute.", "zh-CN": "将标题明确为 OpenAI 发布的“解答主张”，而非 Chronicle 自身对问题已解决的裁决，并记录独立报道中的归属 / 来源争议。" }, "source_ids": [ "openai-navier-stokes-2026", "guardian-openai-navier-stokes-2026" ] } ] }, { "schema_version": 1, "id": "evt-2026-stochbench", "slug": "stochbench-stochastic-processes-lean", "title": { "en": "StochBench brings graduate stochastic processes into Lean theorem-proving evaluation", "zh-CN": "StochBench 将研究生随机过程引入 Lean 定理证明评测" }, "dates": { "event": "2026-09-08", "first_public_claim": "2026-09-08", "paper_release": "2026-09-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "benchmark", "dataset", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "StochBench is a field-level benchmark milestone because it moves Lean theorem-proving evaluation beyond predominantly competition and textbook-style mathematics into a broad graduate applied-mathematics domain, while explicitly representing the gap between direct formalization and abstraction needed when library support is incomplete.", "zh-CN": "StochBench 是领域级基准里程碑，因为它把 Lean 定理证明评测从以竞赛题和教材型数学为主的场景扩展到广泛的研究生应用数学领域，并显式区分在形式库支持不足时所需的直接形式化与抽象化表达。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "The StochBench paper introduced 450 Lean 4 problems in graduate stochastic processes paired with natural-language sources; the authors report that an Opus 4.8-based proof agent solved 157 of 450 targets within a 15-minute per-problem budget, a 34.9% proof rate.", "zh-CN": "StochBench 论文发布了 450 道研究生随机过程 Lean 4 问题，并与自然语言来源配对；作者报告一个基于 Opus 4.8 的证明 Agent 在每题 15 分钟预算下完成 157/450 个目标，证明率为 34.9%。" }, "summary": { "en": "The benchmark covers Markov chains, renewal processes, random walks, martingales, stopping times, queues, Brownian motion, stochastic calculus, weak convergence, Poisson processes and continuous-time Markov processes. Its released dataset distinguishes 114 direct formalizations from 336 abstracted targets that expose assumptions explicitly when the required stochastic-process infrastructure is not available in the fixed Lean/Mathlib environment.", "zh-CN": "该基准覆盖马尔可夫链、更新过程、随机游走、鞅、停时、排队论、布朗运动、随机微积分、弱收敛、泊松过程与连续时间马尔可夫过程。公开数据集区分 114 个直接形式化目标与 336 个抽象化目标：当固定 Lean / Mathlib 环境缺少所需随机过程基础设施时，后者会把必要性质显式写入假设。" }, "why_it_matters": { "en": "Formal theorem-proving benchmarks can overstate general mathematical coverage when they concentrate on domains already well represented in proof libraries. StochBench makes domain breadth and library-support limitations part of the evaluation surface, providing a harder test of whether proof agents can operate in applied mathematics with substantial formalization gaps.", "zh-CN": "如果形式定理证明基准主要集中在证明库已充分覆盖的领域，就可能高估系统对一般数学的覆盖能力。StochBench 把领域广度与形式库支持不足本身纳入评测面，为证明 Agent 能否在存在显著形式化缺口的应用数学中工作提供更严格的测试。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "An Opus 4.8-based formalizer assisted in expressing human-written benchmark problems as Lean statements, with Lean feedback and human revision, and an Opus 4.8-based proof agent supplied the reported baseline proofs.", "zh-CN": "一个基于 Opus 4.8 的形式化器协助把人工编写的基准问题表达为 Lean 命题，并结合 Lean 反馈与人工修订；另一个基于 Opus 4.8 的证明 Agent 生成论文报告的基线证明结果。" } }, "human_contribution": { "description": { "en": "Researchers selected and wrote the benchmark-specific problems, definitions, hypotheses and evaluation protocol, reviewed the formal statements against their source problems, fixed the Lean/Mathlib environment and analyzed the baseline results by topic and representation.", "zh-CN": "研究者选择并编写基准专用问题、定义、假设与评测协议，对照来源问题审查形式命题，固定 Lean / Mathlib 环境，并按主题和形式化表示分析基线结果。" } }, "systems": [ "stochbench", "lean" ], "organizations": [ "case-western-reserve-university" ], "people": [], "problems": [ "stochastic-processes", "graduate-applied-mathematics" ], "methods": [ "benchmarking", "lean-formalization", "proof-agents", "autoformalization" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2026-09-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record defines the 450-problem benchmark, its stochastic-process scope and the reported 157/450 baseline under a 15-minute per-problem budget.", "zh-CN": "arXiv 研究记录定义了 450 题基准、随机过程覆盖范围，以及在每题 15 分钟预算下报告的 157/450 基线结果。" } }, { "date": "2026-09-14", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public StochBench dataset exposes the informal statements, Lean statements, representation labels and stored proof records. E3 records artifact-level inspectability and does not imply an independent replay of the full baseline evaluation.", "zh-CN": "StochBench 公开数据集提供自然语言陈述、Lean 命题、表示类别与已存储证明记录。E3 表示证据达到可检查 artifact 层级，并不表示完整基线评测已被独立重放。" } } ] }, "sources": [ { "id": "arxiv-stochbench-2609.09264", "tier": "S1", "type": "paper", "title": "StochBench: A Domain-Specific Benchmark for Stochastic Processes in Lean", "url": "https://arxiv.org/abs/2609.09264", "primary": true, "published_date": "2026-09-08", "accessed_at": "2026-09-14" }, { "id": "huggingface-stochbench", "tier": "S1", "type": "dataset", "title": "StochBench dataset", "url": "https://huggingface.co/datasets/IdanDavidovich/StochBench", "primary": true, "published_date": null, "accessed_at": "2026-09-14" } ], "artifacts": [ { "id": "stochbench-dataset", "kind": "benchmark", "title": "StochBench Lean 4 benchmark dataset", "url": "https://huggingface.co/datasets/IdanDavidovich/StochBench" } ], "relationships": { "predecessors": [ "evt-2023-proofnet" ], "successors": [], "related": [ "evt-2025-mathesis" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "stochbench", "lean", "benchmark", "stochastic-processes", "theorem-proving", "autoformalization", "applied-mathematics" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-claude-flt-formalization", "slug": "claude-fermat-last-theorem-formalization", "title": { "en": "Anthropic releases a Claude-generated complete Lean formalization of Fermat's Last Theorem", "zh-CN": "Anthropic 发布由 Claude 生成的费马大定理完整 Lean 形式化" }, "dates": { "event": "2026-09-04", "first_public_claim": "2026-09-04", "paper_release": null, "artifact_release": "2026-09-04", "independently_verified": "2026-09-04", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "formalization", "proof", "system" ], "significance": { "tier": "H1", "rationale": { "en": "The release demonstrated unusually large-scale AI-driven formalization of a landmark modern theorem: Claude worked largely autonomously for 11 days to translate the established Wiles and Taylor-Wiles argument into a Lean artifact that can be checked by proof kernels.", "zh-CN": "该发布展示了规模异常巨大的 AI 驱动形式化：Claude 在 11 天内大部分时间自主工作，将既有的 Wiles 与 Taylor-Wiles 论证转化为可由证明内核检查的 Lean 产物，目标是一个现代数学标志性定理。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "Anthropic described the release as the first complete computer-checked formalization of Fermat's Last Theorem. The public Lean repository states the standard theorem, contains no admitted proof gaps in the built package, and reports successful checking by Lean, comparator and a second Rust Lean kernel.", "zh-CN": "Anthropic 将该发布描述为费马大定理首次完整的计算机检查形式化。公开 Lean 仓库陈述了标准定理，在构建包中不包含被承认的证明缺口，并报告已通过 Lean、comparator 以及第二个 Rust Lean 内核的检查。" }, "summary": { "en": "Claude agents used Anthropic's Prove2Me workflow to build a dependency graph of formal subproblems and expand it into millions of lines of Lean code. The repository follows the classical Frey-Serre-Ribet-Wiles-Taylor-Wiles route and exposes the theorem graph, source attribution and reproducible verification procedures.", "zh-CN": "Claude Agent 使用 Anthropic 的 Prove2Me 工作流构建形式化子问题依赖图，并将其扩展为数百万行 Lean 代码。仓库沿用经典的 Frey–Serre–Ribet–Wiles–Taylor-Wiles 路线，并公开定理依赖图、来源归属和可复现验证流程。" }, "why_it_matters": { "en": "The event is important primarily as an autoformalization and proof-engineering milestone rather than a new proof of Fermat's Last Theorem. It tests whether multi-agent systems can assemble and verify a very large existing mathematical argument while preserving machine-checkable correctness.", "zh-CN": "该事件的重要性主要在自动形式化与证明工程，而不是发现费马大定理的新证明。它检验了多 Agent 系统能否组装并验证一个极其庞大的既有数学论证，同时保持机器可检查的正确性。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Claude agents generated the bulk of the Lean formalization, decomposed proof obligations and iteratively repaired code against Lean feedback; proof kernels determined whether the resulting formal terms type-checked.", "zh-CN": "Claude Agent 生成了大部分 Lean 形式化内容、分解证明义务，并根据 Lean 反馈迭代修复代码；证明内核负责判定最终形式项是否通过类型检查。" } }, "human_contribution": { "description": { "en": "The underlying mathematics comes from Fermat's Last Theorem research culminating in Wiles and Taylor-Wiles, together with later expositions and open Lean libraries. Anthropic researchers designed and orchestrated the agent workflow, selected sources, integrated existing formal libraries and documented verification and attribution.", "zh-CN": "底层数学来自最终由 Wiles 与 Taylor-Wiles 完成的费马大定理研究，以及后续阐释和开放 Lean 数学库。Anthropic 研究者设计并编排 Agent 工作流、选择来源、整合既有形式库，并记录验证和归属信息。" } }, "systems": [ "claude", "prove2me", "lean", "mathlib" ], "organizations": [ "anthropic", "imperial-college-london", "lean-community" ], "people": [ "tianyi-peng", "kevin-buzzard", "andrew-wiles", "richard-taylor" ], "problems": [ "fermats-last-theorem" ], "methods": [ "multi-agent", "autoformalization", "formal-theorem-proving", "lean", "proof-dag" ], "verification": { "evidence_level": "E3", "status": "independently_verified", "formal_assurance": "independently_replayed", "history": [ { "date": "2026-09-04", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "Anthropic released the full Lean artifact. Its verification documentation reports a from-scratch Lean build, a comparator replay against a stock-Mathlib challenge statement and acceptance by the independent nanoda Lean kernel implementation.", "zh-CN": "Anthropic 公开完整 Lean 产物；其验证文档报告了从头 Lean 构建、针对标准 Mathlib 挑战陈述的 comparator 重放，以及独立 nanoda Lean 内核实现的通过结果。" } }, { "date": "2026-09-04", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "Kevin Buzzard independently reported compiling the public code base and running comparator successfully. He also manually inspected non-proof/non-definition code for suspicious mechanisms. This supports `independently_replayed` formal assurance without by itself triggering the Chronicle's `independently_verified` editorial status.", "zh-CN": "Kevin Buzzard 独立报告称已编译公开代码库并成功运行 comparator；他还人工检查了并非数学定义或定理证明的代码，以排查可疑机制。这支持将 formal assurance 记为 `independently_replayed`，但其本身不自动触发 Chronicle 的 `independently_verified` 编辑状态。" } }, { "date": "2026-09-07", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "Nature independently reported the formalization and quoted mathematicians assessing its scale and significance. AI4Math Chronicle does not assign independently_verified status without a separate editorial review of artifact replay and mathematical faithfulness.", "zh-CN": "Nature 独立报道了该形式化，并引用数学家对其规模与意义的评价。AI4Math Chronicle 在未单独审核产物重放与数学忠实性之前，不授予 independently_verified 状态。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "Under the Chronicle's event-level verification semantics, Kevin Buzzard's independent compilation and comparator replay together with Nature's independent reporting substantively corroborate the core event description. This status verifies the event record and released formalization, not the ultimate mathematical correctness of every underlying dependency or claim.", "zh-CN": "按 Chronicle 的事件级 verification 语义，Kevin Buzzard 的独立编译与 comparator 重放，加上 Nature 的独立报道，已经对该事件的核心描述形成实质性独立佐证。该状态核验的是事件记录与公开形式化产物，而不是由 Chronicle 对所有底层数学依赖或主张的最终正确性作裁决。" } } ] }, "sources": [ { "id": "anthropic-flt-2026", "tier": "S2", "type": "official_announcement", "title": "Formalizing Fermat's Last Theorem", "url": "https://www.anthropic.com/research/formalizing-fermats-last-theorem", "primary": true, "published_date": "2026-09-04", "accessed_at": "2026-09-10" }, { "id": "github-anthropic-flt", "tier": "S1", "type": "formal_artifact", "title": "Fermat's Last Theorem in Lean 4", "url": "https://github.com/anthropics/fermats-last-theorem", "primary": true, "published_date": "2026-09-04", "accessed_at": "2026-09-10" }, { "id": "kevin-buzzard-xena-flt-2026", "tier": "S3", "type": "independent_analysis", "title": "FLT: Anthropic has beaten me to it", "url": "https://xenaproject.wordpress.com/2026/09/04/flt-anthropic-has-beaten-me-to-it/", "primary": false, "published_date": "2026-09-04", "accessed_at": "2026-09-10" }, { "id": "nature-claude-flt-2026", "tier": "S4", "type": "media", "title": "Anthropic AI formalizes proof of Fermat's last theorem — a milestone for mathematics", "url": "https://www.nature.com/articles/d41586-026-02822-9", "primary": false, "published_date": "2026-09-07", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "anthropic-flt-lean-repository", "kind": "proof", "title": "Complete Lean 4 formalization and verification tooling", "url": "https://github.com/anthropics/fermats-last-theorem" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f", "evt-2023-leandojo" ], "successors": [], "related": [ "evt-2026-alphaproof-nexus" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "fermat-last-theorem", "lean", "autoformalization", "multi-agent", "claude", "formal-verification" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-openai-prime-gaps-186", "slug": "openai-gpt6-astra-prime-gaps-186", "title": { "en": "GPT-6 Astra is credited with improving the bounded prime-gap record to 186", "zh-CN": "GPT-6 Astra 被归因于将有界素数间隔纪录推进至 186" }, "dates": { "event": "2026-08-30", "first_public_claim": "2026-08-30", "paper_release": "2026-08-30", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-27", "last_updated": "2026-09-27" }, "event_types": [ "discovery", "proof", "formalization" ], "significance": { "tier": "H1", "rationale": { "en": "This result is a Historical Milestone because it is an AI-attributed advance on a prominent frontier problem in analytic number theory rather than a benchmark or a reformulation of known mathematics. The OpenAI preprint claims the bound liminf(p_(n+1)-p_n) <= 186, improving the long-standing 246 record of Polymath8b; Terence Tao's Optimization Problems record lists 186 as the current best known upper bound and notes that 246 had stood for twelve years. The result is accompanied by a substantial Lean and numerical verification artifact. Historical significance is recorded separately from the still-incomplete verification of the mathematical inputs and provenance.", "zh-CN": "该结果被列为 Historical Milestone，因为它不是 benchmark 提升或对已知数学的重新 形式化，而是一个被归因于 AI 的解析数论前沿推进。OpenAI 预印本声称得到 liminf(p_(n+1)-p_n) <= 186，把 Polymath8b 长期保持的 246 上界进一步降低； Terence Tao 的 Optimization Problems 记录把 186 列为当前最好已知上界，并注明 246 纪录保持了十二年。该成果同时提供大规模 Lean 与数值验证产物。这里的历史 重要性与数学输入及 provenance 仍未完全验证的状态严格分开记录。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "OpenAI's 30 August 2026 preprint claims that GPT-6 Astra found a proof establishing DHL[40,2], which, when applied to an explicit admissible 40-tuple of diameter 186, yields liminf_(n->infinity)(p_(n+1)-p_n) <= 186 for consecutive prime gaps. The result improves the prior 246 record associated with Polymath8b and predates Julia Stadlmann's independently obtained 240 bound by one day.", "zh-CN": "OpenAI 在 2026 年 8 月 30 日发布的预印本声称 GPT-6 Astra 找到了一项证明， 建立 DHL[40,2]；将其应用于一个直径为 186 的显式 admissible 40-tuple，可得到 连续素数间隔满足 liminf_(n->infinity)(p_(n+1)-p_n) <= 186。该结果改进了 Polymath8b 对应的 246 纪录，并比 Julia Stadlmann 独立得到的 240 上界早一天发布。" }, "summary": { "en": "The public PrimeGaps186 repository contains a Lean 4 development for DHL[40,2] and the 186 prime-gap consequence together with a Python/FLINT numerical certificate. The registered main Lean declarations contain no sorry, and OpenAI reports that Comparator, Nanoda and Lean's kernel accepted the conditional proofs. The formal development nevertheless depends on three explicit project axioms: a rank-three hyper-Kloosterman estimate, a rank-two Kloosterman correlation estimate, and a collection of physical-integral and cap bounds. The first two are attributed to established literature; the numerical input is checked by the companion certificate rather than proved inside Lean. OpenAI's own metadata labels the review self-assessed and states that no independent human semantic review had been completed.", "zh-CN": "公开的 PrimeGaps186 仓库包含 DHL[40,2] 与 186 素数间隔结论的 Lean 4 开发， 并附带 Python/FLINT 数值 certificate。登记的主要 Lean declaration 均无 sorry， OpenAI 报告 Comparator、Nanoda 与 Lean kernel 均接受这些条件式证明。但形式化 仍依赖三个显式项目公理：一个 rank-three hyper-Kloosterman 估计、一个 rank-two Kloosterman correlation 估计，以及一组 physical-integral 与 cap bounds。前两个 输入来自既有文献；数值输入由配套 certificate 检查，而没有在 Lean 内证明。 OpenAI 自身的 metadata 将审查状态标为 self-assessed，并明确说明尚无独立人类 semantic review。" }, "why_it_matters": { "en": "The bounded-prime-gap problem is one of the best-known modern examples of sustained progress on the distribution of primes. Moving the unconditional published record from 246 to 186 after roughly twelve years would be mathematically notable on its own; having the proof publicly attributed to a frontier AI model makes the event a direct test case for AI systems contributing new frontier mathematics. The accompanying formal artifact also illustrates a new verification boundary: machine checking can strongly validate a large conditional derivation while still leaving cited and numerical inputs outside the proof assistant.", "zh-CN": "有界素数间隔问题是现代素数分布研究中最知名的持续推进路线之一。在约十二年后把公开 无条件纪录从 246 推进至 186，本身就具有显著数学意义；而证明又被公开归因于前沿 AI 模型，使该事件成为 AI 系统直接贡献新前沿数学的代表案例。配套形式化同时清楚展示一种 新的验证边界：机器检查可以强力验证庞大的条件式推导，但被引用的数学估计和数值输入 仍可能位于 proof assistant 之外。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "OpenAI and the public formalization metadata attribute the proof to GPT-6 Astra operating through Codex. The metadata also states that the artifact was refined through human-guided edits and automated proof checks. This AI-role classification records the disclosed workflow; it does not mean that Chronicle independently reconstructed the full model-human derivation trace.", "zh-CN": "OpenAI 及公开 formalization metadata 将证明归因于通过 Codex 工作的 GPT-6 Astra， 同时注明产物经过 human-guided edits 与自动证明检查。本 AI-role 分类记录的是公开 披露的工作流，并不表示 Chronicle 已独立重建完整的模型—人类推导轨迹。" } }, "human_contribution": { "description": { "en": "Humans selected and released the research target and artifacts, guided refinement of the generated formal development, connected unproved mathematical estimates to the literature, and built or reviewed the numerical-certificate and checking pipeline. The public metadata does not provide a complete person-by-person division of intellectual labor.", "zh-CN": "人类负责研究目标与成果的选择和发布，引导生成式形式化的修订，把未在 Lean 中证明的 数学估计对应到既有文献，并建立或审查数值 certificate 与验证流程。公开 metadata 没有提供完整的逐人智力分工记录。" } }, "systems": [ "gpt-6-astra", "lean", "comparator", "nanoda" ], "organizations": [ "openai" ], "people": [], "problems": [ "bounded-prime-gaps" ], "methods": [ "maynard-tao-sieve", "multidimensional-selberg-sieve", "prime-equidistribution", "numerical-optimization", "formal-verification" ], "verification": { "evidence_level": "E3", "status": "under_verification", "formal_assurance": "machine_checked", "history": [ { "date": "2026-08-30", "status": "paper_released", "evidence_level": "E3", "note": { "en": "OpenAI released the preprint and a public Lean/numerical verification artifact. The repository records machine-checked conditional proofs of DHL[40,2] and the 186 bound, with three explicit non-standard input axioms.", "zh-CN": "OpenAI 发布预印本以及公开 Lean/数值验证产物。仓库记录了 DHL[40,2] 和 186 上界的机器检查条件式证明，并明确列出三个非标准输入公理。" } }, { "date": "2026-09-27", "status": "under_verification", "evidence_level": "E3", "note": { "en": "Terence Tao's Optimization Problems record independently lists 186 as the current best known bounded-prime-gap upper bound, records the 30 August preprint and the GPT-6 Astra attribution, and separately documents the same three-axiom formalization caveat. Chronicle has not located an independent semantic review or full replay that discharges the project inputs, so the Event remains under verification rather than independently_verified.", "zh-CN": "Terence Tao 的 Optimization Problems 记录独立把 186 列为当前最好已知的有界素数 间隔上界，记录了 8 月 30 日预印本及 GPT-6 Astra 归因，并另行说明相同的三公理 形式化限制。Chronicle 尚未找到能够消除这些项目输入、并完成独立语义审查或完整 重放的证据，因此当前 Event 保持 under_verification，而不是 independently_verified。" } } ] }, "sources": [ { "id": "openai-improved-short-gaps-2026", "tier": "S1", "type": "paper", "title": "Improved short gaps between primes", "url": "https://cdn.openai.com/pdf/51126fac-1b68-4128-9666-c908bcc16033/short_gaps.pdf", "primary": true, "published_date": "2026-08-30", "accessed_at": "2026-09-27" }, { "id": "openai-primegaps186-repository", "tier": "S1", "type": "repository", "title": "Prime Gaps at Most 186", "url": "https://github.com/openai/PrimeGaps186", "primary": true, "published_date": null, "accessed_at": "2026-09-27" }, { "id": "openai-primegaps186-formalization-metadata", "tier": "S1", "type": "formal_artifact", "title": "PrimeGaps186 formalization metadata", "url": "https://github.com/openai/PrimeGaps186/blob/main/formalization.yaml", "primary": true, "published_date": null, "accessed_at": "2026-09-27" }, { "id": "tao-bounded-prime-gap-record", "tier": "S3", "type": "independent_analysis", "title": "Bounded prime gap constant", "url": "https://teorth.github.io/optimizationproblems/constants/88a.html", "primary": false, "published_date": null, "accessed_at": "2026-09-27" } ], "artifacts": [ { "id": "primegaps186-lean", "kind": "proof", "title": "PrimeGaps186 Lean 4 development", "url": "https://github.com/openai/PrimeGaps186" }, { "id": "primegaps186-numerical-certificate", "kind": "supplement", "title": "Prime-gap numerical certificate", "url": "https://github.com/openai/PrimeGaps186/blob/main/prime_gap_186_certificate.py" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2026-astra-liouville-goldbach" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "prime-gaps", "bounded-prime-gaps", "analytic-number-theory", "gpt-6-astra", "lean", "comparator", "nanoda", "numerical-certificate", "ai-generated-mathematics" ], "editorial": { "created_at": "2026-09-27", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-palomar-registry", "slug": "palomar-lean-verified-mathematics-registry", "title": { "en": "Palomar opens a public registry for Lean-verified mathematics", "zh-CN": "Palomar 开放面向 Lean 验证数学的公共注册库" }, "dates": { "event": "2026-08-18", "first_public_claim": "2026-08-18", "paper_release": null, "artifact_release": "2026-08-18", "independently_verified": null, "added_to_chronicle": "2026-09-27", "last_updated": "2026-09-27" }, "event_types": [ "infrastructure", "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "Palomar is a field milestone because it creates durable institutional and technical infrastructure for recording Lean-verified research results at fixed source revisions. Its workflow separates proof replay from semantic and provenance review, publishes exact statements and dependencies, and responds directly to the rapid growth of AI-assisted and AI-generated formal mathematics. The registry materially organizes the field without claiming to replace mathematical peer review or certify novelty.", "zh-CN": "Palomar 构成领域级里程碑，因为它为固定源码版本上的 Lean 验证研究成果建立了持续性的 制度与技术注册基础设施。其工作流把 proof replay 与语义、provenance 审查分离， 公开精确定理陈述和依赖关系，并直接回应 AI 辅助及 AI 生成形式数学快速增长带来的 记录与核验问题。该注册库显著组织了领域实践，但并不声称替代数学同行评议或认证新颖性。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal" ], "claim": { "en": "On 18 August 2026, Palomar opened for submissions as a public registry of Lean-verified mathematics, jointly incubated by the Lean Focused Research Organization and ICARM. Each registered result is tied to a fixed public source revision and records the exact formal statement, dependencies and verification metadata. Palomar uses Comparator for statement/proof separation and proof replay, rechecks exported proofs with Lean's kernel and NanoDa, requires formalization.yaml provenance disclosures, and applies an automated semantic review without presenting registration as a certificate of novelty or mathematical importance.", "zh-CN": "2026 年 8 月 18 日，Palomar 作为 Lean 验证数学的公共注册库开放投稿，由 Lean Focused Research Organization 与 ICARM 共同孵化。每个注册结果都绑定固定的公开 源码版本，并记录精确形式陈述、依赖和验证元数据。Palomar 使用 Comparator 分离 statement 与 proof 并重放证明，同时通过 Lean kernel 与 NanoDa 再检查导出的证明， 要求提交 formalization.yaml provenance 信息，并加入自动语义审查；注册本身不被 表述为对新颖性或数学重要性的认证。" }, "summary": { "en": "Palomar was created in response to the increasing volume of machine-assisted and machine-generated mathematics and the difficulty of auditing claims scattered across repositories and announcements. Its public statement positions the service as analogous to a preprint or repository layer for formalizations: it provides an immutable, searchable and inspectable record of what was mechanically checked while leaving novelty, relevance and deeper mathematical judgment to the research community.", "zh-CN": "Palomar 的设立背景是 machine-assisted / machine-generated mathematics 数量快速增加， 而成果分散在代码仓库和公告中，外部读者难以核查。其公开声明把该服务定位为形式化成果 的 preprint / repository 层：提供不可变、可搜索、可检查的机械验证记录，同时把新颖性、 相关性和更深层数学判断留给研究共同体。" }, "why_it_matters": { "en": "Formal proof checking alone does not establish that a public theorem statement faithfully represents the informal research claim, nor does a repository URL create a stable scholarly record. Palomar makes these boundaries explicit and turns statement identity, proof replay, AI-use disclosure and source pinning into reusable infrastructure for an era of high-volume AI-assisted formalization.", "zh-CN": "单纯的形式证明检查不能保证公开形式定理忠实表达非形式研究主张，一个代码仓库链接也不能 自动形成稳定学术记录。Palomar 明确这些边界，并把 statement identity、proof replay、 AI 使用披露和源码固定版本转化为可复用基础设施，以适应高产量 AI 辅助形式化时代。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "AI is part of Palomar's operating workflow through automated semantic review of whether a formal statement reasonably matches the informal claim and through provenance fields for AI-assisted work. Deterministic proof checking remains separate from this probabilistic review.", "zh-CN": "AI 通过自动语义审查参与 Palomar 的运作，用于判断形式 statement 是否合理对应 非形式主张；系统也专门记录 AI 辅助工作的 provenance。确定性的证明检查与这种 概率式语义审查保持分离。" } }, "human_contribution": { "description": { "en": "Human mathematicians and maintainers designed the registry policies, review boundaries and governance, while submitters remain responsible for the informal claims, provenance disclosures and public source artifacts attached to registrations.", "zh-CN": "人类数学家与维护者设计注册库政策、审查边界和治理结构；提交者仍对非形式主张、 provenance 披露和注册所依赖的公开源码产物负责。" } }, "systems": [ "palomar-registry", "lean", "comparator", "nanoda" ], "organizations": [ "lean-fro", "icarm" ], "people": [ "jeremy-avigad", "matthew-ballard", "jaume-de-dios", "nestor-guillen", "bryna-kra", "kim-morrison", "terence-tao", "ravi-vakil", "akshay-venkatesh" ], "problems": [], "methods": [ "formal-proof-registry", "independent-kernel-replay", "statement-proof-separation", "provenance-metadata", "automated-semantic-review" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "2026-08-18", "status": "claimed", "evidence_level": "E3", "note": { "en": "Palomar's own public statement and service document the registry rules and machine-readable records. Terence Tao's announcement establishes the 18 August opening date, and ICARM independently documents the launch and three-part automated checking workflow. This verifies the infrastructure event, not every registered mathematical result.", "zh-CN": "Palomar 官方声明和服务页面记录注册规则及机器可读记录；Terence Tao 的公告确认 8 月 18 日开放日期，ICARM 另行记录发布及三部分自动检查工作流。这些证据支持 基础设施事件本身，并不等于验证其中每一条注册数学结果。" } } ] }, "sources": [ { "id": "palomar-statement-2026", "tier": "S2", "type": "official_announcement", "title": "Palomar: a registry of Lean-verified mathematics", "url": "https://palomar-registry.org/statement", "primary": true, "published_date": "2026-08-18", "accessed_at": "2026-09-27" }, { "id": "tao-palomar-launch-2026", "tier": "S2", "type": "community", "title": "Palomar – a registry of Lean verified mathematics", "url": "https://terrytao.wordpress.com/2026/08/18/palomar-a-registry-of-lean-verified-mathematics/", "primary": true, "published_date": "2026-08-18", "accessed_at": "2026-09-27" }, { "id": "icarm-palomar-2026", "tier": "S2", "type": "official_announcement", "title": "Announcing Palomar, a registry of Lean verified mathematics", "url": "https://icarm.io/news/announcing-palomar-a-registry-of-lean-verified-mathematics/", "primary": false, "published_date": "2026-08-21", "accessed_at": "2026-09-27" } ], "artifacts": [ { "id": "palomar-registry-site", "kind": "other", "title": "Palomar Registry", "url": "https://palomar-registry.org/" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2026-lean-pool" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "palomar", "lean", "formal-verification", "proof-registry", "field-building", "provenance", "comparator", "nanoda" ], "editorial": { "created_at": "2026-09-27", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-claude-riemann-lower-bound", "slug": "claude-riemann-zeta-lower-bound", "title": { "en": "Claude improves a longstanding lower bound related to the Riemann hypothesis", "zh-CN": "Claude 改进与黎曼猜想相关的长期下界" }, "dates": { "event": "2026-08-10", "first_public_claim": "2026-08-10", "paper_release": null, "artifact_release": null, "independently_verified": "2026-08-11", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "proof", "formalization", "system" ], "significance": { "tier": "H1", "rationale": { "en": "A concrete AI-generated improvement to a longstanding analytic-number-theory bound is a historical AI4Math milestone because it contributes new mathematics rather than merely demonstrating benchmark competence; H1 does not replace the separate verification state.", "zh-CN": "AI 对解析数论中长期下界给出具体改进，属于历史级 AI4Math 里程碑，因为它贡献的是新的数学结果，而非仅展示基准能力；H1 不替代独立的 verification 状态。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "Anthropic reported that an unreleased Claude research model raised the known lower bound for the fraction of Riemann-zeta zeros on the critical line from 41.6% to 67.2%.", "zh-CN": "Anthropic 报告一个未发布 Claude 研究模型把已知的“位于临界线上的黎曼 zeta 零点比例下界”从 41.6% 提升到 67.2%。" }, "summary": { "en": "Claude coordinated dozens of subagents, searched literature and numerical evidence, and produced a paper; Anthropic mathematicians reviewed the result and a Lean formalization passed comparator.", "zh-CN": "Claude 协调数十个子 Agent、检索文献并进行数值检查，随后生成论文；Anthropic 数学家审核结果，Lean 形式化通过 comparator。" }, "why_it_matters": { "en": "It is a notable example of autonomous mathematical exploration yielding an unexpected publishable result while failing at the original, much harder Riemann-hypothesis objective.", "zh-CN": "这是自主数学探索产生意外可发表结果的代表案例，同时也清楚显示模型并未解决最初更困难的黎曼猜想。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Claude generated and explored thousands of ideas with subagents, found the core argument and produced a formalization workflow.", "zh-CN": "Claude 通过多个子 Agent 生成并探索大量想法，找到核心论证并参与形式化流程。" } }, "human_contribution": { "description": { "en": "Anthropic mathematicians reviewed the result, external experts examined it, and staff assisted formalization and publication.", "zh-CN": "Anthropic 数学家审核结果，外部专家进行审阅，工作人员协助形式化与发布。" } }, "systems": [ "claude-research", "lean" ], "organizations": [ "anthropic" ], "people": [], "problems": [ "riemann-hypothesis-related-zero-density" ], "methods": [ "multi-agent", "literature-search", "analytic-number-theory", "formalization" ], "verification": { "evidence_level": "E3", "status": "independently_verified", "formal_assurance": "independently_replayed", "history": [ { "date": "2026-08-10", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-08-11", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "Riemann Labs independently rebuilt the public Lean formalization in its own CI and reported successful statement-equality checks plus replay under the Lean default kernel and nanoda. This supports `independently_replayed` formal assurance, while broader mathematical peer review remains distinct and the Chronicle does not yet assign `independently_verified` status.", "zh-CN": "Riemann Labs 在其独立 CI 中重新构建公开 Lean 形式化，并报告 statement-equality 检查以及 Lean 默认内核与 nanoda 重放均通过。这支持将 formal assurance 记为 `independently_replayed`；更广泛的数学同行评审仍是另一层问题，Chronicle 目前不授予 `independently_verified` 状态。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "Under the Chronicle's event-level verification semantics, Riemann Labs' independent rebuild, statement comparison and dual-kernel replay substantively corroborate the core event description and released formal artifact. This status does not mean the Chronicle independently adjudicates the ultimate correctness, priority or broader mathematical significance of the underlying research claim.", "zh-CN": "按 Chronicle 的事件级 verification 语义，Riemann Labs 的独立重建、statement comparison 与双内核重放已经对该事件的核心描述和公开形式化产物形成实质性独立佐证。该状态不表示 Chronicle 独立裁决底层研究主张的最终正确性、优先权或更广泛数学意义。" } } ] }, "sources": [ { "id": "anthropic-riemann-zeta-2026", "tier": "S2", "type": "official_announcement", "title": "Learning more about Claude's mathematical capabilities", "url": "https://www.anthropic.com/research/riemann-zeta", "primary": true, "published_date": "2026-08-10", "accessed_at": "2026-09-10" }, { "id": "anthropic-zeta-23-lean", "tier": "S1", "type": "formal_artifact", "title": "Zeta23 Lean 4 formalization", "url": "https://github.com/anthropics/zeta-23-lean", "primary": true, "published_date": null, "accessed_at": "2026-09-10" }, { "id": "riemann-labs-zeta-independent-replay", "tier": "S3", "type": "independent_analysis", "title": "Independent Verification — More Than Two Thirds of the Zeros of the Riemann Zeta Function Lie on the Critical Line", "url": "https://github.com/primaryhosting/zeta-two-thirds-verification", "primary": false, "published_date": "2026-08-11", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "anthropic-zeta-23-lean-artifact", "kind": "proof", "title": "Lean 4 formalization of the zeta lower-bound result", "url": "https://github.com/anthropics/zeta-23-lean" }, { "id": "riemann-labs-zeta-replay", "kind": "supplement", "title": "Independent rebuild and dual-kernel replay evidence", "url": "https://github.com/primaryhosting/zeta-two-thirds-verification" } ], "relationships": { "predecessors": [ "evt-2026-first-proof-openai", "evt-2026-frontiermath-open-problems" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "riemann-hypothesis", "number-theory", "claude", "multi-agent" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-openai-ten-advances", "slug": "openai-ten-math-tcs-advances", "title": { "en": "OpenAI publishes ten AI-generated advances across mathematics and theoretical computer science", "zh-CN": "OpenAI 发布十项 AI 生成的数学与理论计算机科学进展" }, "dates": { "event": "2026-08-01", "first_public_claim": "2026-08-01", "paper_release": "2026-08-01", "artifact_release": "2026-08-02", "independently_verified": "2026-08-01", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "proof", "formalization", "system", "controversy" ], "significance": { "tier": "H1", "rationale": { "en": "A portfolio of AI-generated advances across multiple active areas of mathematics and theoretical computer science marks a historical shift from isolated successes toward repeated research-level mathematical contributions; H1 records the historical importance of the publication event separately from the ultimate correctness or reception of each individual result.", "zh-CN": "跨多个活跃数学与理论计算机科学领域的一组 AI 生成研究进展，标志着从孤立成功走向可重复研究级数学贡献的历史性转折；H1 记录的是该发布事件的历史重要性，与其中每项结果最终是否正确或如何被学界接受分开判断。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "formal", "symbolic", "hybrid" ], "claim": { "en": "OpenAI released ten results resolving or substantially advancing longstanding problems in areas including sphere packing, group theory, circuit complexity, quantum complexity, lattice problems and extremal combinatorics.", "zh-CN": "OpenAI 发布十项结果，声称解决或实质推进球堆积、群论、算术电路复杂度、量子复杂性、格问题与极值组合等领域的长期问题。" }, "summary": { "en": "OpenAI states that an internal Astra model generated the mathematical arguments, humans prepared manuscripts with the model, and the model formalized each argument into a Lean certificate. Subsequent reporting documented attribution and training-data provenance concerns around the non-sofic-groups result, including Andreas Thom's unresolved question about whether unpublished mathematical discussions conducted through ChatGPT could have contributed indirectly through model-improvement data.", "zh-CN": "OpenAI 表示内部 Astra 模型生成数学论证，人类与模型共同整理稿件，随后模型把每项论证形式化为 Lean certificate。后续报道记录了围绕非 sofic 群结果的归属与训练数据来源争议，其中包括 Andreas Thom 尚未得到解决的问题：他与同事通过 ChatGPT 进行的未公开数学讨论，是否可能通过模型改进数据间接影响相关系统。" }, "why_it_matters": { "en": "If the individual results survive expert review, the release indicates a shift from isolated AI mathematics successes toward repeated research-level contributions.", "zh-CN": "如果这些结果经受住专家审查，该发布意味着 AI 数学可能从孤立成功转向可重复的研究级贡献。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "OpenAI attributes the mathematical arguments to its internal Astra model and says the model also produced Lean formalizations. The provenance dispute does not establish that unpublished user material was used, but it leaves an unresolved question about whether the model's research route may have been influenced by de-identified model-improvement data.", "zh-CN": "OpenAI 将数学论证归因于内部 Astra 模型，并称模型还生成了 Lean 形式化。当前 provenance 争议并未证明未公开用户材料确实被使用，但仍留下一个尚未解决的问题：模型的研究路径是否可能受到去标识化模型改进数据的间接影响。" } }, "human_contribution": { "description": { "en": "Humans selected problems, prepared manuscripts with the model and take responsibility for correctness; broader community review is still relevant. For the non-sofic-groups result specifically, OpenAI's proof builds substantially on prior work by Gábor Kun and Andreas Thom, whose contribution and the public framing of that result became part of the subsequent attribution discussion.", "zh-CN": "人类选择问题、与模型整理稿件并对正确性负责；更广泛的社区审查仍然重要。具体到非 sofic 群结果，OpenAI 的证明大量建立在 Gábor Kun 与 Andreas Thom 的既有工作之上；两人的贡献以及该结果最初的公开表述随后成为归属讨论的一部分。" } }, "systems": [ "openai-astra-internal", "lean" ], "organizations": [ "openai" ], "people": [ "gabor-kun", "andreas-thom" ], "problems": [ "research-mathematics", "theoretical-computer-science" ], "methods": [ "autonomous-research", "formalization", "lean" ], "verification": { "evidence_level": "E3", "status": "disputed", "formal_assurance": "machine_checked", "history": [ { "date": "2026-08-01", "status": "under_verification", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-10", "status": "under_verification", "evidence_level": "E3", "note": { "en": "The Chronicle confirmed that OpenAI publicly released the 253-page paper and a repository containing Lean 4 certificates for all ten results. These primary artifacts strengthen the evidence record but do not by themselves establish independent mathematical verification.", "zh-CN": "Chronicle 已确认 OpenAI 公开发布 253 页论文，以及包含全部十项结果 Lean 4 certificates 的仓库。这些一手产物加强了证据记录，但其本身不足以构成独立数学验证。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "Independent technical and media coverage corroborates the core publication event: OpenAI released ten claimed mathematics/TCS advances together with a long paper and public Lean certificates. The Chronicle's `independently_verified` label concerns that event-level record; it does not certify that every one of the ten underlying mathematical claims has completed independent expert review.", "zh-CN": "独立技术评论与媒体报道已经对该发布事件的核心事实形成佐证：OpenAI 公开了十项数学 / TCS 研究进展主张、一份长篇论文以及公开 Lean certificates。Chronicle 的 `independently_verified` 标签针对这一事件级记录，并不表示十项底层数学主张都已完成独立专家审查。" } }, { "date": "2026-09-11", "status": "disputed", "evidence_level": "E3", "note": { "en": "Reliable independent reporting and Andreas Thom's public account document a material attribution and provenance dispute around the non-sofic-groups result, one of the ten published advances. The dispute concerns the initial treatment of recent Kun–Thom work and an unresolved question about whether unpublished ChatGPT research discussions could have contributed indirectly through model-improvement training data. The Chronicle does not assert that such data use occurred; the publication event and released artifacts remain independently corroborated.", "zh-CN": "可靠独立报道与 Andreas Thom 的公开说明记录了十项进展之一——非 sofic 群结果——所涉及的实质性归属与来源争议。争议包括最初对 Kun–Thom 近期工作的呈现，以及一个尚未解决的问题：未公开的 ChatGPT 数学研究讨论是否可能通过模型改进训练数据间接产生影响。Chronicle 不断言此类数据使用确实发生；该发布事件及其公开产物本身仍有独立佐证。" } } ] }, "sources": [ { "id": "openai-ten-advances-2026", "tier": "S2", "type": "official_announcement", "title": "Ten advances in mathematics and theoretical computer science", "url": "https://openai.com/index/ten-advances-in-mathematics/", "primary": true, "published_date": "2026-08-01", "accessed_at": "2026-09-10" }, { "id": "openai-ten-advances-paper-2026", "tier": "S1", "type": "paper", "title": "Ten Advances in Mathematics and Theoretical Computer Science", "url": "https://cdn.openai.com/pdf/ten-proofs-oai.pdf", "primary": true, "published_date": "2026-08-01", "accessed_at": "2026-09-10" }, { "id": "github-openai-ten-proofs", "tier": "S1", "type": "formal_artifact", "title": "OpenAI ten-proofs Lean certificates", "url": "https://github.com/openai/ten-proofs", "primary": true, "published_date": "2026-08-02", "accessed_at": "2026-09-10" }, { "id": "simon-willison-openai-ten-advances-2026", "tier": "S4", "type": "media", "title": "Ten advances in mathematics and theoretical computer science", "url": "https://simonwillison.net/2026/Aug/1/ten-advances-in-mathematics/", "primary": false, "published_date": "2026-08-01", "accessed_at": "2026-09-10" }, { "id": "verge-ai-math-openai-astra-2026", "tier": "S4", "type": "media", "title": "Welcome to the AI crisis in math", "url": "https://www.theverge.com/podcast/982434/ai-math-openai-astra-existential-crisis", "primary": false, "published_date": null, "accessed_at": "2026-09-10" }, { "id": "andreas-thom-openai-provenance-2026", "tier": "S2", "type": "community", "title": "Andreas Thom statement on OpenAI non-sofic-group attribution and training-data provenance", "url": "https://mathstodon.xyz/@andreasthom/117240535270608201", "primary": true, "published_date": "2026-09-09", "accessed_at": "2026-09-11" }, { "id": "verge-openai-math-provenance-2026", "tier": "S4", "type": "media", "title": "Mathematicians want proof OpenAI didn't use their work", "url": "https://www.theverge.com/ai-artificial-intelligence/993263/where-does-openai-get-mathematics-training-data", "primary": false, "published_date": "2026-09-10", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "openai-ten-proofs-lean-repository", "kind": "proof", "title": "Lean 4 certificates for the ten published results", "url": "https://github.com/openai/ten-proofs" } ], "relationships": { "predecessors": [ "evt-2026-unit-distance-disproof", "evt-2026-frontiermath-open-problems" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "research-math", "open-problems", "lean", "autonomous-research", "attribution", "provenance" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-frontiermath-open-problems", "slug": "frontiermath-open-problems-50", "title": { "en": "FrontierMath: Open Problems expands to 50 verifiable research problems", "zh-CN": "FrontierMath: Open Problems 扩展到 50 个可验证研究问题" }, "dates": { "event": "2026-07-31", "first_public_claim": "2026-07-31", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "FM:OP created a denominator for autonomous mathematical discovery by tracking significant unsolved problems whose candidate solutions can be computationally verified.", "zh-CN": "FM:OP 通过跟踪可计算验证候选解的显著未解问题，为衡量自主数学发现提供了一个更有意义的“分母”。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric", "hybrid" ], "claim": { "en": "Epoch AI expanded FrontierMath: Open Problems to 50 significant unsolved research problems and tracked AI solutions separately by mathematical notability.", "zh-CN": "Epoch AI 将 FrontierMath: Open Problems 扩展到 50 个重要未解研究问题，并按数学重要性分层跟踪 AI 解答。" }, "summary": { "en": "Problems are selected by mathematicians, paired with bespoke computational verifiers where possible, and categorized by the significance of a solution.", "zh-CN": "问题由数学家筛选，并尽可能配套专用计算验证器，同时按解答的重要性进行分级。" }, "why_it_matters": { "en": "The benchmark focuses evaluation on whether AI advances human mathematical knowledge rather than only reproducing known solutions.", "zh-CN": "该基准把评测重点放在 AI 是否真正推进人类数学知识，而不只是复现已知答案。" }, "ai_role": { "level": "computation_only", "description": { "en": "Frontier systems attempt open problems under long-horizon scaffolds and are tested by problem-specific verifiers.", "zh-CN": "前沿系统在长程脚手架下尝试开放问题，并由问题专用验证器检查候选解。" } }, "human_contribution": { "description": { "en": "Mathematicians propose and review problems while Epoch AI builds verifiers and maintains attribution and solution status.", "zh-CN": "数学家提出并审核问题，Epoch AI 构建验证器并维护归属与解答状态。" } }, "systems": [ "frontiermath-open-problems" ], "organizations": [ "epoch-ai" ], "people": [], "problems": [ "open-research-mathematics" ], "methods": [ "benchmarking", "computational-verification", "expert-curation" ], "verification": { "evidence_level": "E3", "status": "partially_verified", "formal_assurance": "artifact_available", "history": [ { "date": "2026-07-31", "status": "partially_verified", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "epoch-frontiermath-open-problems-2026", "tier": "S1", "type": "benchmark", "title": "FrontierMath: Open Problems", "url": "https://epoch.ai/frontiermath/open-problems?notability=Moderately+interesting", "primary": true, "published_date": "2026-07-31", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "frontiermath-open-problems-benchmark", "kind": "dataset", "title": "FrontierMath: Open Problems benchmark surface", "url": "https://epoch.ai/frontiermath/open-problems?notability=Moderately+interesting" } ], "relationships": { "predecessors": [ "evt-2024-frontiermath", "evt-2026-unit-distance-disproof" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "research-math", "open-problems", "benchmark", "verification" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-aimo-proof-pilot", "slug": "aimo-proof-pilot-open-models", "title": { "en": "AIMO Proof Pilot evaluates fully open models on expert-graded Olympiad-style proofs", "zh-CN": "AIMO Proof Pilot 以专家评分的奥赛式完整证明评测完全开放模型" }, "dates": { "event": "2026-07-07", "first_public_claim": "2026-07-07", "paper_release": null, "artifact_release": "2026-06-26", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "competition", "benchmark" ], "significance": { "tier": "H2", "rationale": { "en": "The AIMO Proof Pilot combined full Olympiad-style proof generation, expert human grading and unusually strict openness requirements covering model checkpoints, training protocols and training data, creating a reproducible proof-writing milestone distinct from final-answer competitions and closed frontier-model demonstrations.", "zh-CN": "AIMO Proof Pilot 将完整奥赛式证明生成、专家人工评分与严格开放要求结合起来，要求公开模型检查点、训练协议和训练数据，形成区别于最终答案竞赛与闭源前沿模型演示的可复现证明写作里程碑。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal" ], "claim": { "en": "AIMO reported that the winning Proof Pilot team led by Yi-Chia Chen scored 29 of 42 across six National-Olympiad-hard to IMO-medium problems using fully open-source models, compared with 1 of 42 for the strongest provided open baseline; every submitted proof was graded independently by at least two expert human graders and the outputs and grading data were released publicly.", "zh-CN": "AIMO 报告称，由 Yi-Chia Chen 领衔的 Proof Pilot 冠军团队使用完全开源模型，在 6 道从国家奥赛高难度到 IMO 中等难度的问题上取得 29/42 分，而提供给参赛者的最强开放基线为 1/42；每份提交证明至少由两名专家独立评分，输出与评分数据均公开。" }, "summary": { "en": "The pilot restricted participants to models whose intermediate checkpoints, training protocols and training data were public. Six teams produced evaluated outputs on six proof problems, and AIMO compared them under the same expert-grading procedure with open-weight and commercial frontier models while publishing the submissions and detailed grading data.", "zh-CN": "该试点仅允许使用中间检查点、训练协议和训练数据均公开的模型。6 支团队在 6 道证明题上产出有效提交；AIMO 使用同一专家评分流程，将这些结果与开放权重及商业前沿模型比较，并公开提交内容与详细评分数据。" }, "why_it_matters": { "en": "The event supplied a concrete proof-quality benchmark for the fully open model ecosystem, where reproducibility and training transparency were part of the competition contract rather than optional release practices, and where success was measured on human-readable proofs instead of only final answers.", "zh-CN": "该事件为完全开放模型生态提供了具体的证明质量基准：可复现性与训练透明度成为竞赛契约的一部分，而非可选发布行为；系统能力也由人类可读的完整证明而不只是最终答案来衡量。" }, "ai_role": { "level": "computation_only", "description": { "en": "Participating AI systems generated complete natural-language proofs and were the objects under evaluation; humans defined the competition protocol, enforced openness requirements and graded proof quality.", "zh-CN": "参赛 AI 系统生成完整自然语言证明并作为被评测对象；人类负责制定竞赛协议、执行开放性要求并评定证明质量。" } }, "human_contribution": { "description": { "en": "Competition organizers selected the proof problems and openness rules, teams trained or adapted open models and systems, and expert graders independently assessed each proof to establish final scores.", "zh-CN": "竞赛组织者选择证明题目并制定开放规则，参赛团队训练或适配开放模型与系统，专家评分者独立评估每份证明以确定最终成绩。" } }, "systems": [ "aimo-proof-pilot" ], "organizations": [ "aimo-prize", "xtx-markets" ], "people": [ "yi-chia-chen" ], "problems": [ "olympiad-proof-generation" ], "methods": [ "open-source-model-training", "proof-generation", "expert-grading", "reproducible-evaluation" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "2026-07-07", "status": "claimed", "evidence_level": "E2", "note": { "en": "AIMO published the Proof Pilot results, team identities, per-problem scores, comparison models and expert-grading procedure.", "zh-CN": "AIMO 公布 Proof Pilot 结果、团队身份、逐题成绩、对比模型及专家评分流程。" } }, { "date": "2026-09-11", "status": "claimed", "evidence_level": "E3", "note": { "en": "AIMO links the anonymized team/model outputs and a public grading dataset on Kaggle. E3 records inspectable competition artifacts and does not imply Chronicle independently regraded every proof or reproduced the teams' training runs.", "zh-CN": "AIMO 链接了 Kaggle 上公开的匿名团队 / 模型输出及评分数据集。E3 表示竞赛产物可直接检查，并不表示 Chronicle 独立重新评分了全部证明或复现了各团队的训练过程。" } } ] }, "sources": [ { "id": "aimo-proof-pilot-results-2026", "tier": "S2", "type": "official_announcement", "title": "AIMO Proof Pilot Winners Announced", "url": "https://aimoprize.com/updates/2026-07-07-aimo-proof-pilot-winners-announced.md", "primary": true, "published_date": "2026-07-07", "accessed_at": "2026-09-11" }, { "id": "aimo-proof-pilot-launch-2026", "tier": "S2", "type": "official_announcement", "title": "AIMO 3 Winners Announced; AIMO Proof Pilot Launched", "url": "https://aimoprize.com/updates/2026-06-24-aimo-3-winners-announced", "primary": true, "published_date": "2026-06-24", "accessed_at": "2026-09-11" }, { "id": "kaggle-aimo-proof-pilot-outputs", "tier": "S1", "type": "dataset", "title": "AIMO Proof Pilot submitted proof outputs", "url": "https://www.kaggle.com/competitions/ai-mathematical-olympiad-proof-pilot/discussion/714666", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "kaggle-aimopp-grading-data", "tier": "S1", "type": "dataset", "title": "AIMO Proof Pilot grading data", "url": "https://www.kaggle.com/datasets/sambealing/aimopp-grading-data", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "aimo-proof-pilot-outputs", "kind": "dataset", "title": "AIMO Proof Pilot team and model outputs", "url": "https://www.kaggle.com/competitions/ai-mathematical-olympiad-proof-pilot/discussion/714666" }, { "id": "aimo-proof-pilot-grading", "kind": "dataset", "title": "AIMO Proof Pilot expert and model grading data", "url": "https://www.kaggle.com/datasets/sambealing/aimopp-grading-data" } ], "relationships": { "predecessors": [ "evt-2024-numinamath-aimo", "evt-2025-matharena" ], "successors": [], "related": [ "evt-2025-openai-imo-gold", "evt-2025-gemini-imo-gold" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "aimo", "competition", "open-source", "proof-writing", "olympiad", "expert-grading" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-leiden-declaration", "slug": "leiden-declaration-ai-mathematics", "title": { "en": "The Leiden Declaration sets community principles for AI in mathematical research", "zh-CN": "Leiden Declaration 为数学研究中的 AI 使用提出共同体原则" }, "dates": { "event": "2026-06-02", "first_public_claim": "2026-06-02", "paper_release": null, "artifact_release": "2026-06-02", "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The Leiden Declaration is a field-building milestone because it turned a broad, cross-institutional consultation into an AI4Math-specific set of recommendations on transparency, attribution, verification, research autonomy, publication practice and scholarly governance. Its endorsement by the International Mathematical Union, independent scholarly discussion in Nature, and presentation at ICM 2026 provide evidence of field-level institutional significance beyond signatory count or short-lived media attention.", "zh-CN": "Leiden Declaration 构成领域建构里程碑，因为它把广泛、跨机构的共同体讨论凝结为一套面向 AI4Math 的具体建议，涉及透明度、署名与归属、验证、研究自主性、出版实践和学术治理。International Mathematical Union 的正式 endorsement、Nature 的独立学术讨论以及 ICM 2026 的公开讨论，表明其领域级制度影响并非仅来自签名数量或短期媒体热度。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "On 2 June 2026, a 16-author international working group published the Leiden Declaration on Artificial Intelligence and Mathematics after a consultation process that grew from the 2025 Mechanization and Mathematical Research meeting in Leiden. The International Mathematical Union endorsed the declaration on publication. The document calls for explicit norms around AI use in mathematical research, including transparency and disclosure, attribution, independent verification, open scholarly practice, research autonomy and institutional responsibility.", "zh-CN": "2026 年 6 月 2 日，一个由 16 位作者组成的国际工作组发布 Leiden Declaration on Artificial Intelligence and Mathematics；该声明源于 2025 年在 Leiden 举行的 Mechanization and Mathematical Research 会议，并经过后续共同体咨询形成。International Mathematical Union 在声明发布时给予正式 endorsement。该文件围绕数学研究中的 AI 使用提出明确规范，包括透明度与披露、署名与归属、独立验证、开放学术实践、研究自主性与机构责任。" }, "summary": { "en": "The declaration grew from a September 2025 Lorentz Center meeting of around 60 participants from 10 countries spanning mathematics, computer science, philosophy, history, social science, industry and government. A smaller working group developed the text over the following months with extensive community feedback. The declaration was archived on Zenodo with a DOI, endorsed by the IMU, later discussed at ICM 2026, and the subject of supportive editorials and reporting in major scientific publications.", "zh-CN": "该声明源于 2025 年 9 月 Lorentz Center 举办的一次会议，约 60 名参与者来自 10 个国家，背景覆盖数学、计算机科学、哲学、历史、社会科学、产业与政府。随后较小的工作组在数月内结合广泛共同体反馈形成文本。声明以 DOI 形式存档于 Zenodo，获得 IMU endorsement，之后在 ICM 2026 公开讨论，并受到主要科学出版物的社论与报道关注。" }, "why_it_matters": { "en": "As AI systems became more capable participants in mathematical research, the declaration moved the discussion from isolated reactions to an explicit community-governance agenda. It supplies a durable reference point for questions that recur across AI4Math results: how AI use should be disclosed, how credit and training data should be handled, what independent verification requires, and how mathematical institutions should preserve rigor, access and human judgment while adopting new tools.", "zh-CN": "随着 AI 系统越来越深地参与数学研究，该声明把零散的个体反应推进为明确的共同体治理议程。它为 AI4Math 中反复出现的问题提供了持续性的参考点：应如何披露 AI 使用、如何处理署名与训练数据、独立验证意味着什么，以及数学机构在采用新工具时如何维护严谨性、可访问性与人类判断。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records a human-authored community governance statement about AI in mathematics rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是人类共同体围绕数学中的 AI 制定治理与规范声明，而不是 AI 系统执行数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "Human participants convened the preceding interdisciplinary meeting, formed the working group, drafted and revised the declaration through community feedback, published the citable record, and sought institutional discussion and endorsement.", "zh-CN": "人类参与者组织前期跨学科会议、组成工作组、依据共同体反馈起草和修订声明、发布可引用记录，并推动机构层面的讨论与 endorsement。" } }, "systems": [], "organizations": [ "international-mathematical-union", "lorentz-center" ], "people": [], "problems": [], "methods": [ "community-governance", "research-integrity", "ai-disclosure", "open-science" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2026-06-02", "status": "claimed", "evidence_level": "E2", "note": { "en": "The declaration website and Zenodo record establish the published text, authorship, date and DOI; the IMU publicly records its endorsement.", "zh-CN": "声明官网与 Zenodo 记录确认了正式文本、作者、发布日期与 DOI；IMU 公开记录其 endorsement。" } }, { "date": "2026-09-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "Nature and Nature Machine Intelligence editorials, together with the declaration's official update record, document substantial scholarly reception and later discussion at ICM 2026. The Chronicle records this reception as significance evidence without treating endorsement as proof that every normative recommendation is universally accepted.", "zh-CN": "Nature 与 Nature Machine Intelligence 的社论以及声明官方更新记录显示，该文件获得了显著的学术共同体关注，并在 ICM 2026 继续公开讨论。Chronicle 将这些材料用于支持历史重要性判断，但不把 endorsement 解释为所有规范建议已经获得普遍共识。" } } ] }, "sources": [ { "id": "leiden-declaration-official", "tier": "S2", "type": "community", "title": "Leiden Declaration on Artificial Intelligence and Mathematics", "url": "https://leidendeclaration.ai/", "primary": true, "published_date": "2026-06-02", "accessed_at": "2026-09-14" }, { "id": "leiden-declaration-zenodo", "tier": "S2", "type": "other", "title": "Leiden Declaration on Artificial Intelligence and Mathematics — Zenodo record", "url": "https://zenodo.org/doi/10.5281/zenodo.20302944", "primary": true, "published_date": "2026-06-02", "accessed_at": "2026-09-14" }, { "id": "imu-leiden-endorsement", "tier": "S2", "type": "official_announcement", "title": "IMU News 137: the IMU endorses the Leiden Declaration on Artificial Intelligence and Mathematics", "url": "https://www.mathunion.org/imu-news/archive/2026/imu-news-137-may-2026", "primary": false, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "nature-leiden-editorial", "tier": "S3", "type": "independent_analysis", "title": "Mathematicians are developing rules for AI use — other fields should follow", "url": "https://www.nature.com/articles/d41586-026-01881-2", "primary": false, "published_date": "2026-06-16", "accessed_at": "2026-09-14" }, { "id": "nature-machine-intelligence-leiden-editorial", "tier": "S3", "type": "independent_analysis", "title": "Solutions, challenges and rising tensions in AI and mathematics", "url": "https://www.nature.com/articles/s42256-026-01269-x", "primary": false, "published_date": "2026-06-23", "accessed_at": "2026-09-14" } ], "artifacts": [ { "id": "leiden-declaration-pdf-record", "kind": "other", "title": "Leiden Declaration on Artificial Intelligence and Mathematics — citable Zenodo record", "url": "https://zenodo.org/doi/10.5281/zenodo.20302944" } ], "relationships": { "predecessors": [ "evt-2023-ams-ai-advisory" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "leiden-declaration", "field-building", "community-governance", "research-integrity", "attribution", "verification", "ai-disclosure", "open-science" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-alphaproof-nexus", "slug": "alphaproof-nexus-open-problem-proof-search", "title": { "en": "AlphaProof Nexus scales Lean-based agents to hundreds of open research problems", "zh-CN": "AlphaProof Nexus 将基于 Lean 的 Agent 扩展到数百个开放研究问题" }, "dates": { "event": "2026-05-21", "first_public_claim": "2026-05-21", "paper_release": "2026-05-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "proof", "formalization", "discovery" ], "significance": { "tier": "H2", "rationale": { "en": "AlphaProof Nexus was reported as the first large-scale evaluation of LLM-driven formal proof search on open research problems, moving Lean-based agents from benchmark theorems to hundreds of active mathematical conjectures with public proof artifacts.", "zh-CN": "AlphaProof Nexus 被论文报告为首次对 LLM 驱动的形式证明搜索在开放研究问题上进行大规模评测，将基于 Lean 的 Agent 从基准定理推进到数百个真实开放猜想，并公开证明产物。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "The paper reported that the most capable AlphaProof Nexus agent autonomously resolved 9 of 353 open Erdős problems and proved 44 of 492 OEIS conjectures, while also contributing to research problems in algebraic geometry, optimization, graph theory and quantum optics.", "zh-CN": "论文报告最强的 AlphaProof Nexus Agent 自主解决了 353 个开放 Erdős 问题中的 9 个，并证明了 492 个 OEIS 猜想中的 44 个，同时还参与代数几何、优化、图论与量子光学中的研究问题。" }, "summary": { "en": "AlphaProof Nexus organized frontier LLM subagents around the Lean compiler and escalated proof search with specialized tools and evolutionary search. The project released Lean proofs for successful Erdős, OEIS and research-collaboration cases together with human-readable proof writeups for selected results.", "zh-CN": "AlphaProof Nexus 让前沿 LLM 子 Agent 围绕 Lean 编译器工作，并通过专用工具与进化搜索逐级增强证明搜索。项目公开了成功解决的 Erdős、OEIS 与科研协作案例的 Lean 证明，并为部分结果提供人类可读证明说明。" }, "why_it_matters": { "en": "The scale and open-problem setting changed the evidentiary standard for formal AI4Math: generated research claims could be paired directly with kernel-checkable proof artifacts rather than only prose reasoning or benchmark scores.", "zh-CN": "其规模与开放问题场景提高了形式化 AI4Math 的证据标准：生成的研究结论可以直接配套内核可检查的证明产物，而不只是自然语言推理或基准分数。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "LLM agents generated and revised Lean proofs using compiler feedback and search; accepted formal proofs were mechanically checked, while researchers curated problems and assessed their research interpretation.", "zh-CN": "LLM Agent 利用编译器反馈与搜索生成并修订 Lean 证明；被接受的形式证明由机器检查，研究者则整理问题并评估其研究含义。" } }, "human_contribution": { "description": { "en": "Researchers designed the agent hierarchy and search methods, formalized or curated open problems, supplied domain context in collaborative deployments, and analyzed whether formal solutions matched the intended mathematical questions.", "zh-CN": "研究者设计 Agent 层级与搜索方法，形式化或整理开放问题，在协作部署中提供领域背景，并分析形式解是否忠实对应原始数学问题。" } }, "systems": [ "alphaproof-nexus", "lean", "gemini" ], "organizations": [ "google-deepmind", "university-of-texas-at-austin" ], "people": [ "george-tsoukalas", "anton-kovsharov", "swarat-chaudhuri", "pushmeet-kohli", "thomas-hubert" ], "problems": [ "erdos-problems", "oeis-conjectures", "research-mathematics" ], "methods": [ "formal-proof-search", "llm-agents", "compiler-feedback", "evolutionary-search", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2026-05-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The preprint reported the open-problem evaluation and research deployments.", "zh-CN": "预印本报告了开放问题评测与科研部署结果。" } }, { "date": "2026-05-21", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Google DeepMind released a repository of generated Lean proofs and natural-language writeups, with instructions for rebuilding the formal artifacts.", "zh-CN": "Google DeepMind 公开了生成的 Lean 证明与自然语言说明仓库，并提供重建形式产物的说明。" } } ] }, "sources": [ { "id": "arxiv-alphaproof-nexus-2605.22763", "tier": "S1", "type": "paper", "title": "Advancing Mathematics Research with AI-Driven Formal Proof Search", "url": "https://arxiv.org/abs/2605.22763", "primary": true, "published_date": "2026-05-21", "accessed_at": "2026-09-10" }, { "id": "github-alphaproof-nexus-results", "tier": "S1", "type": "formal_artifact", "title": "AlphaProof Nexus Results", "url": "https://github.com/google-deepmind/alphaproof-nexus-results", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "alphaproof-nexus-lean-results", "kind": "proof", "title": "AlphaProof Nexus generated Lean proofs", "url": "https://github.com/google-deepmind/alphaproof-nexus-results" } ], "relationships": { "predecessors": [ "evt-2024-alphaproof-alphageometry2-imo", "evt-2023-leandojo", "evt-2024-deepseek-prover-v1-5" ], "successors": [], "related": [ "evt-2026-aletheia" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "open-problems", "erdos", "oeis", "theorem-proving", "agent", "formal-verification" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-unit-distance-disproof", "slug": "openai-unit-distance-conjecture-disproof", "title": { "en": "OpenAI reports an autonomous disproof of Erdős's unit-distance growth conjecture", "zh-CN": "OpenAI 报告 AI 自主反驳 Erdős 单位距离增长猜想" }, "dates": { "event": "2026-05-20", "first_public_claim": "2026-05-20", "paper_release": "2026-05-20", "artifact_release": null, "independently_verified": "2026-05-20", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "proof", "system" ], "significance": { "tier": "H1", "rationale": { "en": "A substantive AI-generated disproof of a longstanding Erdős conjecture is a historical AI4Math milestone because the central contribution is new mathematics rather than benchmark performance or a general model release; the H1 designation does not itself assert independent verification.", "zh-CN": "AI 对长期存在的 Erdős 猜想给出实质性新反例属于历史级 AI4Math 里程碑，因为核心贡献是新的数学结果，而非基准成绩或通用模型发布；H1 定级本身不等同于已完成独立验证。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "OpenAI reported that an internal general reasoning model disproved the longstanding conjectured n^(1+o(1)) upper-growth behavior for planar unit distances by constructing infinitely many configurations with at least n^(1+delta) unit distances for fixed delta>0.", "zh-CN": "OpenAI 报告内部通用推理模型反驳了平面单位距离问题长期流行的 n^(1+o(1)) 增长猜想，构造出无穷多个具有至少 n^(1+delta) 个单位距离的点集，其中 delta>0 为常数。" }, "summary": { "en": "The model found a construction using tools from algebraic number theory; OpenAI released the proof and a companion paper by external mathematicians who checked and contextualized the argument.", "zh-CN": "模型使用代数数论工具发现构造；OpenAI 同时发布证明与由外部数学家撰写的 companion paper，后者检查并解释了论证。" }, "why_it_matters": { "en": "Unlike benchmark progress, the event concerns a longstanding open problem in active mathematics and an AI-generated argument judged substantive by independent experts.", "zh-CN": "与基准进展不同，该事件涉及活跃数学领域的长期开放问题，且 AI 生成论证获得外部专家的实质性认可。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "OpenAI states that the core construction and proof were generated autonomously by an internal general-purpose reasoning model.", "zh-CN": "OpenAI 表示核心构造与证明由内部通用推理模型自主生成。" } }, "human_contribution": { "description": { "en": "External mathematicians checked the proof and wrote companion analysis; OpenAI researchers ran the evaluation and publication process.", "zh-CN": "外部数学家检查证明并撰写 companion analysis；OpenAI 研究者组织评测与发布。" } }, "systems": [ "openai-internal-reasoning-model" ], "organizations": [ "openai" ], "people": [], "problems": [ "erdos-unit-distance-growth-conjecture" ], "methods": [ "algebraic-number-theory", "autonomous-research", "proof-generation" ], "verification": { "evidence_level": "E3", "status": "independently_verified", "formal_assurance": "artifact_available", "history": [ { "date": "2026-05-20", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-05-20", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "OpenAI released the AI-generated proof together with a companion paper by nine external mathematicians describing a human-verified, digested version of the argument. Will Sawin independently published a stronger explicit lower bound building on the new construction. These sources materially strengthen the mathematical evidence while the Chronicle retains the human editorial gate for `independently_verified`.", "zh-CN": "OpenAI 同日公开 AI 生成证明及由九位外部数学家撰写的 companion paper，后者给出经人工核查和整理的论证版本；Will Sawin 还独立发表了建立在该新构造之上的更强显式下界。这些来源显著加强了数学证据，但 Chronicle 仍保留 `independently_verified` 的人工编辑门槛。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E3", "note": { "en": "Under the Chronicle's event-level verification semantics, the nine-mathematician human-verified companion paper and Will Sawin's independent follow-up work substantively corroborate the core event description. This label records independent corroboration of the event and its public evidence trail rather than a Chronicle adjudication of ultimate mathematical correctness.", "zh-CN": "按 Chronicle 的事件级 verification 语义，九位数学家的 human-verified companion paper 与 Will Sawin 的独立后续工作已经对该事件核心描述形成实质性独立佐证。该标签记录的是事件与公开证据链获得独立确认，而不是 Chronicle 对底层数学结论最终正确性的裁决。" } } ] }, "sources": [ { "id": "openai-unit-distance-2026", "tier": "S2", "type": "official_announcement", "title": "An OpenAI model has disproved a central conjecture in discrete geometry", "url": "https://openai.com/index/model-disproves-discrete-geometry-conjecture/", "primary": true, "published_date": "2026-05-20", "accessed_at": "2026-09-10" }, { "id": "openai-unit-distance-proof-2026", "tier": "S1", "type": "paper", "title": "Planar Point Sets with Many Unit Distances", "url": "https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf", "primary": true, "published_date": "2026-05-20", "accessed_at": "2026-09-10" }, { "id": "unit-distance-remarks-2026", "tier": "S3", "type": "paper", "title": "Remarks on the disproof of the unit distance conjecture", "url": "https://arxiv.org/abs/2605.20695", "primary": false, "published_date": "2026-05-20", "accessed_at": "2026-09-10" }, { "id": "sawin-unit-distance-explicit-bound-2026", "tier": "S3", "type": "paper", "title": "An explicit lower bound for the unit distance problem", "url": "https://arxiv.org/abs/2605.20579", "primary": false, "published_date": "2026-05-20", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "openai-unit-distance-proof-pdf", "kind": "proof", "title": "AI-generated proof manuscript", "url": "https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf" }, { "id": "unit-distance-human-verified-remarks", "kind": "supplement", "title": "Human-verified companion remarks", "url": "https://arxiv.org/abs/2605.20695" } ], "relationships": { "predecessors": [ "evt-2026-first-proof-openai", "evt-2025-alphaevolve" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "open-problem", "discrete-geometry", "erdos", "autonomous-research" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-sorrydb", "slug": "sorrydb-real-world-lean-benchmark", "title": { "en": "SorryDB turns live proof holes from real Lean projects into a continuously updated benchmark", "zh-CN": "SorryDB 将真实 Lean 项目的动态证明缺口转化为持续更新的基准" }, "dates": { "event": "2026-03-03", "first_public_claim": "2026-03-03", "paper_release": "2026-03-03", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset", "infrastructure", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "SorryDB shifted formal-theorem-proving evaluation from mostly static curated theorem sets toward continuously refreshed, reproducible proof obligations taken from active public Lean projects, directly measuring whether AI agents can contribute to real formalization codebases.", "zh-CN": "SorryDB 将形式定理证明评测从以静态整理题集为主的模式，推进到从活跃公开 Lean 项目持续提取、可复现的真实证明任务，直接衡量 AI Agent 能否为实际形式化代码库做出贡献。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal" ], "claim": { "en": "The SorryDB paper introduced a dynamically updating benchmark of open Lean tasks drawn from 78 real-world formalization projects on GitHub, evaluated general-purpose models, specialized provers and agentic strategies on a 1,000-task snapshot, and released the dataset, verifier and strategy infrastructure publicly.", "zh-CN": "SorryDB 论文发布了一个从 GitHub 上 78 个真实形式化项目提取开放 Lean 任务并动态更新的基准，在 1,000 个任务快照上评测通用模型、专用证明器与 Agent 策略，并公开数据集、验证器和策略基础设施。" }, "summary": { "en": "SorryDB crawls eligible public Lean repositories, records reproducible repository and toolchain coordinates for unresolved `sorry` statements, and asks proving systems to replace each proof hole in its original project context. A verifier rebuilds the relevant project and checks proposed replacements, while a nightly database refresh supplies new tasks over time.", "zh-CN": "SorryDB 抓取符合条件的公开 Lean 仓库，为尚未完成的 `sorry` 命题记录可复现的仓库与工具链坐标，并要求证明系统在原始项目上下文中填补证明缺口。验证器会重建相应项目并检查候选证明，夜间更新的数据库则持续提供新任务。" }, "why_it_matters": { "en": "A live benchmark grounded in unresolved work from real formalization projects reduces reliance on saturated competition datasets, exposes dependency and environment complexity that synthetic tasks omit, and aligns prover progress more directly with work useful to Lean contributors and mathematicians.", "zh-CN": "基于真实形式化项目未完成工作的动态基准降低了对已趋饱和竞赛数据集的依赖，暴露合成任务常忽略的依赖关系与环境复杂性，并使证明器进展更直接对应 Lean 贡献者和数学家的实际工作需求。" }, "ai_role": { "level": "computation_only", "description": { "en": "AI systems are benchmarked as candidate proof producers; they generate tactics or proofs, while the benchmark infrastructure restores the original project context and Lean checks whether a proposed replacement closes the target proof hole.", "zh-CN": "AI 系统作为候选证明生成器接受评测；它们生成 tactic 或证明，而基准基础设施恢复原始项目上下文，并由 Lean 检查候选替换能否关闭目标证明缺口。" } }, "human_contribution": { "description": { "en": "Researchers designed the crawling, snapshotting, evaluation and verification infrastructure, defined inclusion and reproducibility metadata, implemented baseline strategies and analyzed the benchmark results.", "zh-CN": "研究者设计抓取、快照、评测与验证基础设施，定义纳入标准和可复现元数据，实现基线策略并分析基准结果。" } }, "systems": [ "sorrydb", "lean" ], "organizations": [ "sorrydb" ], "people": [], "problems": [ "real-world-lean-proof-holes", "formal-theorem-proving-evaluation" ], "methods": [ "live-benchmarking", "repository-crawling", "project-context-verification", "agentic-proof-search", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2026-03-03", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv paper introduced SorryDB, its 78-project source pool, the 1,000-task evaluation snapshot and comparative prover results.", "zh-CN": "arXiv 论文发布 SorryDB、其 78 个项目的来源集合、1,000 任务评测快照及不同证明系统的比较结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public SorryDB repository exposes the benchmark snapshot, nightly dataset workflow, verifier and example proving strategies. E3 records inspectable benchmark infrastructure rather than independent verification of every reported model score.", "zh-CN": "SorryDB 公开仓库提供基准快照、夜间数据更新流程、验证器及示例证明策略。E3 表示基准基础设施可直接检查，并不表示所有报告模型分数都获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-sorrydb-2603.02668", "tier": "S1", "type": "paper", "title": "SorryDB: Can AI Provers Complete Real-World Lean Theorems?", "url": "https://arxiv.org/abs/2603.02668", "primary": true, "published_date": "2026-03-03", "accessed_at": "2026-09-11" }, { "id": "github-sorrydb", "tier": "S1", "type": "repository", "title": "SorryDB benchmark, verifier and proving infrastructure", "url": "https://github.com/SorryDB/SorryDB", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "sorrydb-repository", "kind": "benchmark", "title": "SorryDB dynamic Lean benchmark and evaluation infrastructure", "url": "https://github.com/SorryDB/SorryDB" } ], "relationships": { "predecessors": [ "evt-2023-leandojo", "evt-2024-putnambench" ], "successors": [], "related": [ "evt-2026-numina-lean-agent", "evt-2026-alphaproof-nexus" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "sorrydb", "lean", "benchmark", "real-world-formalization", "theorem-proving", "contamination" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-first-proof-openai", "slug": "openai-first-proof-research-challenge", "title": { "en": "OpenAI publishes research-level proof attempts on the First Proof challenge", "zh-CN": "OpenAI 发布 First Proof 研究级数学挑战的证明尝试" }, "dates": { "event": "2026-02-20", "first_public_claim": "2026-02-20", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "benchmark", "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "First Proof moved frontier-model evaluation from contests and hidden benchmarks to expert-designed research proof attempts requiring prolonged community scrutiny.", "zh-CN": "First Proof 把前沿模型评测从竞赛与隐藏基准推进到专家设计的研究级证明尝试，并要求持续社区审查。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "OpenAI published attempts on all ten First Proof problems and said at least five had a high chance of being correct, while explicitly retracting confidence in one earlier attempt after expert feedback.", "zh-CN": "OpenAI 发布全部十道 First Proof 问题的证明尝试，称至少五份有较高概率正确，并在专家反馈后明确撤回对其中一份早期尝试的信心。" }, "summary": { "en": "The internal model worked with limited human supervision; researchers sometimes requested retries or clarifications and selected among attempts.", "zh-CN": "内部模型在有限人工监督下工作；研究者有时要求重试或澄清，并在人类判断下选择候选尝试。" }, "why_it_matters": { "en": "The episode provided unusually transparent evidence of both research-level capability and the verification difficulty of AI-generated mathematics.", "zh-CN": "该事件同时透明展示了研究级能力与 AI 生成数学在验证上的困难。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model produced long research-level proof attempts across specialized domains.", "zh-CN": "模型在多个专业领域生成长篇研究级证明尝试。" } }, "human_contribution": { "description": { "en": "Researchers prompted and selected attempts, experts supplied feedback, and correctness remained an explicit review question.", "zh-CN": "研究者负责提示与选择候选，专家提供反馈，而正确性被明确保留为待审查问题。" } }, "systems": [ "openai-internal-reasoning-model" ], "organizations": [ "openai", "first-proof" ], "people": [], "problems": [ "first-proof" ], "methods": [ "long-horizon-reasoning", "expert-review", "proof-generation" ], "verification": { "evidence_level": "E2", "status": "under_verification", "formal_assurance": "none", "history": [ { "date": "2026-02-20", "status": "under_verification", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "openai-first-proof-2026", "tier": "S2", "type": "official_announcement", "title": "Our First Proof submissions", "url": "https://openai.com/index/first-proof-submissions/", "primary": true, "published_date": "2026-02-20", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2025-openai-imo-gold", "evt-2024-frontiermath" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "research-math", "proof", "expert-review", "openai" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-m2f", "slug": "m2f-project-scale-autoformalization", "title": { "en": "M2F scales autoformalization from isolated theorems to machine-checked Lean projects", "zh-CN": "M2F 将自动形式化从孤立定理扩展到机器检查的 Lean 项目" }, "dates": { "event": "2026-02-19", "first_public_claim": "2026-02-19", "paper_release": "2026-02-19", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "M2F moved automated formalization from single theorem statements toward dependency-aware, document- and project-scale Lean generation, addressing imports, declarations, proof holes and whole-project compilation as one workflow.", "zh-CN": "M2F 将自动形式化从单个定理命题推进到具有依赖关系的文档级与项目级 Lean 生成，把导入、声明、证明缺口与整个项目的编译统一纳入同一工作流。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "The M2F paper reported a two-stage statement-compilation and proof-repair pipeline that converted 479 pages of real- and convex-analysis material into a 153,853-line Lean project and achieved 96% proof success on FATE-H in its fully automatic setting; generated Lean code was released publicly.", "zh-CN": "M2F 论文报告了一套“命题编译 + 证明修复”的两阶段管线，将 479 页实分析与凸分析材料转化为 153,853 行 Lean 项目，并在完全自动设置下于 FATE-H 达到 96% 的证明成功率；生成的 Lean 代码已公开。" }, "summary": { "en": "M2F first translates long mathematical documents into dependency-ordered Lean declaration skeletons and repairs project-level structural inconsistencies, then freezes statement signatures and iteratively closes proof holes using verifier feedback. The companion ReasBook repository exposes generated formalizations from textbooks and research papers.", "zh-CN": "M2F 首先把长篇数学文档翻译为按依赖排序的 Lean 声明骨架，并修复项目层面的结构不一致；随后固定命题签名，利用验证器反馈迭代填补证明缺口。配套 ReasBook 仓库公开了由教材和研究论文生成的形式化项目。" }, "why_it_matters": { "en": "Project-scale autoformalization changes the unit of automation from one problem at a time to coherent mathematical literature with shared definitions and dependencies, a prerequisite for turning large informal corpora into reusable formal libraries.", "zh-CN": "项目级自动形式化把自动化单位从“一次处理一道题”转变为具有共享定义和依赖关系的完整数学文献，这是将大规模非形式数学语料转化为可复用形式库的重要前提。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The system automatically translates statements, repairs declarations and closes proof holes while using Lean toolchain feedback to accept or reject project edits.", "zh-CN": "系统自动翻译命题、修复声明并填补证明缺口，同时利用 Lean 工具链反馈决定项目修改是否被接受。" } }, "human_contribution": { "description": { "en": "Researchers designed the staged formalization pipeline, prepared source documents and evaluation protocol, and report human checks for whether extracted natural-language theorems and their formal statements align with the original mathematics.", "zh-CN": "研究者设计分阶段形式化管线、准备源文档与评测协议，并报告由人类检查抽取的自然语言定理及其形式命题是否与原始数学内容一致。" } }, "systems": [ "m2f", "reasbook", "lean" ], "organizations": [ "peking-university" ], "people": [], "problems": [ "project-scale-autoformalization", "mathematical-literature-formalization" ], "methods": [ "autoformalization", "dependency-ordering", "verifier-guided-repair", "proof-repair", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2026-02-19", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv paper introduced M2F and reported project-scale formalization and FATE-H results.", "zh-CN": "arXiv 论文发布 M2F，并报告项目级形式化与 FATE-H 结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public M2F and ReasBook repositories expose the framework, examples and generated Lean projects. Machine-checked refers to Lean compilation and proof checking in the released workflow; it does not establish independent semantic review of every generated formalization.", "zh-CN": "M2F 与 ReasBook 公开仓库提供框架、示例和生成的 Lean 项目。machine-checked 指发布工作流中的 Lean 编译与证明检查，并不表示每一项生成形式化都获得独立语义审查。" } } ] }, "sources": [ { "id": "arxiv-m2f-2602.17016", "tier": "S1", "type": "paper", "title": "M2F: Automated Formalization of Mathematical Literature at Scale", "url": "https://arxiv.org/abs/2602.17016", "primary": true, "published_date": "2026-02-19", "accessed_at": "2026-09-11" }, { "id": "github-optsuite-m2f", "tier": "S1", "type": "repository", "title": "M2F autoformalization framework", "url": "https://github.com/optsuite/M2F", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-optsuite-reasbook", "tier": "S1", "type": "formal_artifact", "title": "ReasBook generated Lean formalization projects", "url": "https://github.com/optsuite/ReasBook", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "m2f-repository", "kind": "code", "title": "M2F project-scale autoformalization framework", "url": "https://github.com/optsuite/M2F" }, { "id": "reasbook-formalizations", "kind": "proof", "title": "ReasBook generated Lean projects", "url": "https://github.com/optsuite/ReasBook" } ], "relationships": { "predecessors": [ "evt-2022-autoformalization-llm", "evt-2025-mathesis" ], "successors": [], "related": [ "evt-2026-claude-flt-formalization" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "m2f", "autoformalization", "lean", "mathematical-literature", "project-scale", "formalization" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-aletheia", "slug": "aletheia-autonomous-mathematics-research-agent", "title": { "en": "Aletheia extends Deep Think from Olympiad solving into research-level mathematics", "zh-CN": "Aletheia 将 Deep Think 从奥赛解题推进到研究级数学" }, "dates": { "event": "2026-02-10", "first_public_claim": "2026-02-10", "paper_release": "2026-02-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "discovery", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "Aletheia was presented as an end-to-end math research agent that iteratively generates, verifies and revises long-horizon natural-language solutions, with reported applications ranging from PhD-level exercises to new research results and open problems.", "zh-CN": "Aletheia 被提出为端到端数学研究 Agent，可迭代生成、验证并修订长程自然语言解答；论文报告其应用范围从博士层次习题延伸到新的研究结果与开放问题。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "hybrid" ], "claim": { "en": "The Aletheia paper reported several levels of AI-assisted research, including an AI-generated paper on eigenweight structure constants, human-AI collaborative results and a semi-autonomous evaluation of 700 open problems from Bloom's Erdős conjectures database that included autonomous solutions to four open questions.", "zh-CN": "Aletheia 论文报告了多种自主程度的 AI 数学研究，包括关于 eigenweight 结构常数的 AI 生成论文、人机协作结果，以及对 Bloom 的 Erdős 猜想数据库中 700 个开放问题的半自主评测，其中包含对 4 个开放问题的自主解答。" }, "summary": { "en": "Aletheia couples an advanced Gemini Deep Think model with iterative verification, revision and intensive tool use intended for research settings where literature navigation and long proof chains matter. The authors explicitly separated levels of autonomy and novelty rather than treating all AI-assisted results as equivalent.", "zh-CN": "Aletheia 将高级 Gemini Deep Think 模型与迭代验证、修订及密集工具使用结合，面向需要文献导航和长证明链的研究环境。作者还明确区分不同自主性与新颖性层级，而非把所有 AI 辅助结果视为同一种贡献。" }, "why_it_matters": { "en": "The work marked a shift in the public AI4Math frontier from contest performance toward sustained research workflows and made attribution, autonomy and verification part of the system-level discussion.", "zh-CN": "该工作标志着公开 AI4Math 前沿从竞赛表现转向持续科研工作流，并把贡献归属、自主程度与验证问题纳入系统层面的讨论。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Aletheia generated, checked and revised candidate research solutions with tool use; the reported research cases ranged from highly autonomous operation to close collaboration with expert mathematicians.", "zh-CN": "Aletheia 借助工具生成、检查并修订候选研究解答；论文中的案例从高度自主运行到与专家数学家的紧密协作不等。" } }, "human_contribution": { "description": { "en": "Researchers built the agent and verifier loop, selected and formalized research tasks, supplied expert direction where required, and evaluated novelty and mathematical correctness of reported results.", "zh-CN": "研究者构建 Agent 与验证循环、选择并整理研究任务、在需要时提供专家指导，并评估所报告结果的新颖性与数学正确性。" } }, "systems": [ "aletheia", "gemini-deep-think" ], "organizations": [ "google-deepmind" ], "people": [ "tony-feng", "trieu-trinh", "garrett-bingham", "thang-luong" ], "problems": [ "erdos-conjectures-database", "research-level-mathematics" ], "methods": [ "research-agent", "inference-time-scaling", "iterative-verification", "tool-use", "natural-language-proof" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2026-02-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The research paper documented the agent design, evaluations and several research case studies with different autonomy levels.", "zh-CN": "研究论文公开了 Agent 设计、评测，以及多种自主程度的研究案例。" } }, { "date": "2026-02-11", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Google DeepMind published an institutional overview of the research-level mathematics program and Aletheia.", "zh-CN": "Google DeepMind 发布机构介绍，说明研究级数学计划与 Aletheia。" } } ] }, "sources": [ { "id": "arxiv-aletheia-2602.10177", "tier": "S1", "type": "paper", "title": "Towards Autonomous Mathematics Research", "url": "https://arxiv.org/abs/2602.10177", "primary": true, "published_date": "2026-02-10", "accessed_at": "2026-09-10" }, { "id": "deepmind-aletheia-2026", "tier": "S2", "type": "official_announcement", "title": "Accelerating Mathematical and Scientific Discovery with Gemini Deep Think", "url": "https://deepmind.google/blog/accelerating-mathematical-and-scientific-discovery-with-gemini-deep-think/", "primary": true, "published_date": "2026-02-11", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2025-gemini-imo-gold" ], "successors": [], "related": [ "evt-2025-alphaevolve", "evt-2026-alphaproof-nexus" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "research-agent", "gemini", "mathematical-research", "erdos", "tool-use", "verification" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2026-numina-lean-agent", "slug": "numina-lean-agent-general-coding-agent", "title": { "en": "Numina-Lean-Agent turns a general coding agent into an open Lean mathematics reasoner", "zh-CN": "Numina-Lean-Agent 将通用 Coding Agent 转化为开放的 Lean 数学推理系统" }, "dates": { "event": "2026-01-20", "first_public_claim": "2026-01-20", "paper_release": "2026-01-20", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "system", "proof", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "Numina-Lean-Agent showed a distinct formal-mathematics architecture in which a general coding agent could directly operate Lean and call specialized tools through MCP, rather than depending on a task-specific prover pipeline or newly trained formal model.", "zh-CN": "Numina-Lean-Agent 展示了一种不同的形式数学架构：通用 Coding Agent 可以直接操作 Lean，并通过 MCP 自主调用专用工具，而不必依赖任务专用的证明管线或新训练的形式证明模型。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "hybrid" ], "claim": { "en": "The paper reported that Numina-Lean-Agent, built around Claude Code and Numina-Lean-MCP, solved all 12 Putnam 2025 problems with Claude Opus 4.5 and was also used with mathematicians to formalize the Effective Brascamp–Lieb theorem; the agent implementation and formal solutions were released publicly.", "zh-CN": "论文报告称，基于 Claude Code 与 Numina-Lean-MCP 的 Numina-Lean-Agent 在 Claude Opus 4.5 上完成了 2025 Putnam 的全部 12 道题，并与数学家协作完成 Effective Brascamp–Lieb 定理的形式化；Agent 实现与形式证明结果均已公开。" }, "summary": { "en": "The system uses a general-purpose coding-agent loop as the controller for Lean work and extends it with theorem retrieval, informal proving, verification and auxiliary reasoning tools exposed through an MCP-oriented interface. Its public repository includes setup instructions, runnable agent tooling and links to the Putnam proof artifacts.", "zh-CN": "该系统以通用 Coding Agent 循环作为 Lean 工作的控制器，并通过面向 MCP 的接口接入定理检索、非形式证明、验证和辅助推理工具。公开仓库提供安装说明、可运行的 Agent 工具以及 Putnam 形式证明产物。" }, "why_it_matters": { "en": "The work connected the rapidly developing coding-agent ecosystem to formal mathematics and suggested that improvements in general agent harnesses and base models could transfer directly into theorem proving without rebuilding a bespoke prover stack for each task.", "zh-CN": "该工作把快速发展的 Coding Agent 生态直接连接到形式数学，并表明通用 Agent Harness 与基础模型的改进有可能直接迁移到定理证明，而无需为每类任务重新构建专用证明栈。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The coding agent autonomously inspects Lean goals, edits proof code and invokes specialized reasoning and retrieval tools; Lean compiler feedback mechanically constrains accepted formal outputs.", "zh-CN": "Coding Agent 自主检查 Lean 目标、编辑证明代码并调用专用推理与检索工具；Lean 编译器反馈对被接受的形式输出进行机械约束。" } }, "human_contribution": { "description": { "en": "Researchers designed the agent and MCP tool interface, configured evaluation tasks, released the implementation and proof artifacts, and supplied mathematician collaboration and semantic oversight in the research-level formalization case.", "zh-CN": "研究者设计 Agent 与 MCP 工具接口、配置评测任务、公开实现及证明产物，并在研究级形式化案例中提供数学家协作与语义监督。" } }, "systems": [ "numina-lean-agent", "claude-code", "numina-lean-mcp", "lean" ], "organizations": [ "project-numina" ], "people": [], "problems": [ "putnam-2025", "effective-brascamp-lieb-formalization" ], "methods": [ "coding-agent", "model-context-protocol", "compiler-feedback", "theorem-retrieval", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2026-01-20", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv paper introduced the general coding-agent paradigm for formal mathematics and reported the Putnam 2025 and Brascamp–Lieb results.", "zh-CN": "arXiv 论文发布面向形式数学的通用 Coding Agent 范式，并报告 Putnam 2025 与 Brascamp–Lieb 案例结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public Numina-Lean-Agent repository exposes runnable tooling and links to generated Lean proof artifacts. Machine-checked describes Lean acceptance of formal outputs; it does not mean Chronicle independently reproduced every reported run or judged the informal-to-formal correspondence.", "zh-CN": "Numina-Lean-Agent 公开仓库提供可运行工具并链接生成的 Lean 证明产物。machine-checked 表示形式输出可由 Lean 接受，并不表示 Chronicle 独立复现了全部报告运行或裁决非形式表述与形式命题之间的语义对应。" } } ] }, "sources": [ { "id": "arxiv-numina-lean-agent-2601.14027", "tier": "S1", "type": "paper", "title": "Numina-Lean-Agent: An Open and General Agentic Reasoning System for Formal Mathematics", "url": "https://arxiv.org/abs/2601.14027", "primary": true, "published_date": "2026-01-20", "accessed_at": "2026-09-11" }, { "id": "github-project-numina-lean-agent", "tier": "S1", "type": "repository", "title": "Numina-Lean-Agent implementation and proof resources", "url": "https://github.com/project-numina/numina-lean-agent", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "numina-lean-agent-repository", "kind": "code", "title": "Numina-Lean-Agent implementation and Lean proof resources", "url": "https://github.com/project-numina/numina-lean-agent" } ], "relationships": { "predecessors": [ "evt-2023-copra", "evt-2024-putnambench" ], "successors": [], "related": [ "evt-2026-alphaproof-nexus", "evt-2025-mathesis" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "numina-lean-agent", "lean", "coding-agent", "mcp", "theorem-proving", "formal-mathematics" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-gpt5-2-learning-curves", "slug": "gpt5-2-learning-curve-monotonicity", "title": { "en": "GPT-5.2 Pro derives proofs for an open learning-curve monotonicity problem", "zh-CN": "GPT-5.2 Pro 推导开放学习曲线单调性问题的证明" }, "dates": { "event": "2025-12-11", "first_public_claim": "2025-12-11", "paper_release": "2025-12-11", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "The learning-curve paper provided a concrete late-2025 example in which researchers reported that a frontier language model derived the mathematical results and proof arguments for a previously open statistical-learning problem without receiving a human proof strategy, while humans retained responsibility for verification and transcription.", "zh-CN": "这篇学习曲线论文提供了 2025 年末一个具体案例：研究者报告前沿语言模型在未获得人类证明策略的情况下推导出一个此前开放的统计学习问题之数学结果与证明论证，而人类仍负责验证与整理成文。" } }, "mathematical_novelty": { "type": "new_proof" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Sellke and Yin reported new monotonicity guarantees for maximum-likelihood estimators, including a Gaussian case previously highlighted as open, and stated that all results in the paper were derived by variants of GPT-5.2 Pro while humans supplied no proof strategies or intermediate arguments and instead verified and transcribed the proofs.", "zh-CN": "Sellke 与 Yin 报告了最大似然估计量新的单调性保证，其中包括此前文献明确列为开放问题的 Gaussian 情形；论文同时声明，全部结果均由 GPT-5.2 Pro 的不同变体推导，人类没有提供证明策略或中间论证，而是负责验证并整理证明。" }, "summary": { "en": "The paper studies whether expected prediction error for maximum-likelihood estimation improves monotonically as more data are observed. It proves forward-KL monotonicity for several Gaussian and Gamma settings and gives a reverse-KL argument for broad exponential families. OpenAI presented the work as a case study of GPT-5.2 Pro contributing directly to previously unsolved mathematical questions.", "zh-CN": "该论文研究最大似然估计在数据增加时其期望预测误差是否单调改善，证明若干 Gaussian 与 Gamma 情形下的 forward-KL 单调性，并给出适用于广泛指数族的 reverse-KL 论证。OpenAI 将其作为 GPT-5.2 Pro 直接参与此前未解决数学问题的案例公开介绍。" }, "why_it_matters": { "en": "Compared with earlier cases where a model supplied ideas inside a human-led proof process, this record documents a stronger source-attributed AI role: the authors say the model generated the result and proof development itself, with humans focused on validation and exposition.", "zh-CN": "相较于此前模型主要在人类主导证明流程中提供思路的案例，这一记录呈现了来源明确声明的更强 AI 角色：作者称结果与证明发展本身由模型生成，人类主要负责验证与表述。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "According to the paper, variants of GPT-5.2 Pro derived the results and proof arguments without human-provided proof strategies or intermediate steps; humans prompted further exploration, checked the mathematics and transcribed the final proofs.", "zh-CN": "按论文说明，GPT-5.2 Pro 的不同变体在没有人类提供证明策略或中间步骤的情况下推导结果与证明论证；人类负责提出后续探索要求、检查数学内容并整理最终证明。" } }, "human_contribution": { "description": { "en": "Sellke and Yin selected and framed the research question, prompted the model's continued exploration, verified the resulting mathematics, connected it to prior literature and authored the final paper.", "zh-CN": "Sellke 与 Yin 选择并界定研究问题，推动模型继续探索，验证所得数学内容，将结果与既有文献联系起来，并完成最终论文。" } }, "systems": [ "gpt-5-2-pro" ], "organizations": [ "openai" ], "people": [ "mark-sellke", "steven-yin" ], "problems": [ "learning-curve-monotonicity" ], "methods": [ "language-model-proof-generation", "human-verification", "statistical-learning-theory" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2025-12-11", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The primary paper and OpenAI's official case study publicly document the mathematical claims and the stated division of work between GPT-5.2 Pro and the human authors. Chronicle records those claims without independently certifying the proofs or historical priority.", "zh-CN": "原始论文与 OpenAI 官方案例公开记录了数学主张以及 GPT-5.2 Pro 与人类作者之间所声明的工作分工。Chronicle 记录这些主张，但不独立认证证明正确性或历史优先权。" } } ] }, "sources": [ { "id": "arxiv-learning-curve-monotonicity-2512.10220", "tier": "S1", "type": "paper", "title": "On Learning-Curve Monotonicity for Maximum Likelihood Estimators", "url": "https://arxiv.org/abs/2512.10220", "primary": true, "published_date": "2025-12-11", "accessed_at": "2026-09-11" }, { "id": "openai-gpt5-2-science-math-2025", "tier": "S2", "type": "official_announcement", "title": "Advancing science and math with GPT-5.2", "url": "https://openai.com/index/gpt-5-2-for-science-and-math/", "primary": true, "published_date": "2025-12-11", "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2025-gpt5-nag-open-problem" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "gpt-5-2", "mathematical-discovery", "proof-generation", "statistical-learning-theory", "open-problem", "human-verification" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-gpt5-nag-open-problem", "slug": "gpt5-assisted-nesterov-point-convergence", "title": { "en": "An AI-assisted proof resolves the point-convergence question for Nesterov acceleration", "zh-CN": "AI 辅助证明解决 Nesterov 加速法的点收敛问题" }, "dates": { "event": "2025-10-27", "first_public_claim": "2025-10-27", "paper_release": "2025-10-27", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "The result became a concrete case study of a mathematician using a frontier LLM to discover key ideas for a longstanding research problem while retaining human control of the final proof.", "zh-CN": "该结果成为数学家利用前沿 LLM 为长期研究问题发现关键思路、同时由人类掌控最终证明的具体案例。" } }, "mathematical_novelty": { "type": "new_proof" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Jang and Ryu reported a proof resolving the longstanding point-convergence question for Nesterov's accelerated gradient method, with the discovery heavily assisted by ChatGPT/GPT-5.", "zh-CN": "Jang 与 Ryu 报告了 Nesterov 加速梯度法长期点收敛问题的证明，其发现过程受到 ChatGPT/GPT-5 的大量辅助。" }, "summary": { "en": "GPT-5 proposed multiple directions and several key structural ideas; Ryu checked, reformulated and wrote the rigorous final proof with coauthor Uijeong Jang.", "zh-CN": "GPT-5 提出多个方向和若干关键结构性想法；Ryu 负责检查与重构，并与 Uijeong Jang 写成严格的最终证明。" }, "why_it_matters": { "en": "It exemplified human-AI mathematical collaboration in research rather than benchmark solving or autonomous proof search.", "zh-CN": "它展示了真实研究中的人机数学协作，而非仅仅基准求解或自主证明搜索。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "GPT-5 generated candidate approaches and key ideas, some incorrect and some useful, that accelerated exploration.", "zh-CN": "GPT-5 生成候选路径与关键想法，其中既有错误也有有效启发，从而加速研究探索。" } }, "human_contribution": { "description": { "en": "Ryu and Jang validated the mathematics, developed the successful idea rigorously and authored the final paper.", "zh-CN": "Ryu 与 Jang 验证数学内容、严谨发展成功思路并撰写最终论文。" } }, "systems": [ "gpt-5" ], "organizations": [ "ucla", "openai" ], "people": [], "problems": [ "nesterov-accelerated-gradient-point-convergence" ], "methods": [ "human-ai-collaboration", "literature-retrieval", "proof-development" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2025-10-27", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-nag-ai-proof-2510.23513", "tier": "S1", "type": "paper", "title": "Point Convergence of Nesterov's Accelerated Gradient Method: An AI-Assisted Proof", "url": "https://arxiv.org/abs/2510.23513", "primary": true, "published_date": "2025-10-27", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2024-openai-o1" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "optimization", "gpt-5", "human-ai-collaboration", "open-problem" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-aristotle", "slug": "aristotle-imo-level-formal-theorem-proving", "title": { "en": "Aristotle reports gold-equivalent formal performance on IMO 2025", "zh-CN": "Aristotle 报告在 IMO 2025 上达到形式证明金牌等效水平" }, "dates": { "event": "2025-10-01", "first_public_claim": "2025-10-01", "paper_release": "2025-10-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "competition", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Aristotle combined formal search, informal lemma generation and a geometry solver into an integrated system reported at IMO gold-equivalent performance.", "zh-CN": "Aristotle 将形式搜索、非形式引理生成与几何求解器整合，并报告达到 IMO 金牌等效水平。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "Aristotle reported gold-medal-equivalent performance on the 2025 IMO problems using Lean proof search, informal reasoning and a dedicated geometry solver.", "zh-CN": "Aristotle 报告通过 Lean 证明搜索、非形式推理与专用几何求解器，在 IMO 2025 题目上达到金牌等效表现。" }, "summary": { "en": "The architecture generates and formalizes useful lemmas, searches formal proofs and handles geometry through a specialist component.", "zh-CN": "该架构生成并形式化有用引理、搜索形式证明，并通过专用组件处理几何。" }, "why_it_matters": { "en": "It illustrated the emergence of integrated formal-math agents rather than single-model proof generators.", "zh-CN": "它体现了集成式形式数学 Agent 的出现，而不只是单模型证明生成器。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The system coordinates informal reasoning, lemma formalization, proof search and geometry solving.", "zh-CN": "系统协调非形式推理、引理形式化、证明搜索与几何求解。" } }, "human_contribution": { "description": { "en": "Researchers built the integrated architecture and verified formal outputs.", "zh-CN": "研究者构建集成架构并验证形式输出。" } }, "systems": [ "aristotle", "lean" ], "organizations": [ "harmonic" ], "people": [], "problems": [ "imo-2025" ], "methods": [ "formal-proof-search", "lemma-generation", "geometry-solver" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2025-10-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-aristotle-2510.01346", "tier": "S1", "type": "paper", "title": "Aristotle: IMO-level Automated Theorem Proving", "url": "https://arxiv.org/abs/2510.01346", "primary": true, "published_date": "2025-10-01", "accessed_at": "2026-09-10" }, { "id": "github-harmonic-imo2025", "tier": "S1", "type": "formal_artifact", "title": "Harmonic Aristotle IMO 2025 Lean proofs", "url": "https://github.com/harmonic-ai/IMO2025", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "aristotle-imo2025-lean", "kind": "proof", "title": "Aristotle Lean statements and proofs for IMO 2025 Problems 1–5", "url": "https://github.com/harmonic-ai/IMO2025" } ], "relationships": { "predecessors": [ "evt-2025-seed-prover", "evt-2024-alphaproof-alphageometry2-imo" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "imo", "agent", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-goedel-prover-v2", "slug": "goedel-prover-v2-self-correction", "title": { "en": "Goedel-Prover-V2 scales open theorem proving with self-correction", "zh-CN": "Goedel-Prover-V2 通过自我纠错扩展开放定理证明" }, "dates": { "event": "2025-08-05", "first_public_claim": "2025-08-05", "paper_release": "2025-08-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Goedel-Prover-V2 showed that scaffolded synthetic data and Lean-guided self-correction could deliver strong open theorem-proving performance with much smaller models.", "zh-CN": "Goedel-Prover-V2 展示了分阶段合成数据与 Lean 引导自我纠错能让较小开放模型达到很强的形式证明性能。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Goedel-Prover-V2-32B reported 90.4% miniF2F in self-correction mode and 86 solved PutnamBench problems under its reported evaluation.", "zh-CN": "Goedel-Prover-V2-32B 报告在自我纠错模式下 miniF2F 达到 90.4%，并在其评测设置中解出 86 道 PutnamBench。" }, "summary": { "en": "The system uses scaffolded data synthesis, verifier-guided iterative repair and model averaging.", "zh-CN": "系统采用脚手架式数据合成、验证器引导的迭代修复与模型平均。" }, "why_it_matters": { "en": "It strengthened the case for compact open provers that spend computation on correction rather than only increasing parameter count.", "zh-CN": "它强化了“小型开放证明器通过测试时纠错而非只增大参数规模获得能力”的路线。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model generates Lean proofs and iteratively repairs them using compiler feedback.", "zh-CN": "模型生成 Lean 证明并根据编译器反馈迭代修复。" } }, "human_contribution": { "description": { "en": "Researchers designed staged synthesis, self-correction and model-merging procedures.", "zh-CN": "研究者设计分阶段数据合成、自我纠错与模型合并流程。" } }, "systems": [ "goedel-prover-v2", "lean" ], "organizations": [ "princeton-university", "nvidia" ], "people": [], "problems": [ "minif2f", "putnambench" ], "methods": [ "self-correction", "synthetic-data", "formal-proof" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2025-08-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-goedel-prover-v2-2508.03613", "tier": "S1", "type": "paper", "title": "Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction", "url": "https://arxiv.org/abs/2508.03613", "primary": true, "published_date": "2025-08-05", "accessed_at": "2026-09-10" }, { "id": "github-goedel-prover-v2", "tier": "S1", "type": "repository", "title": "Goedel-Prover-V2 model and theorem-proving repository", "url": "https://github.com/Goedel-LM/Goedel-Prover-V2", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "goedel-prover-v2-repository", "kind": "code", "title": "Goedel-Prover-V2 model and evaluation artifacts", "url": "https://github.com/Goedel-LM/Goedel-Prover-V2" } ], "relationships": { "predecessors": [ "evt-2025-deepseek-prover-v2", "evt-2024-lean-workbook" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "open-model", "self-correction", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-seed-prover", "slug": "seed-prover-deep-broad-formal-reasoning", "title": { "en": "Seed-Prover combines deep and broad formal reasoning and proves five IMO 2025 problems", "zh-CN": "Seed-Prover 结合深度与广度形式推理并证明 IMO 2025 五道题" }, "dates": { "event": "2025-07-31", "first_public_claim": "2025-07-31", "paper_release": "2025-07-31", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "competition", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Seed-Prover showed that Lean-verified long-reasoning systems could scale to most of a contemporary IMO and substantially raise PutnamBench performance.", "zh-CN": "Seed-Prover 展示了 Lean 验证的长程推理系统可以扩展到当届 IMO 大多数题目，并显著提升 PutnamBench 表现。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Seed-Prover reported proving 78.1% of formalized past IMO problems, more than half of PutnamBench, and five of six IMO 2025 problems with Seed-Prover plus Seed-Geometry.", "zh-CN": "Seed-Prover 报告证明 78.1% 的形式化历届 IMO 问题、超过一半 PutnamBench，并通过 Seed-Prover 与 Seed-Geometry 完成 IMO 2025 六题中的五题。" }, "summary": { "en": "The system iteratively refines whole proofs from Lean feedback and uses test-time strategies for deep and broad search.", "zh-CN": "系统依据 Lean 反馈迭代改进整段证明，并使用深度与广度相结合的测试时搜索策略。" }, "why_it_matters": { "en": "It pushed formal Olympiad proving from benchmark progress toward near-complete coverage of a live IMO problem set.", "zh-CN": "它把形式奥赛证明从基准进展推进到几乎覆盖一届真实 IMO 题集。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The prover iteratively revises whole Lean proofs and a dedicated geometry engine handles formal geometry.", "zh-CN": "证明器迭代修订整段 Lean 证明，专用几何引擎处理形式几何问题。" } }, "human_contribution": { "description": { "en": "Researchers designed inference strategies, training and the geometry engine and evaluated formal proofs.", "zh-CN": "研究者设计推理策略、训练流程与几何引擎并评测形式证明。" } }, "systems": [ "seed-prover", "seed-geometry", "lean" ], "organizations": [ "bytedance-seed" ], "people": [], "problems": [ "imo-2025", "putnambench", "minif2f" ], "methods": [ "whole-proof-reasoning", "lean-feedback", "test-time-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2025-07-31", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-seed-prover-2507.23726", "tier": "S1", "type": "paper", "title": "Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving", "url": "https://arxiv.org/abs/2507.23726", "primary": true, "published_date": "2025-07-31", "accessed_at": "2026-09-10" }, { "id": "github-seed-prover", "tier": "S1", "type": "repository", "title": "Seed-Prover formal theorem-proving repository", "url": "https://github.com/ByteDance-Seed/Seed-Prover", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "seed-prover-repository", "kind": "proof", "title": "Seed-Prover code and IMO 2025 formal proof artifacts", "url": "https://github.com/ByteDance-Seed/Seed-Prover" } ], "relationships": { "predecessors": [ "evt-2025-deepseek-prover-v2", "evt-2024-alphaproof-alphageometry2-imo" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "imo", "formal-proof", "test-time-search" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-gemini-imo-gold", "slug": "gemini-deep-think-imo-2025-gold", "title": { "en": "Gemini Deep Think reaches officially graded IMO 2025 gold-medal standard in natural language", "zh-CN": "Gemini Deep Think 以自然语言达到经官方评分的 IMO 2025 金牌标准" }, "dates": { "event": "2025-07-21", "first_public_claim": "2025-07-21", "paper_release": null, "artifact_release": null, "independently_verified": "2025-07-21", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "competition", "proof", "system" ], "significance": { "tier": "H1", "rationale": { "en": "The result moved Olympiad-level AI from the manually formalized, multi-day AlphaProof workflow of 2024 to end-to-end natural-language proof generation within the contest time limit, with grading certified by IMO coordinators.", "zh-CN": "该结果把奥赛级 AI 从 2024 年依赖人工形式化且计算数日的 AlphaProof 工作流，推进到在竞赛时限内端到端生成自然语言证明，并由 IMO 协调方进行评分认证。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal" ], "claim": { "en": "An advanced Gemini Deep Think model solved five of the six IMO 2025 problems for 35 out of 42 points, reaching gold-medal standard; Google DeepMind reported that IMO graders evaluated the natural-language solutions under the same criteria used for contestants.", "zh-CN": "一个高级版 Gemini Deep Think 模型解出了 IMO 2025 六道题中的五道，获得 35/42 分并达到金牌标准；Google DeepMind 报告称 IMO 评分人员按与参赛学生相同的标准评阅了这些自然语言解答。" }, "summary": { "en": "Unlike AlphaProof and AlphaGeometry 2 in 2024, the 2025 system consumed official problem statements directly and produced natural-language proofs without manual translation into Lean or another domain-specific formal language. It completed the task within the 4.5-hour competition limit.", "zh-CN": "与 2024 年的 AlphaProof 和 AlphaGeometry 2 不同，2025 年系统直接读取官方题目并生成自然语言证明，无需人工翻译成 Lean 或其他专用形式语言，并在 4.5 小时竞赛时限内完成。" }, "why_it_matters": { "en": "This was a major change in interface and latency, showing that a general reasoning model could reach elite Olympiad performance end-to-end in the language used by human contestants.", "zh-CN": "这是接口与时延上的重要变化，表明通用推理模型能够以人类参赛者使用的语言端到端达到顶尖奥赛水平。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Gemini generated the solutions end-to-end from the natural-language problems; external IMO graders assessed the submitted solutions.", "zh-CN": "Gemini 从自然语言题目端到端生成解答；外部 IMO 评分人员对提交的解答进行评阅。" } }, "human_contribution": { "description": { "en": "DeepMind researchers developed and post-trained the model and supplied general problem-solving guidance; IMO coordinators and graders provided the competition problems and external scoring.", "zh-CN": "DeepMind 研究者开发并后训练模型，并提供一般性解题指导；IMO 协调方和评分人员提供竞赛题目并进行外部评分。" } }, "systems": [ "gemini-deep-think" ], "organizations": [ "google-deepmind", "international-mathematical-olympiad" ], "people": [ "thang-luong", "edward-lockhart", "gregor-dolinar" ], "problems": [ "international-mathematical-olympiad-2025" ], "methods": [ "reasoning-model", "parallel-thinking", "reinforcement-learning", "natural-language-proof" ], "verification": { "evidence_level": "E2", "status": "independently_verified", "formal_assurance": "none", "history": [ { "date": "2025-07-21", "status": "partially_verified", "evidence_level": "E2", "note": { "en": "Google DeepMind published the score and quoted the IMO president confirming 35/42 and gold-medal standard after official grading.", "zh-CN": "Google DeepMind 公布成绩，并引用 IMO 主席确认官方评分后的 35/42 分与金牌标准。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E2", "note": { "en": "The Chronicle records the result as independently corroborated at the event level: IMO coordinators graded the submission, and independent reporting confirmed the 35/42 gold-standard result and the distinction between Google's officially coordinated evaluation and OpenAI's separate evaluation. This status concerns the competition event, not a broader claim about mathematical correctness beyond the grading process.", "zh-CN": "Chronicle 将该结果记为事件级 independently_verified：IMO 协调方参与评分，独立报道也确认了 35/42 金牌标准成绩，并明确区分 Google 的 IMO 协调评测与 OpenAI 的独立评测。该状态针对竞赛事件本身，不表示超出评分过程之外的更广泛数学正确性裁决。" } } ] }, "sources": [ { "id": "deepmind-gemini-imo-2025", "tier": "S2", "type": "official_announcement", "title": "Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad", "url": "https://deepmind.google/blog/advanced-version-of-gemini-with-deep-think-officially-achieves-gold-medal-standard-at-the-international-mathematical-olympiad/", "primary": true, "published_date": "2025-07-21", "accessed_at": "2026-09-10" }, { "id": "techcrunch-google-openai-imo-2025", "tier": "S4", "type": "media", "title": "OpenAI and Google outdo the mathletes, but not each other", "url": "https://techcrunch.com/2025/07/21/openai-and-google-outdo-the-mathletes-but-not-each-other/", "primary": false, "published_date": "2025-07-21", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2022-minerva", "evt-2024-alphaproof-alphageometry2-imo" ], "successors": [ "evt-2026-aletheia" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "imo", "olympiad", "gemini", "natural-language", "reasoning", "competition" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-openai-imo-gold", "slug": "openai-imo-2025-gold-level", "title": { "en": "OpenAI reports gold-level performance on IMO 2025 with a general reasoning model", "zh-CN": "OpenAI 报告通用推理模型在 IMO 2025 达到金牌水平" }, "dates": { "event": "2025-07-19", "first_public_claim": "2025-07-19", "paper_release": null, "artifact_release": null, "independently_verified": "2025-07-21", "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "competition", "proof", "system" ], "significance": { "tier": "H1", "rationale": { "en": "The result was an early public demonstration that a general-purpose reasoning model could produce natural-language solutions at the IMO gold threshold.", "zh-CN": "该结果较早公开展示了通用推理模型能够直接生成达到 IMO 金牌线的自然语言解答。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal" ], "claim": { "en": "OpenAI reported that an experimental reasoning model scored 35/42 on IMO 2025, solving five of six problems in natural language; public proofs were graded by three former IMO medalists.", "zh-CN": "OpenAI 报告一个实验性推理模型在 IMO 2025 获得 35/42 分，以自然语言解出六题中的五题；公开证明由三位前 IMO 奖牌获得者评分。" }, "summary": { "en": "The model worked from official natural-language problem statements without a proof assistant or internet access during the evaluation.", "zh-CN": "该模型直接处理官方自然语言题目，在评测过程中不使用证明助手或互联网。" }, "why_it_matters": { "en": "Alongside Gemini's officially coordinated result days later, it marked the transition of general reasoning models into elite Olympiad-level mathematics.", "zh-CN": "与数日后 Gemini 经 IMO 协调认证的结果一起，它标志着通用推理模型进入顶尖奥赛数学水平。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model generated complete natural-language proof attempts under contest-style constraints.", "zh-CN": "模型在类似竞赛的约束下生成完整自然语言证明。" } }, "human_contribution": { "description": { "en": "OpenAI researchers ran the evaluation and former IMO medalists graded the public solutions.", "zh-CN": "OpenAI 研究者组织评测，前 IMO 奖牌获得者对公开解答进行评分。" } }, "systems": [ "openai-experimental-reasoning-model" ], "organizations": [ "openai" ], "people": [], "problems": [ "international-mathematical-olympiad-2025" ], "methods": [ "reasoning-model", "test-time-compute", "natural-language-proof" ], "verification": { "evidence_level": "E2", "status": "independently_verified", "formal_assurance": "none", "history": [ { "date": "2025-07-19", "status": "partially_verified", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-10", "status": "independently_verified", "evidence_level": "E2", "note": { "en": "Independent reporting corroborated the core event description: OpenAI's separate evaluation used public natural-language solutions graded by three former IMO medalists and produced a reported 35/42 gold-threshold score. The Chronicle preserves the important distinction that this was not the IMO-coordinated grading process used for Google's Gemini result.", "zh-CN": "独立报道已经对该事件核心描述形成佐证：OpenAI 的独立评测公开了自然语言解答，由三位前 IMO 奖牌获得者评分，并报告 35/42 的金牌线成绩。Chronicle 同时保留关键区别：这并不是 Google Gemini 所参加的 IMO 协调评分流程。" } } ] }, "sources": [ { "id": "github-openai-imo-2025-proofs", "tier": "S1", "type": "repository", "title": "OpenAI IMO 2025 Proofs", "url": "https://github.com/aw31/openai-imo-2025-proofs", "primary": true, "published_date": null, "accessed_at": "2026-09-10" }, { "id": "techcrunch-google-openai-imo-2025", "tier": "S4", "type": "media", "title": "OpenAI and Google outdo the mathletes, but not each other", "url": "https://techcrunch.com/2025/07/21/openai-and-google-outdo-the-mathletes-but-not-each-other/", "primary": false, "published_date": "2025-07-21", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2024-openai-o1", "evt-2024-alphaproof-alphageometry2-imo" ], "successors": [], "related": [ "evt-2025-gemini-imo-gold" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "openai", "imo", "natural-language-proof", "reasoning-model" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-leanconjecturer", "slug": "leanconjecturer-formal-conjecture-generation", "title": { "en": "LeanConjecturer scales LLM-generated mathematical conjectures inside Lean", "zh-CN": "LeanConjecturer 在 Lean 中扩展 LLM 数学猜想生成" }, "dates": { "event": "2025-06-27", "first_public_claim": "2025-06-27", "paper_release": "2025-06-27", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "system", "dataset", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "LeanConjecturer made conjecture generation a scalable formal-mathematics pipeline rather than an occasional by-product of theorem proving, combining Mathlib context extraction, LLM generation and Lean-based filtering to create large numbers of candidate training problems.", "zh-CN": "LeanConjecturer 将猜想生成从定理证明的偶发副产品推进为可扩展的形式数学管线，把 Mathlib 上下文抽取、LLM 生成与 Lean 过滤结合起来，大规模产生候选训练问题。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The LeanConjecturer paper reported generating 12,289 university-level Lean conjectures from 40 Mathlib seed files, of which 3,776 were syntactically valid and not discharged by the chosen `aesop` non-triviality filter, and showed that such generated problems could support domain-specific reinforcement learning for theorem proving.", "zh-CN": "LeanConjecturer 论文报告从 40 个 Mathlib 种子文件生成 12,289 条大学层次 Lean 猜想，其中 3,776 条通过语法有效性检查且无法被所采用的 `aesop` 非平凡性过滤器直接证明，并展示这些生成问题可用于面向特定领域的定理证明强化学习。" }, "summary": { "en": "The pipeline extracts definitions and theorem context from Lean files, asks an LLM to propose new formal statements, checks generated statements through Lean and separates harder candidates for subsequent training. The paper also reports several non-trivial topology examples as evidence that the pipeline can produce mathematically useful statements rather than only superficial perturbations.", "zh-CN": "该管线从 Lean 文件提取定义与定理上下文，让 LLM 提出新的形式命题，再通过 Lean 检查生成结果，并把更困难的候选分离出来供后续训练。论文还报告若干非平凡拓扑学示例，用以说明系统可以产生具有数学用途的命题，而不仅是表面扰动。" }, "why_it_matters": { "en": "Formal theorem provers depend heavily on available theorem statements and training tasks. LeanConjecturer supplied a reproducible route for expanding that problem distribution from the formal library itself and linked conjecture generation directly to reinforcement-learning data creation.", "zh-CN": "形式定理证明器高度依赖可用的定理命题与训练任务。LeanConjecturer 提供了从形式数学库本身扩展问题分布的可复现路线，并把猜想生成直接连接到强化学习数据构造。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Language models generate candidate Lean theorem statements from extracted mathematical context, while Lean and rule-based filters test syntax and selected notions of non-triviality before candidates are reused for training.", "zh-CN": "语言模型根据抽取出的数学上下文生成候选 Lean 定理命题，Lean 与规则过滤器检查语法和选定的非平凡性标准，再将候选用于后续训练。" } }, "human_contribution": { "description": { "en": "Researchers designed the context-extraction and filtering pipeline, chose seed files and evaluation criteria, conducted reinforcement-learning experiments, and analyzed representative generated statements.", "zh-CN": "研究者设计上下文抽取与过滤管线，选择种子文件与评测标准，开展强化学习实验，并分析代表性的生成命题。" } }, "systems": [ "leanconjecturer", "lean", "mathlib" ], "organizations": [ "auto-res" ], "people": [], "problems": [ "formal-conjecture-generation", "theorem-proving-data-scarcity" ], "methods": [ "conjecture-generation", "synthetic-formal-data", "context-extraction", "reinforcement-learning", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2025-06-27", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced LeanConjecturer and reported the generated-conjecture counts, filtering procedure and theorem-proving training results.", "zh-CN": "arXiv 研究记录发布 LeanConjecturer，并报告生成猜想数量、过滤流程与定理证明训练结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public LeanConjecturer repository exposes the generation and evaluation pipeline. The generated data directory is not committed in the repository, so E3 records inspectable implementation rather than independent verification of the paper's novelty claims or every generated theorem.", "zh-CN": "LeanConjecturer 公开仓库提供生成与评测管线；生成数据目录并未提交到仓库，因此 E3 表示实现可直接检查，而不是对论文中的新颖性主张或每一条生成定理完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-leanconjecturer-2506.22005", "tier": "S1", "type": "paper", "title": "LeanConjecturer: Automatic Generation of Mathematical Conjectures for Theorem Proving", "url": "https://arxiv.org/abs/2506.22005", "primary": true, "published_date": "2025-06-27", "accessed_at": "2026-09-11" }, { "id": "github-auto-res-leanconjecturer", "tier": "S1", "type": "repository", "title": "LeanConjecturer generation and evaluation repository", "url": "https://github.com/auto-res/LeanConjecturer", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "leanconjecturer-repository", "kind": "code", "title": "LeanConjecturer formal conjecture-generation pipeline", "url": "https://github.com/auto-res/LeanConjecturer" } ], "relationships": { "predecessors": [ "evt-2024-deepseek-prover-v1" ], "successors": [], "related": [ "evt-2025-deepseek-prover-v2" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "leanconjecturer", "lean", "conjecture-generation", "synthetic-data", "theorem-proving", "reinforcement-learning" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-mathesis", "slug": "mathesis-natural-language-formal-proving", "title": { "en": "Mathesis connects natural-language mathematics to end-to-end Lean theorem proving", "zh-CN": "Mathesis 将自然语言数学连接到端到端 Lean 定理证明" }, "dates": { "event": "2025-06-08", "first_public_claim": "2025-06-08", "paper_release": "2025-06-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-14" }, "event_types": [ "formalization", "system", "benchmark" ], "significance": { "tier": "H2", "rationale": { "en": "Mathesis addressed a major interface bottleneck in neural theorem proving by coupling learned autoformalization of ordinary mathematical language with downstream Lean proof generation and feedback, rather than assuming an expert-written formal statement as the starting point.", "zh-CN": "Mathesis 针对神经定理证明的重要接口瓶颈，将普通数学语言的学习式自动形式化与后续 Lean 证明生成和反馈连接起来，不再默认任务必须从专家编写的形式命题开始。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "The Mathesis paper introduced an autoformalization-and-proving pipeline trained with reinforcement and preference feedback, together with LeanScorer and the Gaokao-Formal benchmark, and reported that pairing its autoformalizer with existing provers substantially improved end-to-end proving accuracy on natural-language problems.", "zh-CN": "Mathesis 论文发布了结合强化学习与偏好反馈的自动形式化—证明管线，并提出 LeanScorer 与 Gaokao-Formal 基准；论文报告称，将其自动形式化器与既有证明器配合后，自然语言题目的端到端形式证明准确率获得显著提升。" }, "summary": { "en": "Mathesis translates an informal problem into a Lean 4 statement, scores candidate formalizations for syntactic and semantic quality, and uses downstream prover feedback to prefer statements that can support machine-checked proofs. Gaokao-Formal provides hundreds of challenging proof problems derived from Chinese college-entrance examinations for evaluating this full pipeline.", "zh-CN": "Mathesis 将非形式题目翻译为 Lean 4 命题，对候选形式化结果的语法与语义质量进行评分，并利用下游证明器反馈偏好能够支撑机器检查证明的命题。Gaokao-Formal 则提供数百道源自中国高考的高难度证明题，用于评测完整管线。" }, "why_it_matters": { "en": "The work moved formal-math systems closer to the way mathematical problems are actually presented to humans: in natural language. It also made autoformalization quality part of an end-to-end proving objective rather than an isolated translation task.", "zh-CN": "该工作让形式数学系统更接近人类实际接收数学问题的方式——自然语言，并把自动形式化质量纳入端到端证明目标，而不是把它仅视为孤立的翻译任务。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Learned models generate Lean statements and downstream formal proofs, while Lean compilation, semantic scoring and prover feedback constrain and evaluate the automated pipeline.", "zh-CN": "学习模型自动生成 Lean 命题与后续形式证明，Lean 编译、语义评分和证明器反馈则约束并评估这一自动化管线。" } }, "human_contribution": { "description": { "en": "Researchers designed the autoformalization training procedure, LeanScorer, Gaokao-Formal and the end-to-end evaluation protocol, curated problems and analyzed the resulting system performance.", "zh-CN": "研究者设计自动形式化训练流程、LeanScorer、Gaokao-Formal 与端到端评测协议，整理题目并分析系统表现。" } }, "systems": [ "mathesis", "mathesis-autoformalizer", "leanscorer", "lean" ], "organizations": [ "huawei" ], "people": [], "problems": [ "natural-language-to-formal-theorem-proving", "gaokao-formal" ], "methods": [ "autoformalization", "reinforcement-learning", "preference-optimization", "prover-feedback", "lean" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2025-06-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced Mathesis, LeanScorer and Gaokao-Formal and reported end-to-end formal-proving results.", "zh-CN": "arXiv 研究记录发布 Mathesis、LeanScorer 与 Gaokao-Formal，并报告端到端形式证明结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public Mathesis repository exposes implementation and project resources, and the work later appeared at ICLR 2026. Machine-checked refers to Lean acceptance within the evaluated proof pipeline; it does not imply independent replay of every experiment or semantic equivalence judgment.", "zh-CN": "Mathesis 公开仓库提供实现与项目资源，该工作后来发表于 ICLR 2026。machine-checked 指评测证明管线中的结果可由 Lean 接受，并不表示全部实验或语义等价判断均已获得独立重放。" } } ] }, "sources": [ { "id": "arxiv-mathesis-2506.07047", "tier": "S1", "type": "paper", "title": "Mathesis: Towards Formal Theorem Proving from Natural Languages", "url": "https://arxiv.org/abs/2506.07047", "primary": true, "published_date": "2025-06-08", "accessed_at": "2026-09-11" }, { "id": "github-huawei-ai4math-mathesis", "tier": "S1", "type": "repository", "title": "Mathesis implementation and project resources", "url": "https://github.com/Huawei-AI4Math/Mathesis", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "iclr-mathesis-2026", "tier": "S1", "type": "paper", "title": "Mathesis — ICLR 2026 conference paper", "url": "https://proceedings.iclr.cc/paper_files/paper/2026/hash/93d5797656d3e70dca7535160a1458f3-Abstract-Conference.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "mathesis-repository", "kind": "code", "title": "Mathesis autoformalization and theorem-proving implementation", "url": "https://github.com/Huawei-AI4Math/Mathesis" } ], "relationships": { "predecessors": [ "evt-2022-autoformalization-llm", "evt-2023-proofnet" ], "successors": [ "evt-2026-magenta" ], "related": [ "evt-2025-deepseek-prover-v2" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mathesis", "autoformalization", "lean", "theorem-proving", "natural-language", "gaokao-formal" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-matharena", "slug": "matharena-live-math-competitions", "title": { "en": "MathArena turns newly released math competitions into a live contamination-resistant benchmark", "zh-CN": "MathArena 将最新数学竞赛转化为低污染的实时评测基准" }, "dates": { "event": "2025-05-29", "first_public_claim": "2025-05-29", "paper_release": "2025-05-29", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "MathArena changed mathematical-reasoning evaluation from repeatedly scoring static historical datasets toward evaluating models on newly released competitions close to their publication date, while also incorporating expert-graded proof-writing tasks.", "zh-CN": "MathArena 将数学推理评测从反复使用静态历史数据集，推进到在竞赛题目刚发布时即评测模型，并进一步纳入由专家评分的证明题，从评测机制上直接降低数据污染风险。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "numeric" ], "claim": { "en": "The MathArena paper introduced a continuously updated benchmark built from newly released mathematics competitions, reported evidence of contamination in AIME 2024, and added human-graded proof-writing evaluation alongside final-answer competitions.", "zh-CN": "MathArena 论文发布了一个由最新数学竞赛持续更新的基准，报告 AIME 2024 存在数据污染迹象，并在最终答案型竞赛之外加入由人工专家评分的证明写作评测。" }, "summary": { "en": "MathArena evaluates models on recurring competitions soon after problems are released and records whether a model predates each competition. Its public pipeline supports final-answer parsing as well as proof-based competitions such as USAMO and IMO, where expert graders assess model-generated proofs.", "zh-CN": "MathArena 在竞赛题目发布后尽快评测模型，并记录模型发布时间与竞赛时间的先后关系。其公开管线既支持最终答案解析，也支持 USAMO、IMO 等证明型竞赛，由专家对模型生成证明进行评分。" }, "why_it_matters": { "en": "As static math benchmarks became increasingly vulnerable to contamination and saturation, MathArena supplied a reusable live-evaluation pattern that better separates current reasoning capability from exposure to old benchmark material and makes proof quality part of the evaluation target.", "zh-CN": "当静态数学基准越来越容易受到污染与饱和影响时，MathArena 提供了可持续复用的实时评测范式，更有利于区分当前推理能力与对旧基准材料的接触，并把证明质量本身纳入评测目标。" }, "ai_role": { "level": "computation_only", "description": { "en": "Language models are the systems under evaluation and generate answers or proofs; humans design the benchmark, maintain the competition pipeline and perform expert grading for proof-based tasks.", "zh-CN": "语言模型作为被评测系统生成答案或证明；基准设计、竞赛管线维护以及证明题的专家评分由人类完成。" } }, "human_contribution": { "description": { "en": "Researchers designed the live-evaluation protocol, selected and normalized competitions, built parsing and review tooling, ran model evaluations, and organized expert grading for proof-based responses.", "zh-CN": "研究者设计实时评测协议，选择并规范化竞赛题目，开发解析与复核工具，运行模型评测，并组织证明题回答的专家评分。" } }, "systems": [ "matharena" ], "organizations": [ "eth-zurich", "insait" ], "people": [], "problems": [ "mathematical-competition-reasoning", "proof-writing-evaluation" ], "methods": [ "live-evaluation", "contamination-resistant-evaluation", "competition-benchmarking", "expert-grading" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2025-05-29", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced MathArena and reported the initial live-competition and proof-writing evaluation results.", "zh-CN": "arXiv 研究记录发布 MathArena，并报告最初的实时竞赛与证明写作评测结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public MathArena repository exposes evaluation code, competition configurations and result-inspection tooling; the work also appeared in the NeurIPS 2025 Datasets and Benchmarks Track. E3 records inspectable infrastructure and does not imply independent verification of every model score or contamination finding.", "zh-CN": "MathArena 公开仓库提供评测代码、竞赛配置与结果检查工具，该工作也发表于 NeurIPS 2025 Datasets and Benchmarks Track。E3 表示基础设施可直接检查，并不表示所有模型分数或污染结论均已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-matharena-2505.23281", "tier": "S1", "type": "paper", "title": "MathArena: Evaluating LLMs on Uncontaminated Math Competitions", "url": "https://arxiv.org/abs/2505.23281", "primary": true, "published_date": "2025-05-29", "accessed_at": "2026-09-11" }, { "id": "github-eth-sri-matharena", "tier": "S1", "type": "repository", "title": "MathArena evaluation repository", "url": "https://github.com/eth-sri/matharena", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "neurips-matharena-2025", "tier": "S1", "type": "paper", "title": "MathArena — NeurIPS 2025 Datasets and Benchmarks Track", "url": "https://proceedings.neurips.cc/paper_files/paper/2025/hash/1d27c01ebd3e3aebe226b44fc970d803-Abstract-Datasets_and_Benchmarks_Track.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "matharena-repository", "kind": "benchmark", "title": "MathArena evaluation code and competition configurations", "url": "https://github.com/eth-sri/matharena" } ], "relationships": { "predecessors": [ "evt-2024-gsm-symbolic", "evt-2024-omni-math" ], "successors": [], "related": [ "evt-2025-openai-imo-gold", "evt-2025-gemini-imo-gold" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "matharena", "benchmark", "live-evaluation", "contamination", "math-reasoning", "proof-writing" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-alphaevolve", "slug": "alphaevolve-algorithm-discovery", "title": { "en": "AlphaEvolve generalizes LLM-guided evolutionary search for algorithm discovery", "zh-CN": "AlphaEvolve 将 LLM 引导的进化搜索推广到通用算法发现" }, "dates": { "event": "2025-05-14", "first_public_claim": "2025-05-14", "paper_release": "2025-06-16", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H1", "rationale": { "en": "AlphaEvolve extended the evaluator-guided discovery pattern from domain-specific systems into a general coding agent, reporting new exact algorithms and mathematical constructions across multiple problems.", "zh-CN": "AlphaEvolve 将“生成器 + 自动评估器”的发现范式从专用系统推广为通用代码 Agent，并报告在多个问题上发现新的精确算法与数学构造。" } }, "mathematical_novelty": { "type": "new_algorithm" }, "interfaces": [ "symbolic", "numeric", "hybrid" ], "claim": { "en": "AlphaEvolve used LLM-generated code mutations, automated evaluators and evolutionary selection to discover algorithms that surpassed previous state of the art on several mathematical and computational tasks, including a 48-multiplication procedure for 4-by-4 complex matrix multiplication.", "zh-CN": "AlphaEvolve 通过 LLM 生成代码变异、自动评估器与进化选择，在多个数学和计算任务上发现超过此前最佳结果的算法，其中包括使用 48 次标量乘法完成 4×4 复矩阵乘法的方案。" }, "summary": { "en": "The agent maintains populations of candidate programs, uses language models to propose edits and repeatedly scores outputs with executable evaluators. The accompanying technical report and results repository document mathematical cases where the evolved programs improved known constructions.", "zh-CN": "该 Agent 维护候选程序种群，使用语言模型提出修改，并通过可执行评估器反复评分。技术报告及结果仓库记录了进化程序在若干数学问题上改进已知构造的案例。" }, "why_it_matters": { "en": "AlphaEvolve made algorithm and mathematical-object discovery look less like a single bespoke demonstration and more like a reusable agentic research pattern for problems with objective automated evaluation.", "zh-CN": "AlphaEvolve 使算法与数学对象发现不再只是一次性的专用演示，而更接近一种可复用的 Agent 科研范式，尤其适用于具有客观自动评估器的问题。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "LLMs proposed code changes and the evolutionary loop selected improved candidates using automated evaluators; humans formulated tasks, supplied evaluators and interpreted the resulting discoveries.", "zh-CN": "LLM 提出代码修改，进化循环依据自动评估器选择更优候选；人类负责定义任务、提供评估器并解释所得发现。" } }, "human_contribution": { "description": { "en": "Researchers designed the evolutionary agent, defined optimization problems and evaluators, validated discovered algorithms and analyzed which outputs constituted genuine improvements.", "zh-CN": "研究者设计进化 Agent、定义优化问题与评估器、验证发现的算法，并分析哪些输出构成真正改进。" } }, "systems": [ "alphaevolve", "gemini" ], "organizations": [ "google-deepmind" ], "people": [ "alexander-novikov", "ngan-vu", "adam-zsolt-wagner", "pushmeet-kohli", "matej-balog" ], "problems": [ "matrix-multiplication", "mathematical-construction-search" ], "methods": [ "evolutionary-search", "llm-code-generation", "automated-evaluation", "algorithm-discovery" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2025-05-14", "status": "claimed", "evidence_level": "E1", "note": { "en": "Google DeepMind announced AlphaEvolve and described mathematical and infrastructure results.", "zh-CN": "Google DeepMind 公布 AlphaEvolve，并介绍数学与基础设施方面的结果。" } }, { "date": "2025-06-16", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The technical report and a public results repository documented improved mathematical constructions and verification code.", "zh-CN": "技术报告与公开结果仓库记录了改进的数学构造及验证代码。" } } ] }, "sources": [ { "id": "deepmind-alphaevolve-2025", "tier": "S2", "type": "official_announcement", "title": "AlphaEvolve: A Gemini-powered coding agent for designing advanced algorithms", "url": "https://deepmind.google/blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/", "primary": true, "published_date": "2025-05-14", "accessed_at": "2026-09-10" }, { "id": "arxiv-alphaevolve-2506.13131", "tier": "S1", "type": "paper", "title": "AlphaEvolve: A coding agent for scientific and algorithmic discovery", "url": "https://arxiv.org/abs/2506.13131", "primary": true, "published_date": "2025-06-16", "accessed_at": "2026-09-10" }, { "id": "github-alphaevolve-results", "tier": "S1", "type": "repository", "title": "Results of AlphaEvolve", "url": "https://github.com/google-deepmind/alphaevolve_results", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "alphaevolve-results-repository", "kind": "code", "title": "AlphaEvolve mathematical results and verification code", "url": "https://github.com/google-deepmind/alphaevolve_results" } ], "relationships": { "predecessors": [ "evt-2022-alphatensor", "evt-2023-funsearch-cap-set" ], "successors": [], "related": [ "evt-2026-aletheia" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "agent", "algorithm-discovery", "evolutionary-search", "gemini", "automated-evaluation", "mathematics" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-deepseek-prover-v2", "slug": "deepseek-prover-v2-subgoal-rl", "title": { "en": "DeepSeek-Prover-V2 combines informal subgoal decomposition with Lean reinforcement learning", "zh-CN": "DeepSeek-Prover-V2 将非形式子目标分解与 Lean 强化学习结合" }, "dates": { "event": "2025-04-30", "first_public_claim": "2025-04-30", "paper_release": "2025-04-30", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "DeepSeek-Prover-V2 narrowed the gap between natural-language reasoning and formal proof generation at much larger scale.", "zh-CN": "DeepSeek-Prover-V2 在更大规模上连接自然语言推理与形式证明生成，缩小两者能力差距。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "DeepSeek-Prover-V2-671B reported 88.9% on miniF2F-test and solved 49 of 658 PutnamBench problems.", "zh-CN": "DeepSeek-Prover-V2-671B 报告 miniF2F-test 88.9%，并解出 PutnamBench 658 题中的 49 题。" }, "summary": { "en": "DeepSeek-V3 first decomposes problems into subgoals; successful subgoal proofs become cold-start reasoning traces for reinforcement learning.", "zh-CN": "DeepSeek-V3 先把问题分解为子目标，成功的子目标证明被整理为强化学习的冷启动推理轨迹。" }, "why_it_matters": { "en": "The design made informal planning an explicit training scaffold for high-capacity formal theorem provers.", "zh-CN": "该设计把非形式规划显式变成高容量形式定理证明器的训练脚手架。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Models decompose problems, generate Lean proofs and improve through verifier-backed reinforcement learning.", "zh-CN": "模型分解问题、生成 Lean 证明，并通过验证器反馈强化学习提升能力。" } }, "human_contribution": { "description": { "en": "Researchers designed recursive data generation, subgoal decomposition and RL training.", "zh-CN": "研究者设计递归数据生成、子目标分解与强化学习训练。" } }, "systems": [ "deepseek-prover-v2", "lean" ], "organizations": [ "deepseek" ], "people": [], "problems": [ "minif2f", "putnambench", "proverbench" ], "methods": [ "subgoal-decomposition", "reinforcement-learning", "formal-proof" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2025-04-30", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-deepseek-prover-v2-2504.21801", "tier": "S1", "type": "paper", "title": "DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition", "url": "https://arxiv.org/abs/2504.21801", "primary": true, "published_date": "2025-04-30", "accessed_at": "2026-09-10" }, { "id": "github-deepseek-prover-v2", "tier": "S1", "type": "repository", "title": "DeepSeek-Prover-V2 models, benchmark and solution artifacts", "url": "https://github.com/deepseek-ai/DeepSeek-Prover-V2", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "deepseek-prover-v2-repository", "kind": "code", "title": "DeepSeek-Prover-V2 models, benchmark and proof artifacts", "url": "https://github.com/deepseek-ai/DeepSeek-Prover-V2" } ], "relationships": { "predecessors": [ "evt-2024-deepseek-prover-v1-5", "evt-2025-deepseek-r1" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "deepseek", "lean", "reinforcement-learning", "subgoal-decomposition" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2025-deepseek-r1", "slug": "deepseek-r1-reinforcement-learning-reasoning", "title": { "en": "DeepSeek-R1 shows open reinforcement-learned reasoning at frontier math performance", "zh-CN": "DeepSeek-R1 展示开放强化学习推理模型的前沿数学能力" }, "dates": { "event": "2025-01-22", "first_public_claim": "2025-01-22", "paper_release": "2025-01-22", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "system", "benchmark" ], "significance": { "tier": "H3", "rationale": { "en": "DeepSeek-R1 is historically important to general-purpose reasoning-model development, but its relevance to AI4Math is primarily contextual: mathematics served as a capability benchmark rather than the release contributing a mathematical result, proof, formalization, or math-specific system.", "zh-CN": "DeepSeek-R1 对通用推理模型发展具有重要意义，但对 AI4Math 主要属于背景事件：数学主要作为能力评测，而该发布本身并未贡献数学新结果、证明、形式化或数学专项系统。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "DeepSeek-R1 and R1-Zero demonstrated strong reasoning behavior from large-scale reinforcement learning, with R1 reported as comparable to OpenAI o1 on reasoning tasks.", "zh-CN": "DeepSeek-R1 与 R1-Zero 展示了由大规模强化学习产生的强推理行为，论文报告 R1 在推理任务上可与 OpenAI o1 相比。" }, "summary": { "en": "R1-Zero used reinforcement learning without an SFT cold start, while R1 added multi-stage training and released several distilled open models.", "zh-CN": "R1-Zero 在无 SFT 冷启动的情况下使用强化学习；R1 则加入多阶段训练并开放多个蒸馏模型。" }, "why_it_matters": { "en": "The release accelerated open research on reasoning models, verifier-guided RL and math-specific post-training, providing context for later dedicated AI4Math systems.", "zh-CN": "该发布加速了开放社区对推理模型、验证器引导强化学习与数学专项后训练的研究，为后续专门的 AI4Math 系统提供背景。" }, "ai_role": { "level": "computation_only", "description": { "en": "The models perform extended mathematical reasoning learned through reinforcement-learning objectives.", "zh-CN": "模型通过强化学习目标学习并执行长程数学推理。" } }, "human_contribution": { "description": { "en": "Researchers designed the RL and cold-start recipes, trained the models and released weights.", "zh-CN": "研究者设计 RL 与冷启动方案、训练模型并开放权重。" } }, "systems": [ "deepseek-r1" ], "organizations": [ "deepseek" ], "people": [], "problems": [ "aime", "math-benchmark" ], "methods": [ "reinforcement-learning", "reasoning-model", "distillation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2025-01-22", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-deepseek-r1-2501.12948", "tier": "S1", "type": "paper", "title": "DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning", "url": "https://arxiv.org/abs/2501.12948", "primary": true, "published_date": "2025-01-22", "accessed_at": "2026-09-10" }, { "id": "github-deepseek-r1", "tier": "S1", "type": "repository", "title": "DeepSeek-R1 model and technical release repository", "url": "https://github.com/deepseek-ai/DeepSeek-R1", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "deepseek-r1-repository", "kind": "model", "title": "DeepSeek-R1 model release and technical artifacts", "url": "https://github.com/deepseek-ai/DeepSeek-R1" } ], "relationships": { "predecessors": [ "evt-2024-openai-o1", "evt-2024-deepseekmath" ], "successors": [], "related": [] }, "timeline": { "featured": false, "significance": "context" }, "tags": [ "deepseek", "reasoning-model", "reinforcement-learning", "open-model" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-ramanujan-library", "slug": "ramanujan-library-integer-relations", "title": { "en": "Ramanujan Library reports automated discovery of new relations among mathematical constants", "zh-CN": "Ramanujan Library 报告自动发现数学常数之间的新关系" }, "dates": { "event": "2024-12-16", "first_public_claim": "2024-12-16", "paper_release": "2024-12-16", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "The Ramanujan Library extended automated-conjecture work from searching formulas for individual constants to a structured hypergraph of relations among constants, and the authors reported dozens of previously unknown relations generated during construction and testing of the system.", "zh-CN": "Ramanujan Library 将自动猜想工作从“为单个常数寻找公式”推进到“构建常数之间关系的结构化超图”；作者报告称，在系统构建与测试过程中自动得到数十个此前未知的常数关系。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "symbolic", "numeric" ], "claim": { "en": "The authors reported that a PSLQ-based automated enrichment strategy discovered 75 previously unknown connections between mathematical constants, including a new formula for the first continued-fraction constant, new logarithmic formulas and formulas relating pi and e.", "zh-CN": "作者报告称，基于 PSLQ 的自动扩充策略发现了 75 个此前未知的数学常数关系，其中包括首个连分数常数的新公式、新的对数公式，以及连接 π 与 e 的公式。" }, "summary": { "en": "The project represents mathematical constants as vertices and formulas as hyperedges, then searches for integer relations that can expand this graph. The associated LIReC software provides a public database and numerical relation-identification tools for inspecting and extending the library.", "zh-CN": "该项目把数学常数表示为顶点、公式表示为超边，再搜索能够扩充该关系图的整数关系。配套的 LIReC 软件提供公开数据库与数值关系识别工具，可用于检查和继续扩展这一常数关系库。" }, "why_it_matters": { "en": "The work supplied a concrete research-level example of automated mathematical discovery outside theorem proving and language-model benchmarking, while making the resulting discovery substrate available as reusable experimental-mathematics infrastructure.", "zh-CN": "该工作提供了一个区别于定理证明与语言模型基准的研究级自动数学发现案例，并把支撑这些发现的基础设施作为可复用的实验数学资源公开。" }, "ai_role": { "level": "computation_only", "description": { "en": "Automated numerical and symbolic search based on PSLQ proposed candidate integer relations among constants; this event does not rely on an LLM or autonomous agent making semantic mathematical judgments.", "zh-CN": "基于 PSLQ 的自动数值与符号搜索提出数学常数之间的候选整数关系；该事件并不依赖 LLM 或自主 Agent 进行语义层面的数学判断。" } }, "human_contribution": { "description": { "en": "Researchers designed the hypergraph representation, discovery and filtering procedure, curated the constants database, analyzed the generated relations and prepared the mathematical claims and software infrastructure.", "zh-CN": "研究者设计常数关系的超图表示、发现与筛选流程，维护常数数据库，分析自动生成的关系，并整理数学结论与软件基础设施。" } }, "systems": [ "ramanujan-library", "lirec" ], "organizations": [ "ramanujan-machine", "technion" ], "people": [ "itay-beit-halachmi", "ido-kaminer" ], "problems": [ "mathematical-constants", "integer-relations" ], "methods": [ "pslq", "integer-relation-detection", "automated-discovery", "hypergraph" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-12-16", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record reported the Ramanujan Library method and 75 previously unknown relations. The Chronicle records that claim without independently adjudicating every underlying identity or priority claim.", "zh-CN": "arXiv 研究记录报告了 Ramanujan Library 方法及 75 个此前未知关系。Chronicle 记录这一公开研究主张，但不自行裁决每个恒等式或优先权主张。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public LIReC repository exposes the constants database and integer-relation identification software, and the work later appeared at ICLR 2025. E3 records inspectable research infrastructure rather than independent verification of every reported new relation.", "zh-CN": "公开 LIReC 仓库提供常数数据库与整数关系识别软件，该工作后来发表于 ICLR 2025。E3 表示研究基础设施可直接检查，并不等同于论文报告的每个新关系都已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-ramanujan-library-2412.12361", "tier": "S1", "type": "paper", "title": "The Ramanujan Library — Automated Discovery on the Hypergraph of Integer Relations", "url": "https://arxiv.org/abs/2412.12361", "primary": true, "published_date": "2024-12-16", "accessed_at": "2026-09-11" }, { "id": "ramanujan-machine-library-page", "tier": "S2", "type": "official_announcement", "title": "Ramanujan Library — The Hub for Mathematical Constants and Their Surprising Relations", "url": "https://ramanujanmachine.com/ramanujan-library-the-hub-for-mathematical-constants-and-their-surprising-relations/", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-ramanujan-lirec", "tier": "S1", "type": "repository", "title": "LIReC — Library of Integer RElations and Constants", "url": "https://github.com/RamanujanMachine/LIReC", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "iclr-ramanujan-library-2025", "tier": "S1", "type": "paper", "title": "The Ramanujan Library — ICLR 2025 conference paper", "url": "https://proceedings.iclr.cc/paper_files/paper/2025/hash/6782c18960808848174cfe60742b415a-Abstract-Conference.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "ramanujan-lirec-repository", "kind": "code", "title": "LIReC constants database and integer-relation tools", "url": "https://github.com/RamanujanMachine/LIReC" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2023-funsearch-cap-set", "evt-2022-alphatensor" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mathematical-discovery", "mathematical-constants", "pslq", "integer-relations", "experimental-mathematics", "automated-discovery" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-frontiermath", "slug": "frontiermath-research-level-benchmark", "title": { "en": "FrontierMath introduces expert-crafted research-level mathematics evaluation", "zh-CN": "FrontierMath 引入专家构造的研究级数学评测" }, "dates": { "event": "2024-11-08", "first_public_claim": "2024-11-08", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "FrontierMath shifted informal mathematical evaluation from contest problems toward expert-authored problems spanning advanced and research mathematics.", "zh-CN": "FrontierMath 把非形式数学评测从竞赛题进一步推进到覆盖高阶与研究数学的专家原创问题。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric", "hybrid" ], "claim": { "en": "FrontierMath launched with hundreds of original expert-written problems across modern mathematics; leading models initially solved fewer than 2%.", "zh-CN": "FrontierMath 发布数百道覆盖现代数学的专家原创问题；发布时领先模型的解题率均低于 2%。" }, "summary": { "en": "The benchmark was developed with more than sixty mathematicians and emphasized problems requiring hours or days of expert work.", "zh-CN": "该基准与六十余位数学家合作构建，强调通常需要专家数小时乃至数天才能解决的问题。" }, "why_it_matters": { "en": "It created a visible bridge between benchmarked model reasoning and the difficulty regime of genuine mathematical research.", "zh-CN": "它在可量化模型推理与真实数学研究难度之间建立了更直接的桥梁。" }, "ai_role": { "level": "computation_only", "description": { "en": "Frontier models are evaluated with extended reasoning and computational tools on expert-created problems.", "zh-CN": "前沿模型在专家原创问题上使用长程推理和计算工具接受评测。" } }, "human_contribution": { "description": { "en": "Mathematicians authored and vetted problems while Epoch AI designed the evaluation infrastructure.", "zh-CN": "数学家编写并审查问题，Epoch AI 设计评测基础设施。" } }, "systems": [ "frontiermath" ], "organizations": [ "epoch-ai" ], "people": [], "problems": [ "research-mathematics" ], "methods": [ "benchmarking", "expert-curation" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "2024-11-08", "status": "claimed", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "claimed", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "epoch-frontiermath-2024", "tier": "S1", "type": "benchmark", "title": "FrontierMath: A benchmark for evaluating advanced mathematical reasoning in AI", "url": "https://epoch.ai/frontiermath/tiers-1-4/the-benchmark", "primary": true, "published_date": "2024-11-08", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "frontiermath-benchmark", "kind": "dataset", "title": "FrontierMath benchmark surface", "url": "https://epoch.ai/frontiermath/tiers-1-4/the-benchmark" } ], "relationships": { "predecessors": [ "evt-2024-openai-o1", "evt-2024-omni-math" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "research-math", "expert-evaluation", "frontier-models" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-internlm-step-prover", "slug": "internlm-step-prover-expert-iteration", "title": { "en": "InternLM2.5-StepProver scales expert iteration over large Lean problem sets", "zh-CN": "InternLM2.5-StepProver 在大规模 Lean 问题集上扩展专家迭代" }, "dates": { "event": "2024-10-21", "first_public_claim": "2024-10-21", "paper_release": "2024-10-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "StepProver showed how large problem banks and compute-intensive expert iteration can steadily raise open formal theorem-proving performance.", "zh-CN": "StepProver 展示了大规模问题库与高算力专家迭代如何持续提升开放形式定理证明性能。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "InternLM2.5-StepProver reported 65.9% on miniF2F-test and proved or disproved 17.0% of Lean-Workbook-Plus problems.", "zh-CN": "InternLM2.5-StepProver 报告 miniF2F-test 65.9%，并证明或反驳 Lean-Workbook-Plus 中 17.0% 的问题。" }, "summary": { "en": "The system performs expert iteration over large Lean datasets and uses a critic to prioritize easier problems and guide deeper proof searches.", "zh-CN": "系统在大规模 Lean 数据上执行专家迭代，并使用 critic 选择相对容易的问题、引导更深证明搜索。" }, "why_it_matters": { "en": "It provided an open empirical example of theorem-proving performance scaling with data, search and compute.", "zh-CN": "它提供了一个开放实证案例，显示形式证明性能如何随数据、搜索和算力扩展。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The prover searches for Lean proofs, trains on successful outputs and uses a learned critic to allocate effort.", "zh-CN": "证明器搜索 Lean 证明、用成功结果继续训练，并通过学习式 critic 分配搜索资源。" } }, "human_contribution": { "description": { "en": "Researchers built the large-scale expert-iteration pipeline and curated Lean datasets.", "zh-CN": "研究者构建大规模专家迭代管线并整理 Lean 数据。" } }, "systems": [ "internlm2.5-stepprover", "lean" ], "organizations": [ "shanghai-ai-laboratory" ], "people": [], "problems": [ "minif2f", "lean-workbook-plus", "putnambench" ], "methods": [ "expert-iteration", "critic-model", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-10-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-internlm-step-prover-2410.15700", "tier": "S1", "type": "paper", "title": "InternLM2.5-StepProver: Advancing Automated Theorem Proving via Expert Iteration on Large-Scale LEAN Problems", "url": "https://arxiv.org/abs/2410.15700", "primary": true, "published_date": "2024-10-21", "accessed_at": "2026-09-10" }, { "id": "github-internlm-math-stepprover", "tier": "S1", "type": "repository", "title": "InternLM-Math repository containing StepProver release links and resources", "url": "https://github.com/InternLM/InternLM-Math", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "internlm-stepprover-model", "kind": "model", "title": "InternLM2.5-Step-Prover model release", "url": "https://huggingface.co/internlm/internlm2_5-step-prover" } ], "relationships": { "predecessors": [ "evt-2024-lean-workbook", "evt-2024-lean-star" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "expert-iteration", "open-model", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-omni-math", "slug": "omni-math-olympiad-benchmark", "title": { "en": "Omni-MATH refreshes Olympiad evaluation after older math benchmarks begin saturating", "zh-CN": "Omni-MATH 在旧数学基准趋于饱和后更新奥赛级评测" }, "dates": { "event": "2024-10-10", "first_public_claim": "2024-10-10", "paper_release": "2024-10-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "Omni-MATH responded to rapid benchmark saturation by collecting a larger, finer-grained set of Olympiad-level mathematics problems.", "zh-CN": "Omni-MATH 针对数学基准快速饱和的问题，构建了更大且难度划分更细的奥赛级数学题集。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Omni-MATH introduced 4,428 human-annotated competition problems spanning more than 33 subdomains and more than 10 difficulty levels.", "zh-CN": "Omni-MATH 引入 4,428 道人工标注的竞赛数学题，覆盖 33 个以上子领域和 10 个以上难度等级。" }, "summary": { "en": "The benchmark was designed after frontier reasoning models approached saturation on older datasets such as MATH.", "zh-CN": "该基准在前沿推理模型逐渐接近 MATH 等旧数据集饱和后设计。" }, "why_it_matters": { "en": "It provided a more discriminating informal-math benchmark during the transition to reasoning-specialized models.", "zh-CN": "它在推理专用模型兴起阶段提供了更有区分度的非形式数学评测。" }, "ai_role": { "level": "computation_only", "description": { "en": "Frontier language models are evaluated across difficulty levels and mathematical subdomains.", "zh-CN": "前沿语言模型在多个难度等级和数学子领域接受评测。" } }, "human_contribution": { "description": { "en": "Researchers curated and annotated competition problems and designed the taxonomy and scoring.", "zh-CN": "研究者整理并标注竞赛问题，设计分类体系与评分。" } }, "systems": [ "omni-math" ], "organizations": [ "shenzhen-research-institute-of-big-data" ], "people": [], "problems": [ "olympiad-mathematics" ], "methods": [ "benchmarking", "difficulty-stratification" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-10-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-omni-math-2410.07985", "tier": "S1", "type": "paper", "title": "Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models", "url": "https://arxiv.org/abs/2410.07985", "primary": true, "published_date": "2024-10-10", "accessed_at": "2026-09-10" }, { "id": "github-omni-math", "tier": "S1", "type": "repository", "title": "Official Omni-MATH benchmark repository", "url": "https://github.com/KbsdJames/Omni-MATH", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "omni-math-repository", "kind": "dataset", "title": "Omni-MATH dataset and evaluation code", "url": "https://github.com/KbsdJames/Omni-MATH" } ], "relationships": { "predecessors": [ "evt-2024-olympiadbench", "evt-2024-openai-o1" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "olympiad", "reasoning-model", "dataset" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-leanagent", "slug": "leanagent-lifelong-theorem-proving", "title": { "en": "LeanAgent brings lifelong learning to theorem proving across evolving Lean repositories", "zh-CN": "LeanAgent 将终身学习引入持续演化 Lean 仓库的定理证明" }, "dates": { "event": "2024-10-08", "first_public_claim": "2024-10-08", "paper_release": "2024-10-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "LeanAgent reframed neural theorem proving as a continual-learning problem over evolving mathematical repositories rather than a fixed benchmark, combining a dynamic knowledge database, curriculum ordering and progressive retriever training to preserve and extend proof capability across domains.", "zh-CN": "LeanAgent 将神经定理证明重新表述为面向持续演化数学仓库的终身学习问题，而非固定基准任务；它结合动态知识数据库、课程排序和渐进式检索器训练，使证明能力能够跨领域持续保留与扩展。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The LeanAgent paper reported formal proofs for 155 theorems whose Lean repositories previously contained missing proofs across 23 repositories, while improving lifelong-learning stability and backward transfer relative to a static theorem-proving baseline.", "zh-CN": "LeanAgent 论文报告在 23 个 Lean 仓库中为 155 个此前缺少形式证明的定理生成了形式证明，并相较静态定理证明基线改善终身学习中的稳定性与向后迁移表现。" }, "summary": { "en": "LeanAgent repeatedly ingests new Lean repositories, traces theorem and premise data through LeanDojo, updates a dynamic database, progressively retrains premise retrieval and searches for proofs of `sorry` theorems. Successful proofs can be added back to the knowledge base for later learning.", "zh-CN": "LeanAgent 持续接收新的 Lean 仓库，通过 LeanDojo 抽取定理与前提数据，更新动态数据库，渐进训练前提检索器，并搜索带有 `sorry` 的定理证明；成功证明还可回流知识库供后续学习。" }, "why_it_matters": { "en": "The work introduced a durable systems perspective for AI theorem proving in which mathematical knowledge, repositories and model competence evolve together, addressing a limitation of provers trained once on static snapshots.", "zh-CN": "该工作为 AI 定理证明引入一种持续性的系统视角：数学知识、代码仓库与模型能力共同演化，从而回应“一次训练于静态快照”的证明器难以适应持续增长数学库的问题。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Learned premise retrieval and tactic generation drove automated proof search across Lean repositories, while Lean mechanically checked candidate tactic sequences and accepted successful formal proofs.", "zh-CN": "学习式前提检索与 tactic 生成驱动跨 Lean 仓库的自动证明搜索，Lean 则机械检查候选 tactic 序列并接受成功的形式证明。" } }, "human_contribution": { "description": { "en": "Researchers designed the lifelong-learning architecture, repository curriculum, dynamic database and progressive training procedure, selected evaluation repositories, and analyzed stability and transfer.", "zh-CN": "研究者设计终身学习架构、仓库课程、动态数据库与渐进训练流程，选择评测仓库，并分析稳定性与迁移表现。" } }, "systems": [ "leanagent", "lean", "leandojo" ], "organizations": [ "caltech" ], "people": [ "adarsh-kumarappan", "mo-tiwari", "peiyang-song", "robert-joseph-george", "chaowei-xiao", "anima-anandkumar" ], "problems": [ "lean-theorem-proving" ], "methods": [ "lifelong-learning", "continual-learning", "premise-selection", "curriculum-learning", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-10-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced LeanAgent and reported its continual-learning and formal-proof results across multiple Lean repositories.", "zh-CN": "arXiv 研究记录发布 LeanAgent，并报告其跨多个 Lean 仓库的持续学习与形式证明结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public LeanAgent repository exposes implementation, tests and reproduction setup, and the work later appeared at ICLR 2025. Machine-checked describes Lean acceptance of generated formal proofs; it does not imply independent replay of the complete experiment or new informal mathematical results.", "zh-CN": "公开的 LeanAgent 仓库提供实现、测试与复现实验配置，该工作后来发表于 ICLR 2025。machine-checked 表示生成的形式证明由 Lean 接受，并不表示完整实验已获独立重放，也不表示产生了新的非形式数学结果。" } } ] }, "sources": [ { "id": "arxiv-leanagent-2410.06209", "tier": "S1", "type": "paper", "title": "LeanAgent: Lifelong Learning for Formal Theorem Proving", "url": "https://arxiv.org/abs/2410.06209", "primary": true, "published_date": "2024-10-08", "accessed_at": "2026-09-11" }, { "id": "github-leanagent", "tier": "S1", "type": "repository", "title": "LeanAgent implementation and reproduction repository", "url": "https://github.com/lean-dojo/LeanAgent", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "iclr-leanagent-2025", "tier": "S1", "type": "paper", "title": "LeanAgent — ICLR 2025 conference paper", "url": "https://proceedings.iclr.cc/paper_files/paper/2025/hash/b67c77f8db8b991d73d6f2e16f491840-Abstract-Conference.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "leanagent-repository", "kind": "code", "title": "LeanAgent lifelong theorem-proving implementation", "url": "https://github.com/lean-dojo/LeanAgent" } ], "relationships": { "predecessors": [ "evt-2023-leandojo" ], "successors": [], "related": [ "evt-2024-lean-star", "evt-2024-deepseek-prover-v1" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "theorem-proving", "lifelong-learning", "continual-learning", "proof-search", "infrastructure" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-gsm-symbolic", "slug": "gsm-symbolic-robustness-benchmark", "title": { "en": "GSM-Symbolic exposes robustness failures behind high math-reasoning benchmark scores", "zh-CN": "GSM-Symbolic 揭示高数学推理基准分数背后的鲁棒性缺陷" }, "dates": { "event": "2024-10-07", "first_public_claim": "2024-10-07", "paper_release": "2024-10-07", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "GSM-Symbolic shifted mathematical-reasoning evaluation from a single static score toward controlled robustness tests by regenerating semantically equivalent problems from symbolic templates and measuring sensitivity to changed values and irrelevant clauses.", "zh-CN": "GSM-Symbolic 将数学推理评测从单一静态分数推进到可控鲁棒性测试：通过符号模板生成语义等价题目，并检验模型对数值变化与无关条件的敏感性。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "numeric" ], "claim": { "en": "Apple researchers introduced GSM-Symbolic and reported substantial performance variance across different instantiations of the same GSM8K-style problem templates, with further degradation as problem complexity increased and with irrelevant-but-plausible clauses causing drops of up to 65% in the evaluated models.", "zh-CN": "Apple 研究者发布 GSM-Symbolic，并报告同一类 GSM8K 风格题目在不同模板实例化下会产生显著性能波动；随着题目复杂度增加，性能进一步下降，而加入看似相关但实际无关的条件时，所测模型的成绩最高可下降 65%。" }, "summary": { "en": "The benchmark derives controllable families of grade-school mathematics problems from symbolic templates. This lets evaluators vary numerical values, clause counts and distractors while preserving the underlying reasoning structure, testing whether model success is stable rather than tied to a fixed benchmark instance.", "zh-CN": "该基准从符号模板生成可控的小学数学题族，在保持底层推理结构的同时改变数值、条件数量与干扰项，从而检验模型成功是否具有稳定性，而非只适用于固定基准实例。" }, "why_it_matters": { "en": "GSM-Symbolic made benchmark robustness itself a first-class question in AI4Math evaluation and provided a reusable way to distinguish headline accuracy from consistency under controlled perturbations.", "zh-CN": "GSM-Symbolic 把“基准鲁棒性”本身提升为 AI4Math 评测中的核心问题，并提供可复用的方法，用于区分表面准确率与受控扰动下的稳定推理能力。" }, "ai_role": { "level": "computation_only", "description": { "en": "Language models were the systems under evaluation and generated answers to controlled benchmark variants; the benchmark templates, perturbation design and analysis were created by human researchers.", "zh-CN": "语言模型作为被评测系统，对受控变体题目生成答案；基准模板、扰动设计与分析由研究者完成。" } }, "human_contribution": { "description": { "en": "Researchers designed the symbolic templates and perturbation families, selected and ran the evaluated models, analyzed robustness failures, and released generated benchmark data.", "zh-CN": "研究者设计符号模板与扰动题族，选择并运行被测模型，分析鲁棒性缺陷，并公开生成后的基准数据。" } }, "systems": [ "gsm-symbolic", "gsm8k" ], "organizations": [ "apple" ], "people": [ "iman-mirzadeh", "keivan-alizadeh", "hooman-shahrokhi", "oncel-tuzel", "samy-bengio", "mehrdad-farajtabar" ], "problems": [ "grade-school-math-word-problems" ], "methods": [ "symbolic-templates", "robustness-evaluation", "controlled-perturbations", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-10-07", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The public research record introduced GSM-Symbolic and reported robustness results across controlled variants of GSM8K-style problems.", "zh-CN": "公开研究记录发布 GSM-Symbolic，并报告在 GSM8K 风格受控变体上的鲁棒性结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Apple's public repository exposes the benchmark templates and generated GSM-Symbolic, P1 and P2 data. E3 records inspectability and does not imply independent verification of every reported model result.", "zh-CN": "Apple 公开仓库提供基准模板以及生成后的 GSM-Symbolic、P1、P2 数据。E3 表示产物可直接检查，并不表示论文报告的全部模型结果都已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-gsm-symbolic-2410.05229", "tier": "S1", "type": "paper", "title": "GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models", "url": "https://arxiv.org/abs/2410.05229", "primary": true, "published_date": "2024-10-07", "accessed_at": "2026-09-11" }, { "id": "apple-gsm-symbolic-2024", "tier": "S2", "type": "official_announcement", "title": "GSM-Symbolic — Apple Machine Learning Research", "url": "https://machinelearning.apple.com/research/gsm-symbolic", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-apple-gsm-symbolic", "tier": "S1", "type": "repository", "title": "GSM-Symbolic templates and generated data", "url": "https://github.com/apple/ml-gsm-symbolic", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "gsm-symbolic-dataset", "kind": "benchmark", "title": "GSM-Symbolic templates and generated benchmark variants", "url": "https://github.com/apple/ml-gsm-symbolic" } ], "relationships": { "predecessors": [ "evt-2021-gsm8k" ], "successors": [], "related": [ "evt-2023-mathvista" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "gsm-symbolic", "gsm8k", "benchmark", "robustness", "math-reasoning", "evaluation" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-openai-o1", "slug": "openai-o1-reasoning-aime", "title": { "en": "OpenAI o1 introduces inference-time reasoning with a large AIME performance jump", "zh-CN": "OpenAI o1 以推理时思考带来 AIME 能力跃升" }, "dates": { "event": "2024-09-12", "first_public_claim": "2024-09-12", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "benchmark" ], "significance": { "tier": "H3", "rationale": { "en": "OpenAI o1 was a major general-purpose reasoning-model release, but its place in the AI4Math Chronicle is contextual: AIME demonstrated capability rather than the release itself contributing a new mathematical result, proof, formalization, or math-specific system.", "zh-CN": "OpenAI o1 是重要的通用推理模型发布，但在 AI4Math Chronicle 中主要承担背景作用：AIME 用于展示模型能力，而该发布本身并未贡献新的数学结果、证明、形式化或数学专项系统。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "OpenAI reported o1 at 74% single-sample accuracy on AIME 2024 and 93% after reranking 1,000 samples, far above GPT-4o's 12% baseline.", "zh-CN": "OpenAI 报告 o1 在 AIME 2024 上单样本准确率为 74%，对 1,000 个样本重排序后达到 93%，显著高于 GPT-4o 的 12%。" }, "summary": { "en": "The o1 series was trained to spend more inference-time computation on multi-step reasoning before producing an answer.", "zh-CN": "o1 系列被训练为在给出答案前投入更多推理时计算执行多步思考。" }, "why_it_matters": { "en": "The release helped establish test-time compute and long reasoning traces as central levers for frontier mathematical performance, providing context for later math-specific systems.", "zh-CN": "该发布推动“测试时计算”和长程推理轨迹成为提升前沿数学能力的重要杠杆，为后续数学专项系统提供背景。" }, "ai_role": { "level": "computation_only", "description": { "en": "The model performs extended internal reasoning before answering mathematical problems.", "zh-CN": "模型在回答数学问题前执行更长的内部推理。" } }, "human_contribution": { "description": { "en": "OpenAI researchers designed the reasoning training method and benchmark evaluations.", "zh-CN": "OpenAI 研究者设计推理训练方法与基准评测。" } }, "systems": [ "openai-o1" ], "organizations": [ "openai" ], "people": [], "problems": [ "aime-2024" ], "methods": [ "reasoning-model", "test-time-compute", "reinforcement-learning" ], "verification": { "evidence_level": "E1", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2024-09-12", "status": "claimed", "evidence_level": "E1", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "openai-o1-reasoning-2024", "tier": "S2", "type": "official_announcement", "title": "Learning to reason with LLMs", "url": "https://openai.com/index/learning-to-reason-with-llms/", "primary": true, "published_date": "2024-09-12", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2022-minerva", "evt-2021-math-benchmark" ], "successors": [], "related": [] }, "timeline": { "featured": false, "significance": "context" }, "tags": [ "openai", "reasoning-model", "aime", "test-time-compute" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-deepseek-prover-v1-5", "slug": "deepseek-prover-v1-5-lean-proof-search", "title": { "en": "DeepSeek-Prover-V1.5 combines proof-assistant feedback, reinforcement learning and tree search", "zh-CN": "DeepSeek-Prover-V1.5 结合证明助手反馈、强化学习与树搜索" }, "dates": { "event": "2024-08-15", "first_public_claim": "2024-08-15", "paper_release": "2024-08-15", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "proof", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "DeepSeek-Prover-V1.5 made proof-assistant feedback a training signal through reinforcement learning and combined it with Monte Carlo tree search, while releasing the 7B model and proof-search implementation openly.", "zh-CN": "DeepSeek-Prover-V1.5 将证明助手反馈直接用作强化学习训练信号，并与蒙特卡洛树搜索结合，同时公开 7B 模型和证明搜索实现。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "DeepSeek-Prover-V1.5 reported 63.5% success on miniF2F-test and 25.3% on ProofNet using reinforcement learning from proof-assistant feedback plus RMaxTS proof search, improving on the earlier DeepSeek-Prover line.", "zh-CN": "DeepSeek-Prover-V1.5 通过证明助手反馈强化学习与 RMaxTS 证明搜索，在 miniF2F-test 上报告 63.5% 成功率，在 ProofNet 上报告 25.3%，较此前 DeepSeek-Prover 系列进一步提升。" }, "summary": { "en": "The model was specialized for Lean 4 formal mathematics, refined with reinforcement learning from Lean feedback and paired with an intrinsic-reward Monte Carlo tree-search variant to explore diverse proof paths. DeepSeek released model weights and code for reproducing the proof-search setup.", "zh-CN": "该模型针对 Lean 4 形式数学进行专门训练，使用 Lean 反馈进行强化学习，并配合带内在奖励的蒙特卡洛树搜索变体探索多样证明路径。DeepSeek 公开了模型权重和复现实验的代码。" }, "why_it_matters": { "en": "The system is a clear bridge from static proof generation toward learned agents that train and search against a formal verifier, while remaining small enough and open enough to become a widely reusable research baseline.", "zh-CN": "该系统清晰连接了静态证明生成与“面向形式验证器进行训练和搜索”的学习式 Agent，同时凭借较小规模与开放发布成为可广泛复用的研究基线。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The language model generated Lean proofs and tree-search actions, while Lean supplied correctness feedback for both training and inference-time verification.", "zh-CN": "语言模型生成 Lean 证明与树搜索动作，Lean 同时为训练和推理阶段提供正确性反馈与验证。" } }, "human_contribution": { "description": { "en": "Researchers assembled formal training data, designed reinforcement-learning and RMaxTS procedures, trained the models and selected benchmark protocols.", "zh-CN": "研究者构建形式训练数据，设计强化学习与 RMaxTS 流程，训练模型并选择评测协议。" } }, "systems": [ "deepseek-prover-v1-5", "lean" ], "organizations": [ "deepseek-ai" ], "people": [ "huajian-xin", "z-z-ren", "junxiao-song", "zhihong-shao", "fuli-luo" ], "problems": [ "minif2f", "proofnet" ], "methods": [ "reinforcement-learning-from-proof-feedback", "monte-carlo-tree-search", "formal-theorem-proving", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-08-15", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The paper reported the training method and benchmark results.", "zh-CN": "论文公开了训练方法与基准结果。" } }, { "date": "2024-08-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Model weights, Lean integration and proof-search code were released publicly.", "zh-CN": "模型权重、Lean 集成与证明搜索代码被公开发布。" } } ] }, "sources": [ { "id": "arxiv-deepseek-prover-v1-5-2408.08152", "tier": "S1", "type": "paper", "title": "DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search", "url": "https://arxiv.org/abs/2408.08152", "primary": true, "published_date": "2024-08-15", "accessed_at": "2026-09-10" }, { "id": "github-deepseek-prover-v1-5", "tier": "S1", "type": "repository", "title": "DeepSeek-Prover-V1.5 repository", "url": "https://github.com/deepseek-ai/DeepSeek-Prover-V1.5", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "deepseek-prover-v1-5-repository", "kind": "code", "title": "DeepSeek-Prover-V1.5 models and prover code", "url": "https://github.com/deepseek-ai/DeepSeek-Prover-V1.5" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f", "evt-2021-minif2f", "evt-2023-leandojo" ], "successors": [ "evt-2026-alphaproof-nexus" ], "related": [ "evt-2023-copra", "evt-2024-alphaproof-alphageometry2-imo" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "theorem-proving", "reinforcement-learning", "tree-search", "open-model", "proof-feedback" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-minictx", "slug": "minictx-long-context-theorem-proving", "title": { "en": "miniCTX tests theorem provers on long, unseen project context", "zh-CN": "miniCTX 测试定理证明器使用长篇、未见项目上下文的能力" }, "dates": { "event": "2024-08-05", "first_public_claim": "2024-08-05", "paper_release": "2024-08-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "miniCTX moved evaluation toward repository-scale theorem proving where definitions and lemmas live in long, previously unseen context.", "zh-CN": "miniCTX 把评测推进到仓库级定理证明：所需定义与引理存在于长篇、训练时未见的上下文中。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "miniCTX introduced Lean theorem-proving tasks with repository context spanning up to tens of thousands of tokens and showed that context-aware methods outperform state-only baselines.", "zh-CN": "miniCTX 引入带有可达数万 token 仓库上下文的 Lean 定理证明任务，并显示利用上下文的方法明显优于只看 proof state 的基线。" }, "summary": { "en": "The benchmark draws theorems from real Lean projects and textbooks and includes tooling for extracting new project contexts.", "zh-CN": "该基准从真实 Lean 项目和教材中抽取定理，并提供提取新项目上下文的工具。" }, "why_it_matters": { "en": "It better approximated the conditions faced by practical proof agents operating inside large formal codebases.", "zh-CN": "它更接近实际证明 Agent 在大型形式化代码库中工作的真实条件。" }, "ai_role": { "level": "computation_only", "description": { "en": "Models must retrieve and use relevant definitions and lemmas from long project context while proving.", "zh-CN": "模型在证明过程中必须从长篇项目上下文中检索并利用相关定义与引理。" } }, "human_contribution": { "description": { "en": "Researchers constructed the benchmark and ntp-toolkit for context-aware theorem-proving data extraction.", "zh-CN": "研究者构建基准与 ntp-toolkit，用于提取上下文感知的定理证明数据。" } }, "systems": [ "minictx", "ntp-toolkit", "lean" ], "organizations": [ "carnegie-mellon-university" ], "people": [], "problems": [ "repository-level-theorem-proving" ], "methods": [ "long-context", "retrieval", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-08-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-minictx-2408.03350", "tier": "S1", "type": "paper", "title": "miniCTX: Neural Theorem Proving with (Long-)Contexts", "url": "https://arxiv.org/abs/2408.03350", "primary": true, "published_date": "2024-08-05", "accessed_at": "2026-09-10" }, { "id": "github-minictx-eval", "tier": "S1", "type": "repository", "title": "miniCTX evaluation repository", "url": "https://github.com/cmu-l3/minictx-eval", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "minictx-eval-repository", "kind": "dataset", "title": "miniCTX benchmark and evaluation resources", "url": "https://github.com/cmu-l3/minictx-eval" } ], "relationships": { "predecessors": [ "evt-2023-leandojo", "evt-2024-putnambench" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "long-context", "benchmark", "retrieval" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-ai-for-math-icml", "slug": "ai-for-math-icml-workshop-series", "title": { "en": "AI for Math @ ICML establishes a recurring AI4Math workshop series", "zh-CN": "AI for Math @ ICML 建立持续性的 AI4Math workshop 系列" }, "dates": { "event": "2024-07-26", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "AI for Math @ ICML is a field-building milestone because the 2024 inaugural workshop developed into three consecutive ICML editions through 2026 with a stable AI4Math identity, reviewed submissions, OpenReview records, paper awards and recurring challenge activity. That combination provides evidence of an organized scholarly venue rather than a one-off session attached to a general machine-learning conference.", "zh-CN": "AI for Math @ ICML 构成领域建构里程碑，因为 2024 年首届 workshop 已发展为持续至 2026 年的三届 ICML 系列，并保持稳定的 AI4Math 身份、投稿评审、OpenReview 记录、论文奖项与持续性 challenge 活动。这些机制共同表明其已经形成组织化学术 venue，而不是依附于通用机器学习会议的一次性 session。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The first AI for Math Workshop was held at ICML 2024 in Vienna on 26 July 2024. The series returned as the 2nd AI for Math Workshop at ICML 2025 and the 3rd edition at ICML 2026 on 11 July 2026. Across the later editions it used OpenReview-based paper submission and review, presented accepted research, awarded papers and operated AI4Math challenges, while focusing on theorem proving, autoformalization, mathematical reasoning, scientific problem solving and human-AI collaboration.", "zh-CN": "首届 AI for Math Workshop 于 2024 年 7 月 26 日在维也纳 ICML 2024 举行。该系列随后以第二届 AI for Math Workshop @ ICML 2025 与 2026 年 7 月 11 日第三届 workshop 持续举办。后续各届通过 OpenReview 进行论文投稿与评审，展示录用研究、设置论文奖项并运行 AI4Math challenges，主题覆盖定理证明、自动形式化、数学推理、科学问题求解与人机协作。" }, "summary": { "en": "The workshop series was created specifically around AI technologies for mathematical reasoning and discovery. By its third edition, the venue reported hundreds of submissions and accepted papers, a multi-level program committee, paper awards and four challenge tracks covering autoformalization alignment, theoretical-computer-science proving, visual scientific reasoning and end-to-end Lean proof generation.", "zh-CN": "该 workshop 系列从建立之初就以面向数学推理与数学发现的 AI 技术为核心。到第三届时，官方统计已记录数百篇投稿与录用论文、多层级 program committee、论文奖项，以及覆盖自动形式化语义对齐、理论计算机科学证明、视觉科学推理与端到端 Lean 证明生成的四个 challenge track。" }, "why_it_matters": { "en": "AI for Math @ ICML shows the consolidation of AI4Math as a recognizable research community inside a major machine-learning conference. Its recurring review process, paper program and challenge infrastructure provide a venue for work that spans informal reasoning, formal theorem proving and scientific agents, helping institutionalize AI4Math beyond individual papers or model releases.", "zh-CN": "AI for Math @ ICML 表明 AI4Math 已在大型机器学习会议内部逐步凝结为可识别的研究共同体。其持续性的投稿评审、论文计划与 challenge 基础设施，为非形式推理、形式定理证明和科学 Agent 等工作提供共同 venue，使 AI4Math 的制度化不再依赖单篇论文或单次模型发布。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records the establishment and continuity of a scholarly venue rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是学术 venue 的建立与持续运行，而不是某个 AI 系统执行数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "Human organizers and reviewers established the workshop, built the program and review process, selected papers and awards, operated challenge tracks and sustained the series across three ICML editions.", "zh-CN": "人类组织者与评审者建立 workshop、构建议程与评审流程、筛选论文和奖项、运行 challenge tracks，并在三届 ICML 中持续维护该系列。" } }, "systems": [], "organizations": [ "icml" ], "people": [], "problems": [], "methods": [ "scholarly-venue", "ai4math-community", "workshop-challenges" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2024-07-26", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official ICML 2024 schedule records the inaugural AI for Math Workshop on 26 July 2024.", "zh-CN": "ICML 2024 官方日程记录了 2024 年 7 月 26 日举行的首届 AI for Math Workshop。" } }, { "date": "2026-09-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official 2025 and 2026 workshop records document the second and third editions, OpenReview-based paper workflow, awards, challenges and a three-edition history, supporting the Chronicle's durability assessment.", "zh-CN": "2025 与 2026 年官方 workshop 记录明确记载第二、第三届会议、基于 OpenReview 的论文流程、奖项、challenges 与三届历史，由此支持 Chronicle 对该系列持续性的判断。" } } ] }, "sources": [ { "id": "icml-2024-ai-for-math-schedule", "tier": "S2", "type": "official_announcement", "title": "ICML 2024 Schedule — AI for Math Workshop", "url": "https://icml.cc/virtual/2024/calendar", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "icml-2025-ai-for-math", "tier": "S2", "type": "official_announcement", "title": "2nd AI for Math Workshop @ ICML 2025", "url": "https://icml.cc/virtual/2025/workshop/39979", "primary": false, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "ai4math-icml-2026-official", "tier": "S2", "type": "official_announcement", "title": "3rd AI for Math Workshop @ ICML 2026", "url": "https://ai4math2026.github.io/", "primary": false, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "ai4math-icml-2026-stats", "tier": "S2", "type": "official_announcement", "title": "AI4Math @ ICML 2026 — Statistics across three editions", "url": "https://ai4math2026.github.io/stats.html", "primary": false, "published_date": null, "accessed_at": "2026-09-14" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "ai-for-math", "ai4math", "field-building", "workshop-series", "icml", "theorem-proving", "autoformalization", "mathematical-reasoning", "scientific-agents" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-alphaproof-alphageometry2-imo", "slug": "alphaproof-alphageometry2-imo-2024", "title": { "en": "AlphaProof and AlphaGeometry 2 reach silver-medal standard on IMO 2024 problems", "zh-CN": "AlphaProof 与 AlphaGeometry 2 在 IMO 2024 题目上达到银牌标准" }, "dates": { "event": "2024-07-25", "first_public_claim": "2024-07-25", "paper_release": "2025-11-12", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "competition", "proof", "formalization", "system" ], "significance": { "tier": "H1", "rationale": { "en": "The combined system was reported as the first AI system to achieve medal-level performance on a full set of current IMO problems, while also exposing the practical trade-offs of manual formalization and multi-day computation.", "zh-CN": "该组合系统被报告为首个在当届完整 IMO 题集上达到奖牌水平的 AI 系统，同时也清楚暴露了人工形式化与多日计算的实际代价。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "AlphaProof solved three non-geometry IMO 2024 problems and AlphaGeometry 2 solved the geometry problem. The four perfect solutions totaled 28/42 points, equivalent to the top end of the silver-medal range and one point below the gold threshold that year.", "zh-CN": "AlphaProof 解出 3 道非几何的 IMO 2024 题目，AlphaGeometry 2 解出几何题；4 道满分解答合计 28/42 分，对应当年银牌区间上沿，距金牌线 1 分。" }, "summary": { "en": "AlphaProof used reinforcement learning in Lean for formal proof search, while AlphaGeometry 2 handled the geometry problem with a faster neuro-symbolic system. The 2024 workflow required experts to translate problems into formal representations and used up to several days of computation.", "zh-CN": "AlphaProof 在 Lean 中使用强化学习进行形式证明搜索，AlphaGeometry 2 则以更快的神经符号系统处理几何题。2024 年的流程需要专家将题目翻译为形式化表示，并使用最长数日的计算时间。" }, "why_it_matters": { "en": "The result connected formal proof search with a recognizable external benchmark at medal level and became a reference point for later end-to-end natural-language olympiad systems.", "zh-CN": "该结果把形式证明搜索与一个公众熟知的外部竞赛基准连接到奖牌水平，并成为后续端到端自然语言奥赛系统的重要参照点。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "AlphaProof searched for Lean proofs using reinforcement learning and test-time adaptation; AlphaGeometry 2 generated and checked geometry proofs in its specialized system.", "zh-CN": "AlphaProof 通过强化学习与测试时适应搜索 Lean 证明；AlphaGeometry 2 在其专用系统中生成并检查几何证明。" } }, "human_contribution": { "description": { "en": "Experts manually translated the contest problems into formal or specialized representations, the research teams designed and trained the systems, and mathematicians graded the resulting solutions under IMO scoring rules.", "zh-CN": "专家将竞赛题人工翻译为形式化或专用表示，研究团队设计并训练系统，数学家按 IMO 评分规则评阅最终解答。" } }, "systems": [ "alphaproof", "alphageometry-2" ], "organizations": [ "google-deepmind", "international-mathematical-olympiad" ], "people": [ "thomas-hubert", "rishi-mehta", "laurent-sartran", "thang-luong" ], "problems": [ "international-mathematical-olympiad-2024" ], "methods": [ "reinforcement-learning", "lean", "formal-theorem-proving", "neuro-symbolic-reasoning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-07-25", "status": "claimed", "evidence_level": "E1", "note": { "en": "Google DeepMind published the competition result and described external scoring by mathematicians.", "zh-CN": "Google DeepMind 公布竞赛结果，并说明由数学家按竞赛规则进行外部评分。" } }, { "date": "2025-11-12", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The AlphaProof methodology and IMO 2024 result were published in a peer-reviewed Nature article.", "zh-CN": "AlphaProof 方法与 IMO 2024 结果在经同行评审的 Nature 论文中发表。" } } ] }, "sources": [ { "id": "deepmind-imo-2024", "tier": "S2", "type": "official_announcement", "title": "AI achieves silver-medal standard solving International Mathematical Olympiad problems", "url": "https://deepmind.google/blog/ai-solves-imo-problems-at-silver-medal-level/", "primary": true, "published_date": "2024-07-25", "accessed_at": "2026-09-10" }, { "id": "nature-alphaproof-2025", "tier": "S1", "type": "paper", "title": "Olympiad-level formal mathematical reasoning with reinforcement learning", "url": "https://www.nature.com/articles/s41586-025-09833-y", "primary": true, "published_date": "2025-11-12", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2024-alphageometry" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "imo", "olympiad", "lean", "reinforcement-learning", "formal-proof", "geometry" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-putnambench", "slug": "putnambench-formal-undergraduate-competition", "title": { "en": "PutnamBench raises formal theorem-proving evaluation to Putnam-level mathematics", "zh-CN": "PutnamBench 将形式定理证明评测提升到 Putnam 级本科数学" }, "dates": { "event": "2024-07-15", "first_public_claim": "2024-07-15", "paper_release": "2024-07-15", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "PutnamBench created a difficult multi-system benchmark from the premier North American undergraduate mathematics competition and exposed a large capability gap.", "zh-CN": "PutnamBench 基于北美顶尖本科数学竞赛构建高难度多形式系统基准，并揭示当时证明器与高水平本科数学之间的巨大能力差距。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "PutnamBench released 1,692 hand-constructed formalizations of 640 Putnam theorems in Lean 4 and Isabelle, with a substantial Coq subset.", "zh-CN": "PutnamBench 发布 640 道 Putnam 定理的 1,692 个手工形式化版本，覆盖 Lean 4、Isabelle，并包含相当规模的 Coq 子集。" }, "summary": { "en": "Initial neural and symbolic provers solved only a handful of benchmark problems, making the collection a high-difficulty target for formal reasoning.", "zh-CN": "初始神经与符号证明器只能解决极少数题目，使该集合成为高难度形式推理目标。" }, "why_it_matters": { "en": "It shifted formal theorem-prover evaluation from high-school Olympiad problems toward broad advanced undergraduate mathematics.", "zh-CN": "它把形式定理证明评测从高中奥赛进一步推进到覆盖广泛的高阶本科数学。" }, "ai_role": { "level": "computation_only", "description": { "en": "Automated theorem provers are evaluated on the formalized Putnam problems.", "zh-CN": "自动定理证明器在形式化 Putnam 问题上接受评测。" } }, "human_contribution": { "description": { "en": "Researchers hand-formalized competition problems across multiple proof assistants and built the benchmark.", "zh-CN": "研究者在多个证明助手中手工形式化竞赛题并构建基准。" } }, "systems": [ "putnambench", "lean", "isabelle", "coq" ], "organizations": [ "university-of-texas-at-austin" ], "people": [], "problems": [ "putnam-competition" ], "methods": [ "benchmarking", "formalization" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-07-15", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-putnambench-2407.11214", "tier": "S1", "type": "paper", "title": "PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition", "url": "https://arxiv.org/abs/2407.11214", "primary": true, "published_date": "2024-07-15", "accessed_at": "2026-09-10" }, { "id": "github-putnambench", "tier": "S1", "type": "repository", "title": "PutnamBench formal benchmark repository", "url": "https://github.com/trishullab/PutnamBench", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "putnambench-repository", "kind": "dataset", "title": "PutnamBench Lean, Isabelle and Coq formalizations", "url": "https://github.com/trishullab/PutnamBench" } ], "relationships": { "predecessors": [ "evt-2023-proofnet", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "putnam", "benchmark", "lean", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-lean-star", "slug": "lean-star-thinking-and-proving", "title": { "en": "Lean-STaR trains theorem provers to interleave informal thinking with Lean tactics", "zh-CN": "Lean-STaR 训练定理证明器交替执行非形式思考与 Lean tactic" }, "dates": { "event": "2024-07-14", "first_public_claim": "2024-07-14", "paper_release": "2024-07-14", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Lean-STaR explicitly inserted learned informal thoughts before proof steps and combined them with expert iteration.", "zh-CN": "Lean-STaR 在形式证明步骤前显式插入学习到的非形式思考，并与专家迭代结合。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "Lean-STaR improved miniF2F pass@64 from 43.4% to 46.3% by training models to generate synthetic informal thoughts before tactics.", "zh-CN": "Lean-STaR 通过训练模型在 tactic 前生成合成的非形式思考，将 miniF2F pass@64 从 43.4% 提升到 46.3%。" }, "summary": { "en": "The method generates retrospective thoughts from known tactics and then uses expert iteration on newly discovered verified proofs.", "zh-CN": "该方法从已知 tactic 反向生成思考文本，并对新发现且验证通过的证明执行专家迭代。" }, "why_it_matters": { "en": "It explored a direct bridge between chain-of-thought-style reasoning and proof-assistant feedback.", "zh-CN": "它探索了思维链式推理与证明助手反馈之间的直接桥接方式。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model generates both informal thoughts and Lean tactics, while Lean verifies the proof state.", "zh-CN": "模型同时生成非形式思考与 Lean tactic，Lean 负责验证证明状态。" } }, "human_contribution": { "description": { "en": "Researchers designed synthetic-thought generation, expert iteration and evaluation.", "zh-CN": "研究者设计合成思考生成、专家迭代与评测。" } }, "systems": [ "lean-star", "lean" ], "organizations": [ "carnegie-mellon-university" ], "people": [], "problems": [ "minif2f" ], "methods": [ "expert-iteration", "synthetic-thought", "lean" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-07-14", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-lean-star-2407.10040", "tier": "S1", "type": "paper", "title": "Lean-STaR: Learning to Interleave Thinking and Proving", "url": "https://arxiv.org/abs/2407.10040", "primary": true, "published_date": "2024-07-14", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2023-leandojo", "evt-2022-htps" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "chain-of-thought", "expert-iteration", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-numinamath-aimo", "slug": "numinamath-aimo-progress-prize", "title": { "en": "NuminaMath wins the first AIMO Progress Prize with an open tool-using math model", "zh-CN": "NuminaMath 以开放工具型数学模型赢得首届 AIMO Progress Prize" }, "dates": { "event": "2024-07-11", "first_public_claim": "2024-07-11", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "competition", "system" ], "significance": { "tier": "H2", "rationale": { "en": "NuminaMath showed that a relatively small open model plus tool-integrated reasoning and carefully curated math data could win a public math-AI competition.", "zh-CN": "NuminaMath 展示了较小规模的开放模型配合工具集成推理与高质量数学数据，也能在公开 AI 数学竞赛中取得领先。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "numeric", "hybrid" ], "claim": { "en": "NuminaMath-7B-TIR won the first AIMO Progress Prize by solving 29 of 50 problems on the private test set.", "zh-CN": "NuminaMath-7B-TIR 在私有测试集 50 道题中解出 29 道，赢得首届 AIMO Progress Prize。" }, "summary": { "en": "The winning system fine-tuned DeepSeekMath-Base 7B and combined chain-of-thought with Python tool execution, self-consistency and internal validation sets.", "zh-CN": "获胜系统在 DeepSeekMath-Base 7B 上微调，并结合思维链、Python 工具执行、自一致性与内部验证集。" }, "why_it_matters": { "en": "It provided an open and reproducible counterpoint to closed frontier math systems and helped popularize tool-integrated math reasoning.", "zh-CN": "它为封闭前沿数学系统提供了开放可复现的对照，并推动工具集成数学推理进入主流。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model generates reasoning and invokes Python during inference to solve competition problems.", "zh-CN": "模型在推理过程中生成解题步骤并调用 Python 求解竞赛问题。" } }, "human_contribution": { "description": { "en": "The Numina and Hugging Face teams curated training data, designed TIR decoding and tuned the competition system.", "zh-CN": "Numina 与 Hugging Face 团队整理训练数据、设计 TIR 解码并调优竞赛系统。" } }, "systems": [ "numinamath" ], "organizations": [ "numina", "hugging-face" ], "people": [], "problems": [ "aimo-progress-prize" ], "methods": [ "tool-integrated-reasoning", "self-consistency", "fine-tuning" ], "verification": { "evidence_level": "E3", "status": "partially_verified", "formal_assurance": "artifact_available", "history": [ { "date": "2024-07-11", "status": "partially_verified", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "partially_verified", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "huggingface-numinamath-aimo-2024", "tier": "S2", "type": "official_announcement", "title": "How NuminaMath Won the 1st AIMO Progress Prize", "url": "https://huggingface.co/blog/winning-aimo-progress-prize", "primary": true, "published_date": "2024-07-11", "accessed_at": "2026-09-10" }, { "id": "github-numinamath-aimo", "tier": "S1", "type": "repository", "title": "Numina solution to the first AIMO Progress Prize", "url": "https://github.com/project-numina/aimo-progress-prize", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "numinamath-aimo-repository", "kind": "code", "title": "NuminaMath winning-solution training and inference code", "url": "https://github.com/project-numina/aimo-progress-prize" } ], "relationships": { "predecessors": [ "evt-2024-deepseekmath", "evt-2023-tora" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "aimo", "open-model", "tool-use", "competition" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-lean-workbook", "slug": "lean-workbook-synthetic-formalization-dataset", "title": { "en": "Lean Workbook releases a large formal-informal mathematics dataset", "zh-CN": "Lean Workbook 发布大规模形式—非形式数学数据集" }, "dates": { "event": "2024-06-06", "first_public_claim": "2024-06-06", "paper_release": "2024-06-06", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "dataset", "formalization", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Lean Workbook expanded the supply of paired natural-language and Lean problems for training autoformalizers and provers.", "zh-CN": "Lean Workbook 扩大了自然语言数学与 Lean 形式问题配对数据的规模，为自动形式化和证明训练提供资源。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "Lean Workbook released about 57,000 formal-informal question pairs together with searched proofs and 21 new IMO questions.", "zh-CN": "Lean Workbook 发布约 57,000 个形式—非形式问题对、搜索得到的证明以及 21 道新的 IMO 题目。" }, "summary": { "en": "An iterative generation-and-filtering pipeline translates natural-language math problems to Lean 4 statements and back.", "zh-CN": "迭代式生成与过滤管线把自然语言数学问题翻译为 Lean 4 陈述，并进行反向转换。" }, "why_it_matters": { "en": "The dataset lowered a key bottleneck for training larger Lean provers: the scarcity of aligned formal and informal mathematics.", "zh-CN": "该数据集缓解了训练大型 Lean 证明器的关键瓶颈——形式与非形式数学对齐数据稀缺。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Models participate in synthetic translation and proof search used to construct the dataset.", "zh-CN": "模型参与用于构建数据集的合成翻译与证明搜索。" } }, "human_contribution": { "description": { "en": "Researchers designed the iterative data pipeline, filtering criteria and release.", "zh-CN": "研究者设计迭代数据管线、过滤标准与公开发布。" } }, "systems": [ "lean-workbook", "lean" ], "organizations": [ "shanghai-ai-laboratory" ], "people": [], "problems": [ "formalization-data" ], "methods": [ "synthetic-data", "autoformalization", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-06-06", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-lean-workbook-2406.03847", "tier": "S1", "type": "paper", "title": "Lean Workbook: A large-scale Lean problem set formalized from natural language math problems", "url": "https://arxiv.org/abs/2406.03847", "primary": true, "published_date": "2024-06-06", "accessed_at": "2026-09-10" }, { "id": "huggingface-lean-workbook", "tier": "S1", "type": "dataset", "title": "Lean Workbook dataset release", "url": "https://huggingface.co/datasets/internlm/Lean-Workbook", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "lean-workbook-dataset", "kind": "dataset", "title": "Lean Workbook formal-informal dataset", "url": "https://huggingface.co/datasets/internlm/Lean-Workbook" } ], "relationships": { "predecessors": [ "evt-2023-proofnet", "evt-2024-deepseek-prover-v1" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "dataset", "autoformalization", "synthetic-data" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-deepseek-prover-v1", "slug": "deepseek-prover-synthetic-lean-data", "title": { "en": "DeepSeek-Prover scales Lean theorem proving with millions of synthetic formal statements", "zh-CN": "DeepSeek-Prover 用数百万合成形式命题扩展 Lean 定理证明" }, "dates": { "event": "2024-05-23", "first_public_claim": "2024-05-23", "paper_release": "2024-05-23", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "system", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "DeepSeek-Prover demonstrated that large-scale synthetic Lean data could materially raise whole-proof generation performance.", "zh-CN": "DeepSeek-Prover 展示了大规模合成 Lean 数据能够显著提升整段形式证明生成能力。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "DeepSeek-Prover trained on a synthetic corpus containing about eight million formal statements with proofs and reported 52% cumulative accuracy on Lean 4 miniF2F plus five FIMO proofs.", "zh-CN": "DeepSeek-Prover 在包含约 800 万条带证明形式命题的合成语料上训练，并报告 Lean 4 miniF2F 累计 52% 的证明率以及 5 道 FIMO 证明。" }, "summary": { "en": "Natural-language competition problems are translated into Lean statements, filtered, proved and recycled as synthetic training data.", "zh-CN": "自然语言竞赛题被翻译为 Lean 陈述、过滤、搜索证明，再作为合成训练数据回流。" }, "why_it_matters": { "en": "The work established synthetic formal-data generation as a scalable route to stronger neural theorem provers.", "zh-CN": "该工作确立了“合成形式数据生成”作为扩展神经定理证明器的重要路线。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Models generate formal statements and whole proofs that Lean checks mechanically.", "zh-CN": "模型生成形式命题与整段证明，由 Lean 进行机械检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the translation, filtering, proof-generation and training pipeline.", "zh-CN": "研究者设计翻译、过滤、证明生成与训练管线。" } }, "systems": [ "deepseek-prover", "lean" ], "organizations": [ "deepseek" ], "people": [], "problems": [ "minif2f", "fimo" ], "methods": [ "synthetic-data", "whole-proof-generation", "lean" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2024-05-23", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-deepseek-prover-2405.14333", "tier": "S1", "type": "paper", "title": "DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data", "url": "https://arxiv.org/abs/2405.14333", "primary": true, "published_date": "2024-05-23", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2024-deepseekmath", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "synthetic-data", "formal-proof", "deepseek" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-olympiadbench", "slug": "olympiadbench-bilingual-multimodal", "title": { "en": "OlympiadBench scales Olympiad-level evaluation to bilingual multimodal science", "zh-CN": "OlympiadBench 将奥赛级评测扩展到双语多模态科学问题" }, "dates": { "event": "2024-02-21", "first_public_claim": "2024-02-21", "paper_release": "2024-02-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "OlympiadBench provided a large bilingual benchmark that combined mathematics, physics and multimodal problem statements at Olympiad difficulty.", "zh-CN": "OlympiadBench 提供大规模双语奥赛级基准，把数学、物理和多模态题目结合起来。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric" ], "claim": { "en": "OlympiadBench introduced 8,476 bilingual multimodal Olympiad-level math and physics problems with expert step-by-step annotations.", "zh-CN": "OlympiadBench 引入 8,476 道双语多模态奥赛级数学与物理问题，并提供专家逐步推理标注。" }, "summary": { "en": "The benchmark was designed to remain difficult for frontier text and multimodal models and includes detailed evaluation methodology.", "zh-CN": "该基准面向前沿文本与多模态模型保持较高难度，并提供细致的评测方法。" }, "why_it_matters": { "en": "It broadened AI4Math evaluation beyond English text-only competition problems.", "zh-CN": "它把 AI4Math 评测从英语纯文本竞赛题扩展到双语与多模态场景。" }, "ai_role": { "level": "computation_only", "description": { "en": "Language and multimodal models are evaluated on the benchmark.", "zh-CN": "语言模型与多模态模型在该基准上接受评测。" } }, "human_contribution": { "description": { "en": "Researchers curated problems, annotations and evaluation rules.", "zh-CN": "研究者整理题目、专家标注与评测规则。" } }, "systems": [ "olympiadbench" ], "organizations": [ "tsinghua-university", "openbmb" ], "people": [], "problems": [ "olympiad-mathematics", "olympiad-physics" ], "methods": [ "benchmarking", "multimodal-evaluation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-02-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-olympiadbench-2402.14008", "tier": "S1", "type": "paper", "title": "OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems", "url": "https://arxiv.org/abs/2402.14008", "primary": true, "published_date": "2024-02-21", "accessed_at": "2026-09-10" }, { "id": "github-olympiadbench", "tier": "S1", "type": "repository", "title": "OlympiadBench dataset and evaluation repository", "url": "https://github.com/OpenBMB/OlympiadBench", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "olympiadbench-repository", "kind": "dataset", "title": "OlympiadBench dataset and evaluation code", "url": "https://github.com/OpenBMB/OlympiadBench" } ], "relationships": { "predecessors": [ "evt-2021-math-benchmark", "evt-2022-minerva" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "olympiad", "bilingual", "multimodal" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-internlm-math", "slug": "internlm-math-verifiable-reasoning", "title": { "en": "InternLM-Math unifies informal, tool-assisted and formal mathematical reasoning", "zh-CN": "InternLM-Math 统一非形式、工具辅助与形式数学推理" }, "dates": { "event": "2024-02-09", "first_public_claim": "2024-02-09", "paper_release": "2024-02-09", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "InternLM-Math explored a single open model family spanning chain-of-thought, verification, code assistance and Lean theorem proving.", "zh-CN": "InternLM-Math 探索用同一开放模型族覆盖思维链、验证、代码辅助与 Lean 定理证明。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "formal", "symbolic", "numeric", "hybrid" ], "claim": { "en": "InternLM-Math reported open-source state-of-the-art results across several math benchmarks and a 30.3% miniF2F score from its pretrained model without theorem-proving fine-tuning.", "zh-CN": "InternLM-Math 在多项数学基准上报告开放模型领先结果，其预训练模型在未进行定理证明专项微调时于 miniF2F 达到 30.3%。" }, "summary": { "en": "The project encodes reasoning, reward modeling, formal tasks, data augmentation and code-interpreter behavior in a unified sequence-to-sequence format.", "zh-CN": "项目把推理、奖励建模、形式任务、数据增强与代码解释器行为统一到序列到序列格式。" }, "why_it_matters": { "en": "It represented a move toward general-purpose mathematical models that can switch between natural language, code and proof-assistant interfaces.", "zh-CN": "它代表了面向通用数学模型的方向：模型能够在自然语言、代码和证明助手接口之间切换。" }, "ai_role": { "level": "computation_only", "description": { "en": "The model acts as reasoner, verifier, prover and data augmenter across several interfaces.", "zh-CN": "模型在多种接口下充当推理器、验证器、证明器与数据增强器。" } }, "human_contribution": { "description": { "en": "Researchers unified the training tasks, curated data and open-sourced models, code and data.", "zh-CN": "研究者统一训练任务、整理数据并开放模型、代码与数据。" } }, "systems": [ "internlm-math" ], "organizations": [ "shanghai-ai-laboratory" ], "people": [], "problems": [ "minif2f", "math-benchmark" ], "methods": [ "multi-task-learning", "code-interpreter", "formal-reasoning" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-02-09", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-internlm-math-2402.06332", "tier": "S1", "type": "paper", "title": "InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning", "url": "https://arxiv.org/abs/2402.06332", "primary": true, "published_date": "2024-02-09", "accessed_at": "2026-09-10" }, { "id": "github-internlm-math", "tier": "S1", "type": "repository", "title": "InternLM-Math models, evaluation code and formal-math resources", "url": "https://github.com/InternLM/InternLM-Math", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "internlm-math-repository", "kind": "code", "title": "InternLM-Math models and evaluation resources", "url": "https://github.com/InternLM/InternLM-Math" } ], "relationships": { "predecessors": [ "evt-2023-llemma", "evt-2024-deepseekmath" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "open-model", "lean", "verifier", "code-interpreter" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-deepseekmath", "slug": "deepseekmath-grpo-open-math-model", "title": { "en": "DeepSeekMath couples large-scale math pretraining with GRPO", "zh-CN": "DeepSeekMath 将大规模数学预训练与 GRPO 结合" }, "dates": { "event": "2024-02-05", "first_public_claim": "2024-02-05", "paper_release": "2024-02-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "DeepSeekMath paired a strong open mathematical corpus pipeline with GRPO, a reinforcement-learning method that later became influential in reasoning-model training.", "zh-CN": "DeepSeekMath 将高质量开放数学语料管线与 GRPO 强化学习结合，后者随后成为推理模型训练中的重要方法。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "DeepSeekMath-7B reached 51.7% on MATH without external tools or voting and introduced Group Relative Policy Optimization (GRPO).", "zh-CN": "DeepSeekMath-7B 在不使用外部工具或投票的情况下于 MATH 达到 51.7%，并提出 Group Relative Policy Optimization（GRPO）。" }, "summary": { "en": "The model continued pretraining on 120B math-related tokens and then used supervised and reinforcement-learning stages for mathematical reasoning.", "zh-CN": "该模型在 120B 数学相关 token 上继续预训练，再通过监督与强化学习阶段提升数学推理。" }, "why_it_matters": { "en": "It linked open math-model scaling with a verifier-friendly RL recipe that influenced subsequent reasoning systems.", "zh-CN": "它把开放数学模型扩展与适合可验证任务的强化学习方法连接起来，并影响了后续推理系统。" }, "ai_role": { "level": "computation_only", "description": { "en": "The trained model performs competition-level mathematical reasoning.", "zh-CN": "训练后的模型执行竞赛级数学推理。" } }, "human_contribution": { "description": { "en": "Researchers built the data pipeline, model training recipe and GRPO optimization method.", "zh-CN": "研究者构建数据管线、模型训练方案与 GRPO 优化方法。" } }, "systems": [ "deepseekmath" ], "organizations": [ "deepseek" ], "people": [], "problems": [ "math-benchmark" ], "methods": [ "grpo", "continued-pretraining", "reinforcement-learning" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-02-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-deepseekmath-2402.03300", "tier": "S1", "type": "paper", "title": "DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models", "url": "https://arxiv.org/abs/2402.03300", "primary": true, "published_date": "2024-02-05", "accessed_at": "2026-09-10" }, { "id": "github-deepseek-math", "tier": "S1", "type": "repository", "title": "DeepSeekMath code, evaluation and model release repository", "url": "https://github.com/deepseek-ai/DeepSeek-Math", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "deepseekmath-repository", "kind": "code", "title": "DeepSeekMath evaluation code and model links", "url": "https://github.com/deepseek-ai/DeepSeek-Math" } ], "relationships": { "predecessors": [ "evt-2023-llemma", "evt-2023-math-shepherd" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "deepseek", "grpo", "open-model", "math-reasoning" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2024-alphageometry", "slug": "alphageometry-olympiad-geometry", "title": { "en": "AlphaGeometry reaches near gold-medallist performance on olympiad geometry benchmark", "zh-CN": "AlphaGeometry 在奥林匹克几何基准上达到接近金牌选手的表现" }, "dates": { "event": "2024-01-17", "first_public_claim": "2024-01-17", "paper_release": "2024-01-17", "artifact_release": "2024-01-17", "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "system", "benchmark" ], "significance": { "tier": "H2", "rationale": { "en": "AlphaGeometry sharply improved automated performance on a curated olympiad-geometry benchmark and provided a prominent neuro-symbolic example of synthetic-data-driven theorem proving.", "zh-CN": "AlphaGeometry 在精选奥赛几何基准上显著提升自动定理证明表现，并成为合成数据驱动的神经符号定理证明的重要案例。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "symbolic", "hybrid" ], "claim": { "en": "On IMO-AG-30, a benchmark of 30 translated olympiad-level geometry problems, AlphaGeometry solved 25 problems versus 10 for the previous reported best method, approaching the estimated average performance of an IMO gold medallist on the same set.", "zh-CN": "在由 30 道经翻译的奥赛级几何题组成的 IMO-AG-30 基准上，AlphaGeometry 解出 25 题，而论文所述此前最佳方法解出 10 题；其表现接近同一题集上 IMO 金牌选手的估计平均水平。" }, "summary": { "en": "AlphaGeometry combines a neural language model trained on synthetic theorem/proof data with a symbolic deduction engine. The language model proposes auxiliary constructions and the symbolic engine checks deductions.", "zh-CN": "AlphaGeometry 将基于合成定理与证明数据训练的神经语言模型同符号推理引擎结合；语言模型提出辅助构造，符号引擎检查推导。" }, "why_it_matters": { "en": "It showed that synthetic data plus neuro-symbolic search could overcome a scarcity of human formalized geometry proofs and produce machine-checkable, human-readable olympiad-style solutions.", "zh-CN": "它展示了合成数据与神经符号搜索可以绕开人工形式化几何证明稀缺的问题，并生成可机器检查、也可供人阅读的奥赛风格解答。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The learned model proposed proof-relevant constructions while the symbolic engine performed rule-bound deductions and checked the resulting proof structure.", "zh-CN": "学习模型提出与证明相关的构造，符号引擎执行规则约束下的推导并检查所得证明结构。" } }, "human_contribution": { "description": { "en": "Researchers built the geometry representation, symbolic engines, synthetic-data pipeline, model and evaluation benchmark; human experts also evaluated selected outputs.", "zh-CN": "研究人员构建几何表示、符号引擎、合成数据流程、模型与评测基准，并由人类专家评估部分输出。" } }, "systems": [ "alphageometry" ], "organizations": [ "google-deepmind", "new-york-university" ], "people": [ "trieu-h-trinh", "yuhuai-wu", "quoc-v-le", "he-he", "thang-luong" ], "problems": [ "imo-ag-30" ], "methods": [ "neuro-symbolic-reasoning", "synthetic-data", "theorem-proving" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2024-01-17", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Nature paper, supplementary solutions, source data, and an official code/model release were available.", "zh-CN": "Nature 论文、补充解答、源数据以及官方代码/模型发布均已公开。" } } ] }, "sources": [ { "id": "nature-alphageometry-2024", "tier": "S1", "type": "paper", "title": "Solving olympiad geometry without human demonstrations", "url": "https://www.nature.com/articles/s41586-023-06747-5", "primary": true, "published_date": "2024-01-17", "accessed_at": "2026-09-10" }, { "id": "deepmind-alphageometry-2024", "tier": "S2", "type": "official_announcement", "title": "AlphaGeometry — An Olympiad-level AI system for geometry", "url": "https://deepmind.google/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/", "primary": false, "published_date": "2024-01-17", "accessed_at": "2026-09-10" }, { "id": "github-alphageometry", "tier": "S1", "type": "repository", "title": "google-deepmind/alphageometry", "url": "https://github.com/google-deepmind/alphageometry", "primary": true, "published_date": "2024-01-17", "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "alphageometry-code", "kind": "code", "title": "AlphaGeometry source code and model repository", "url": "https://github.com/google-deepmind/alphageometry" } ], "relationships": { "predecessors": [], "successors": [ "evt-2024-alphaproof-alphageometry2-imo" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "geometry", "olympiad", "theorem-proving", "neuro-symbolic", "synthetic-data" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-funsearch-cap-set", "slug": "funsearch-mathematical-discovery", "title": { "en": "FunSearch reports new cap-set constructions with LLM-guided program search", "zh-CN": "FunSearch 通过 LLM 引导的程序搜索报告新的 cap set 构造" }, "dates": { "event": "2023-12-14", "first_public_claim": "2023-12-14", "paper_release": "2023-12-14", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H1", "rationale": { "en": "The Nature paper demonstrated an LLM-based search loop producing improved constructions for an established extremal-combinatorics problem, making it a useful early reference point for AI-assisted mathematical discovery.", "zh-CN": "Nature 论文展示了基于 LLM 的搜索闭环在一个既有极值组合问题上产生改进构造，是 AI 辅助数学发现的重要早期参照点。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "numeric" ], "claim": { "en": "FunSearch found cap-set constructions exceeding previously known constructions in finite-dimensional and asymptotic settings, and also found improved heuristics for online bin packing.", "zh-CN": "FunSearch 在有限维与渐近情形中找到超过此前已知结果的 cap set 构造，并在在线装箱问题上找到改进启发式算法。" }, "summary": { "en": "Google DeepMind paired a pretrained language model with an evaluator and evolutionary program search. The resulting system searched over executable programs rather than directly emitting final mathematical answers.", "zh-CN": "Google DeepMind 将预训练语言模型、评估器与进化式程序搜索结合，让系统搜索可执行程序，而不是直接生成最终数学答案。" }, "why_it_matters": { "en": "The result supplied a concrete, checkable example of LLM-generated code participating in a search process that improved the known solution landscape of an established mathematical problem.", "zh-CN": "该结果提供了一个可检查的具体案例：LLM 生成的代码参与系统化搜索，并改进了一个既有数学问题的已知解空间。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The language model generated candidate programs inside an automated evolutionary loop, while deterministic evaluators selected and scored candidates.", "zh-CN": "语言模型在自动化进化搜索闭环中生成候选程序，确定性的评估器负责筛选与评分。" } }, "human_contribution": { "description": { "en": "Researchers designed the search procedure and evaluators, chose the mathematical tasks and representations, interpreted the discovered programs, and authored the scientific analysis.", "zh-CN": "研究人员设计搜索流程与评估器，选择数学任务和表示方式，解释发现的程序，并完成科学分析。" } }, "systems": [ "funsearch" ], "organizations": [ "google-deepmind" ], "people": [ "alhussein-fawzi", "bernardino-romera-paredes" ], "problems": [ "cap-set-problem", "online-bin-packing" ], "methods": [ "large-language-models", "evolutionary-search", "program-search" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2023-12-14", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Peer-reviewed Nature article and official institutional announcement were public.", "zh-CN": "经同行评审的 Nature 论文与机构官方公告已公开。" } } ] }, "sources": [ { "id": "nature-funsearch-2023", "tier": "S1", "type": "paper", "title": "Mathematical discoveries from program search with large language models", "url": "https://www.nature.com/articles/s41586-023-06924-6", "primary": true, "published_date": "2023-12-14", "accessed_at": "2026-09-10" }, { "id": "deepmind-funsearch-2023", "tier": "S2", "type": "official_announcement", "title": "FunSearch — Making new discoveries in mathematical sciences using Large Language Models", "url": "https://deepmind.google/blog/funsearch-making-new-discoveries-in-mathematical-sciences-using-large-language-models/", "primary": false, "published_date": "2023-12-14", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mathematical-discovery", "combinatorics", "program-search", "llm" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-math-shepherd", "slug": "math-shepherd-process-reward-model", "title": { "en": "Math-Shepherd automates step-level process supervision for math reasoning", "zh-CN": "Math-Shepherd 自动化数学推理的步骤级过程监督" }, "dates": { "event": "2023-12-14", "first_public_claim": "2023-12-14", "paper_release": "2023-12-14", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "Math-Shepherd made process reward modeling more scalable by generating step-level supervision without manual annotation.", "zh-CN": "Math-Shepherd 通过自动生成步骤级监督降低人工标注依赖，使过程奖励模型更容易扩展。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Math-Shepherd trained a process reward model from automatically constructed step-wise supervision and improved both reranking and reinforcement-learning performance on GSM8K and MATH.", "zh-CN": "Math-Shepherd 使用自动构造的步骤级监督训练过程奖励模型，并在 GSM8K 与 MATH 上同时提升重排序与强化学习效果。" }, "summary": { "en": "The verifier scores intermediate reasoning steps rather than only final answers and can be used for selection or reinforcement learning.", "zh-CN": "该验证器对中间推理步骤评分，而非只判断最终答案，并可用于候选选择或强化学习。" }, "why_it_matters": { "en": "Process-level verification became a central ingredient in the later generation of reasoning models and verifier-guided math systems.", "zh-CN": "步骤级验证后来成为推理模型和验证器引导数学系统的重要组成部分。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "A learned verifier judges intermediate reasoning steps and supplies selection or training signals.", "zh-CN": "学习式验证器判断中间推理步骤，并提供选择或训练信号。" } }, "human_contribution": { "description": { "en": "Researchers designed automatic supervision construction, reward modeling and evaluation.", "zh-CN": "研究者设计自动监督构造、奖励建模与评测。" } }, "systems": [ "math-shepherd" ], "organizations": [ "peking-university", "deepseek" ], "people": [], "problems": [ "gsm8k", "math-benchmark" ], "methods": [ "process-reward-model", "reinforcement-learning", "verification" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2023-12-14", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-math-shepherd-2312.08935", "tier": "S1", "type": "paper", "title": "Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations", "url": "https://arxiv.org/abs/2312.08935", "primary": true, "published_date": "2023-12-14", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2023-tora", "evt-2023-llemma" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "process-reward-model", "verifier", "reinforcement-learning", "math-reasoning" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-llemma", "slug": "llemma-open-math-language-model", "title": { "en": "Llemma releases open language models and data specialized for mathematics", "zh-CN": "Llemma 发布面向数学的开放语言模型与训练数据" }, "dates": { "event": "2023-10-16", "first_public_claim": "2023-10-16", "paper_release": "2023-10-16", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "system", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "Llemma established a reproducible open math-language-model stack, including model weights, Proof-Pile-2 and training code.", "zh-CN": "Llemma 建立了可复现的开放数学语言模型栈，包括模型权重、Proof-Pile-2 与训练代码。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "formal", "symbolic" ], "claim": { "en": "Llemma released 7B and 34B math-specialized models that outperformed known open base models on MATH and showed tool-use and formal-proof capabilities without task-specific fine-tuning.", "zh-CN": "Llemma 发布 7B 与 34B 数学专用模型，在 MATH 上超过当时已知开放基础模型，并在无任务专项微调下展示工具使用与形式证明能力。" }, "summary": { "en": "The project continued pretraining Code Llama on Proof-Pile-2, a mixture of mathematical web text, scientific papers and mathematical code.", "zh-CN": "该项目在 Proof-Pile-2 上继续预训练 Code Llama；该语料混合数学网页、科学论文与数学代码。" }, "why_it_matters": { "en": "It gave the community an open base model and corpus for studying how mathematical specialization transfers across informal, tool and formal settings.", "zh-CN": "它为社区提供开放基础模型与语料，支持研究数学专项预训练如何迁移到非形式推理、工具使用和形式证明。" }, "ai_role": { "level": "computation_only", "description": { "en": "The trained models perform mathematical reasoning, tool use and formal proof generation.", "zh-CN": "训练后的模型执行数学推理、工具使用与形式证明生成。" } }, "human_contribution": { "description": { "en": "Researchers assembled Proof-Pile-2, continued pretraining the models and released the full artifacts.", "zh-CN": "研究者构建 Proof-Pile-2、继续预训练模型并公开完整产物。" } }, "systems": [ "llemma" ], "organizations": [ "eleutherai", "princeton-university" ], "people": [], "problems": [ "math-benchmark" ], "methods": [ "continued-pretraining", "math-corpus", "language-model" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-10-16", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-llemma-2310.10631", "tier": "S1", "type": "paper", "title": "Llemma: An Open Language Model For Mathematics", "url": "https://arxiv.org/abs/2310.10631", "primary": true, "published_date": "2023-10-16", "accessed_at": "2026-09-10" }, { "id": "github-eleutherai-math-lm", "tier": "S1", "type": "repository", "title": "Llemma models, Proof-Pile-2 data and training code repository", "url": "https://github.com/EleutherAI/math-lm", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "llemma-math-lm-repository", "kind": "code", "title": "Llemma code, model and Proof-Pile-2 data links", "url": "https://github.com/EleutherAI/math-lm" } ], "relationships": { "predecessors": [ "evt-2022-minerva", "evt-2021-math-benchmark" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "open-model", "math-language-model", "proof-pile-2", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-copra", "slug": "copra-in-context-formal-proof-agent", "title": { "en": "COPRA turns a general LLM into a stateful formal proof-search agent", "zh-CN": "COPRA 将通用大模型转化为有状态的形式证明搜索 Agent" }, "dates": { "event": "2023-10-06", "first_public_claim": "2023-10-06", "paper_release": "2023-10-06", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "formalization", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "COPRA was an early explicit agentic theorem-proving design in which a general-purpose LLM repeatedly acted inside Lean or Coq, consumed proof-assistant feedback and backtracked through a maintained search state rather than answering in one shot.", "zh-CN": "COPRA 是较早明确采用 Agent 结构的定理证明系统之一：通用大模型反复在 Lean 或 Coq 中行动，读取证明助手反馈并维护可回溯的搜索状态，而不是一次性生成答案。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "COPRA used GPT-4 in a stateful backtracking loop with proof-environment feedback and retrieval, outperforming few-shot GPT-4 and reporting competitive results against finetuned provers on Lean miniF2F while also operating on Coq tasks.", "zh-CN": "COPRA 将 GPT-4 置于带证明环境反馈、检索和回溯机制的有状态循环中；论文报告其明显优于 few-shot GPT-4，并在 Lean miniF2F 上与微调证明器竞争，同时还能处理 Coq 任务。" }, "summary": { "en": "At each step the agent proposed a tactic, executed it in the proof assistant, incorporated errors or new goals into the next prompt and maintained a search history for backtracking. The architecture showed how a frontier general model could be wrapped in a proof-oriented agent harness without task-specific finetuning.", "zh-CN": "Agent 在每一步提出战术、在证明助手中执行，将错误或新的目标写回下一轮提示，并维护搜索历史以支持回溯。该架构展示了无需针对任务专门微调，也能把前沿通用模型封装为证明导向 Agent。" }, "why_it_matters": { "en": "COPRA made the proof assistant an interactive environment for an LLM agent, anticipating the generate-execute-observe-revise loop that later became central to formal mathematical agents.", "zh-CN": "COPRA 把证明助手变成 LLM Agent 的交互环境，提前体现了后来形式数学 Agent 中核心的“生成—执行—观察—修订”循环。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "GPT-4 proposed tactics and navigated the proof search, while Lean or Coq checked each accepted proof action mechanically.", "zh-CN": "GPT-4 提出战术并推进证明搜索，Lean 或 Coq 对每个被接受的证明动作进行机械检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the agent state, retrieval, backtracking and prompting protocol, selected benchmarks and built the interfaces to the proof assistants.", "zh-CN": "研究者设计 Agent 状态、检索、回溯与提示协议，选择基准并构建与证明助手之间的接口。" } }, "systems": [ "copra", "gpt-4", "lean", "coq" ], "organizations": [ "university-of-texas-at-austin" ], "people": [ "amitayush-thakur", "george-tsoukalas", "yeming-wen", "jimmy-xin", "swarat-chaudhuri" ], "problems": [ "minif2f", "compcert" ], "methods": [ "agentic-proof-search", "in-context-learning", "backtracking", "retrieval", "proof-assistant-feedback" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-10-06", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The authors released the paper describing the agent and its Lean and Coq evaluations.", "zh-CN": "作者公开论文，说明 Agent 设计以及 Lean 与 Coq 评测。" } }, { "date": "2023-10-06", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Code and experiment infrastructure were made available in the public COPRA repository.", "zh-CN": "代码与实验基础设施通过公开 COPRA 仓库提供。" } } ] }, "sources": [ { "id": "arxiv-copra-2310.04353", "tier": "S1", "type": "paper", "title": "An In-Context Learning Agent for Formal Theorem-Proving", "url": "https://arxiv.org/abs/2310.04353", "primary": true, "published_date": "2023-10-06", "accessed_at": "2026-09-10" }, { "id": "github-trishullab-copra", "tier": "S1", "type": "repository", "title": "COPRA repository", "url": "https://github.com/trishullab/copra", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "copra-repository", "kind": "code", "title": "COPRA formal theorem-proving agent", "url": "https://github.com/trishullab/copra" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f", "evt-2021-minif2f" ], "successors": [ "evt-2024-deepseek-prover-v1-5", "evt-2026-alphaproof-nexus" ], "related": [ "evt-2023-leandojo" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "agent", "theorem-proving", "lean", "coq", "gpt-4", "proof-feedback", "backtracking" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-mathvista", "slug": "mathvista-visual-math-benchmark", "title": { "en": "MathVista establishes a benchmark for mathematical reasoning in visual contexts", "zh-CN": "MathVista 建立视觉场景中的数学推理评测基准" }, "dates": { "event": "2023-10-03", "first_public_claim": "2023-10-03", "paper_release": "2023-10-03", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "MathVista made mathematical reasoning in visual contexts a dedicated evaluation target, consolidating diagrams, charts, geometry, scientific figures and other multimodal tasks into a large benchmark before multimodal mathematical evaluation became a standard capability axis.", "zh-CN": "MathVista 将视觉场景中的数学推理确立为独立评测目标，把图表、几何图形、科学图像等多模态任务整合成大规模基准，早于多模态数学评测成为通用能力维度。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric" ], "claim": { "en": "MathVista introduced 6,141 visual mathematical-reasoning examples drawn from 28 existing multimodal datasets and three newly created datasets, and used them to systematically evaluate 12 foundation models across mathematical and visual task types.", "zh-CN": "MathVista 引入 6,141 个视觉数学推理样例，来源包括 28 个既有多模态数据集和 3 个新建数据集，并据此系统评测 12 个基础模型在不同数学与视觉任务上的能力。" }, "summary": { "en": "The benchmark combines visual perception with compositional mathematical reasoning. The initial study found a substantial gap between frontier multimodal models and human performance, while the public project provides dataset access, evaluation code and model-result tooling.", "zh-CN": "该基准把视觉感知与组合式数学推理结合起来。初始研究显示前沿多模态模型与人类表现之间仍有明显差距，公开项目同时提供数据访问、评测代码与模型结果工具。" }, "why_it_matters": { "en": "It broadened AI4Math evaluation beyond text-only word problems and formal statements, creating a reference point for later multimodal and Olympiad-level benchmarks that require models to reason over mathematical information embedded in images.", "zh-CN": "它把 AI4Math 评测从纯文本文字题和形式陈述扩展到图像中承载的数学信息，为后续多模态与奥赛级评测提供了重要参照。" }, "ai_role": { "level": "computation_only", "description": { "en": "Language and multimodal foundation models were evaluated on visual mathematical-reasoning tasks; the benchmark itself was curated and designed by researchers.", "zh-CN": "语言模型与多模态基础模型在视觉数学推理任务上接受评测；基准的数据整理与设计由研究者完成。" } }, "human_contribution": { "description": { "en": "Researchers assembled and normalized datasets, created new visual reasoning tasks, defined the taxonomy and evaluation protocol, and manually analyzed model failure modes and human baselines.", "zh-CN": "研究者整理并规范化数据集、创建新的视觉推理任务、定义分类与评测协议，并人工分析模型失败模式和人类基线。" } }, "systems": [ "mathvista" ], "organizations": [], "people": [ "pan-lu", "hritik-bansal", "tony-xia", "jiacheng-liu" ], "problems": [ "visual-mathematical-reasoning" ], "methods": [ "multimodal-evaluation", "benchmarking", "visual-reasoning" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-10-03", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced MathVista and its initial evaluation of foundation models.", "zh-CN": "arXiv 研究记录公开 MathVista，并报告其对基础模型的初始评测。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public MathVista repository and project site expose benchmark data access and evaluation tooling. E3 records artifact-level inspectability rather than independent verification of every reported score.", "zh-CN": "公开的 MathVista 仓库与项目页面提供基准数据访问和评测工具。E3 表示产物层级可检查，并不等同于所有报告分数都已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-mathvista-2310.02255", "tier": "S1", "type": "paper", "title": "MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts", "url": "https://arxiv.org/abs/2310.02255", "primary": true, "published_date": "2023-10-03", "accessed_at": "2026-09-11" }, { "id": "mathvista-project", "tier": "S1", "type": "other", "title": "MathVista project page", "url": "https://mathvista.github.io/", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-mathvista", "tier": "S1", "type": "repository", "title": "MathVista benchmark repository", "url": "https://github.com/lupantech/MathVista", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "mathvista-repository", "kind": "dataset", "title": "MathVista dataset and evaluation code", "url": "https://github.com/lupantech/MathVista" } ], "relationships": { "predecessors": [ "evt-2021-math-benchmark" ], "successors": [ "evt-2024-olympiadbench" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "multimodal", "visual-reasoning", "math-reasoning", "dataset" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-lego-prover", "slug": "lego-prover-growing-library", "title": { "en": "LEGO-Prover grows a reusable library of machine-checked lemmas during proof search", "zh-CN": "LEGO-Prover 在证明过程中持续扩展可复用的机器检查引理库" }, "dates": { "event": "2023-10-01", "first_public_claim": "2023-10-01", "paper_release": "2023-10-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "LEGO-Prover made a growing library of reusable, machine-checked lemmas part of the proving loop itself, moving beyond fixed theorem libraries and one-off proof trajectories toward accumulated formal skills that can support later problems.", "zh-CN": "LEGO-Prover 把持续增长的可复用、机器检查引理库直接纳入证明循环，从固定定理库和一次性证明轨迹迈向能够为后续问题积累形式技能的路线。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "LEGO-Prover decomposed miniF2F problems into subgoal lemmas, retrieved or generated reusable skills, verified them with Isabelle through PISA and accumulated more than 20,000 skills in a growing library; the paper reported a 57.0% pass rate on miniF2F-valid and gains from the newly added skills.", "zh-CN": "LEGO-Prover 将 miniF2F 问题分解为子目标引理，检索或生成可复用技能，通过 PISA 调用 Isabelle 进行验证，并在增长式技能库中积累超过 20,000 个技能；论文报告 miniF2F-valid 通过率达到 57.0%，且新增技能能够带来性能提升。" }, "summary": { "en": "The system couples a prover and an evolver through a shared skill library. The prover constructs modular proofs from retrieved and newly generated lemmas, while the evolver transforms verified skills to increase their generality, reuse and complexity.", "zh-CN": "该系统通过共享技能库连接 prover 与 evolver：prover 利用检索到的和新生成的引理构造模块化证明，evolver 则对已验证技能进行变换，以提高其通用性、可复用性与复杂度。" }, "why_it_matters": { "en": "It provided an early concrete design for cumulative formal reasoning, where successful proof fragments become durable resources for future proof attempts rather than disappearing after a single theorem is solved.", "zh-CN": "它提供了较早的“累积式形式推理”具体设计：成功的证明片段不会在单个定理解决后消失，而是转化为后续证明可继续使用的持久资源。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Large language models proposed subgoal lemmas, proof blocks and skill transformations, while Isabelle mechanically checked formal code before skills were admitted to the reusable library.", "zh-CN": "大语言模型提出子目标引理、证明块和技能变换，Isabelle 则在技能进入可复用库之前对形式代码进行机械检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the prover/evolver architecture, skill-library lifecycle, retrieval and prompting procedures, integrated PISA and Isabelle, and evaluated the system on miniF2F.", "zh-CN": "研究者设计 prover/evolver 架构、技能库生命周期、检索与提示流程，集成 PISA 和 Isabelle，并在 miniF2F 上评测系统。" } }, "systems": [ "lego-prover", "isabelle", "pisa" ], "organizations": [], "people": [ "haiming-wang", "huajian-xin", "chuanyang-zheng", "zhengying-liu" ], "problems": [ "minif2f" ], "methods": [ "theorem-proving", "growing-skill-library", "lemma-generation", "retrieval", "modular-proof-construction" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-10-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The public research record introduced the growing verified-skill-library architecture and reported miniF2F evaluations.", "zh-CN": "公开研究记录提出增长式已验证技能库架构，并报告 miniF2F 评测结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The authors' public repository exposes the LEGO-Prover implementation, miniF2F integration and generated results. E3 records inspectability; it does not claim an independent replay of the reported experiments.", "zh-CN": "作者公开仓库提供 LEGO-Prover 实现、miniF2F 集成与生成结果。E3 表示产物可检查，并不表示论文实验已经获得独立重放。" } } ] }, "sources": [ { "id": "arxiv-lego-prover-2310.00656", "tier": "S1", "type": "paper", "title": "LEGO-Prover: Neural Theorem Proving with Growing Libraries", "url": "https://arxiv.org/abs/2310.00656", "primary": true, "published_date": "2023-10-01", "accessed_at": "2026-09-11" }, { "id": "github-lego-prover", "tier": "S1", "type": "repository", "title": "LEGO-Prover implementation and generated skills", "url": "https://github.com/wiio12/LEGO-Prover", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "iclr-lego-prover-2024", "tier": "S1", "type": "paper", "title": "LEGO-Prover: Neural Theorem Proving with Growing Libraries", "url": "https://proceedings.iclr.cc/paper_files/paper/2024/hash/85dca46374dc0f27b4bb5f265b3d17f0-Abstract-Conference.html", "primary": true, "published_date": "2024-05-07", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "lego-prover-repository", "kind": "code", "title": "LEGO-Prover code and generated theorem-proving resources", "url": "https://github.com/wiio12/LEGO-Prover" } ], "relationships": { "predecessors": [ "evt-2021-minif2f", "evt-2022-thor" ], "successors": [], "related": [ "evt-2023-leandojo", "evt-2023-copra" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "isabelle", "skill-library", "lemma-generation", "minif2f" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-tora", "slug": "tora-tool-integrated-math-reasoning", "title": { "en": "ToRA makes tool-integrated reasoning a competitive open math-agent paradigm", "zh-CN": "ToRA 将工具集成推理推进为有竞争力的开放数学 Agent 范式" }, "dates": { "event": "2023-09-29", "first_public_claim": "2023-09-29", "paper_release": "2023-09-29", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "ToRA demonstrated that language reasoning interleaved with executable tools could substantially improve difficult mathematical problem solving in open models.", "zh-CN": "ToRA 展示了自然语言推理与可执行工具交替使用能够显著提升开放模型的高难度数学求解能力。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic", "numeric", "hybrid" ], "claim": { "en": "ToRA-7B reached 44.6% on MATH and ToRA-Code-34B exceeded 50%, using trajectories that interleave reasoning with computational tools.", "zh-CN": "ToRA-7B 在 MATH 上达到 44.6%，ToRA-Code-34B 超过 50%，其推理轨迹交替使用自然语言推理与计算工具。" }, "summary": { "en": "The agents learn interactive tool-use trajectories involving computation libraries and symbolic solvers rather than relying on text-only chain-of-thought.", "zh-CN": "这些 Agent 学习调用计算库与符号求解器的交互轨迹，而不是仅依赖纯文本思维链。" }, "why_it_matters": { "en": "Tool-integrated reasoning became a reusable pattern for later math systems that need exact arithmetic or programmatic checking.", "zh-CN": "工具集成推理随后成为数学系统在需要精确计算或程序化检查时反复采用的设计模式。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model decides when to reason in language and when to call external computational tools.", "zh-CN": "模型自行决定何时进行语言推理、何时调用外部计算工具。" } }, "human_contribution": { "description": { "en": "Researchers curated tool-use trajectories, trained the agents and designed evaluations.", "zh-CN": "研究者构造工具调用轨迹、训练 Agent 并设计评测。" } }, "systems": [ "tora" ], "organizations": [ "microsoft-research", "tsinghua-university" ], "people": [], "problems": [ "math-benchmark" ], "methods": [ "tool-integrated-reasoning", "code-execution", "symbolic-tools" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-09-29", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-tora-2309.17452", "tier": "S1", "type": "paper", "title": "ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving", "url": "https://arxiv.org/abs/2309.17452", "primary": true, "published_date": "2023-09-29", "accessed_at": "2026-09-10" }, { "id": "github-microsoft-tora", "tier": "S1", "type": "repository", "title": "ToRA training, inference and evaluation repository", "url": "https://github.com/microsoft/ToRA", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "tora-repository", "kind": "code", "title": "ToRA code, evaluation outputs and model links", "url": "https://github.com/microsoft/ToRA" } ], "relationships": { "predecessors": [ "evt-2022-minerva", "evt-2021-math-benchmark" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "tool-use", "math-agent", "code-execution", "reasoning" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-ams-ai-advisory", "slug": "ams-ai-advisory-group", "title": { "en": "AMS establishes an AI advisory group for the mathematical community", "zh-CN": "AMS 建立面向数学共同体的 AI 咨询组" }, "dates": { "event": "2023-07-10", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The American Mathematical Society's 2023 Advisory Group on Artificial Intelligence and the Mathematical Community is a field-building milestone because it created a formal society-level mechanism specifically for AI's effects on mathematical research, publication, education and the profession. The group subsequently produced policy-oriented white papers on publishing, professional practice, education, equity and science policy, showing institutional follow-through rather than a temporary discussion response.", "zh-CN": "American Mathematical Society 于 2023 年建立的 Advisory Group on Artificial Intelligence and the Mathematical Community 构成领域建构里程碑，因为它以正式学会机制持续处理 AI 对数学研究、出版、教育与职业共同体的影响。该小组随后形成面向出版、职业实践、教育、公平与科学政策的系列 white papers，体现出制度性后续行动，而非短期讨论响应。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "AMS President Bryna Kra authorized the Advisory Group on Artificial Intelligence and the Mathematical Community on 10 July 2023. Its charge covered the role of mathematics in AI development and deployment, AI's impact on mathematical research, use of AI in publications, education and research, and effects on the mathematical community. The group later produced an AMS White Paper on AI and committee-specific papers, including a January 2024 paper on publishing in mathematics that examined peer review, research integrity, copyright, training data and attribution.", "zh-CN": "AMS 主席 Bryna Kra 于 2023 年 7 月 10 日授权成立 Advisory Group on Artificial Intelligence and the Mathematical Community。其职责涵盖数学在 AI 开发与部署中的作用、AI 对数学研究的影响、AI 在出版 / 教育 / 研究中的使用，以及 AI 对数学共同体的影响。该小组随后形成 AMS White Paper on AI 与面向不同委员会的专题文件，其中 2024 年 1 月的数学出版 white paper 讨论了同行评审、研究诚信、版权、训练数据与归属等问题。" }, "summary": { "en": "The AMS response developed during the first year of widespread generative-AI use. A Notices article records that the Society had already amended its Ethical Guidelines and Journal Policies in June 2023 to adopt the COPE position that AI tools cannot be authors and AI use must be disclosed. The July advisory group then broadened the response from immediate journal rules to sustained governance questions for mathematical research and the profession. Its 2024 white papers were explicitly intended as living resources for AMS policy committees and the wider community.", "zh-CN": "AMS 的这套响应形成于生成式 AI 广泛进入学术活动的第一年。Notices 文章记录，AMS 已在 2023 年 6 月修订 Ethical Guidelines and Journal Policies，采纳 COPE 关于 AI 工具不能作为作者、AI 使用必须披露的立场。7 月建立的咨询组则把响应从即时 journal rules 扩展为对数学研究与职业共同体的持续治理议题；其 2024 年 white papers 被明确设计为供 AMS 政策委员会与更广泛共同体持续更新使用的资源。" }, "why_it_matters": { "en": "This event marks an early transition from generic publisher responses to AI toward mathematics-specific institutional governance. It put research practice, publication, attribution, education and community effects into one formal agenda, creating a documented predecessor to later community-wide efforts such as the Leiden Declaration.", "zh-CN": "本事件标志着数学共同体开始从通用出版机构的 AI 响应转向数学领域自身的制度治理：研究实践、出版、归属、教育和共同体影响被纳入同一个正式议程，并成为后来 Leiden Declaration 等更广泛共同体规范工作的可追溯前史节点。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records mathematical-community governance of AI use rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是数学共同体对 AI 使用的治理，而不是某个 AI 系统执行数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "AMS leadership, advisory-group members and policy committees defined the governance agenda, consulted the community, drafted committee-specific white papers and developed publication and professional guidance for mathematicians.", "zh-CN": "AMS 领导层、咨询组成员与政策委员会界定治理议程、征询共同体意见、起草各委员会专题 white papers，并形成面向数学研究者的出版与职业实践指导。" } }, "systems": [], "organizations": [ "american-mathematical-society" ], "people": [ "bryna-kra", "akshay-venkatesh" ], "problems": [], "methods": [ "scholarly-governance", "publication-policy", "attribution-policy" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2023-07-10", "status": "claimed", "evidence_level": "E2", "note": { "en": "An AMS Notices communication records the advisory group's authorization by AMS President Bryna Kra on 10 July 2023 and quotes its charge concerning research, publications, education and the mathematical community.", "zh-CN": "AMS Notices 的专题文章记录了 Bryna Kra 主席于 2023 年 7 月 10 日授权该咨询组，并直接说明其围绕研究、出版、教育与数学共同体的职责范围。" } }, { "date": "2026-09-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "AMS governance records and the Society's 2024 AI white papers document continued committee activity and concrete outputs on publishing, professional practice, education, equity and science policy, supporting the Chronicle's durability assessment.", "zh-CN": "AMS 治理记录与 2024 年 AI white papers 记录了该机制持续运作，并在出版、职业实践、教育、公平与科学政策方面形成具体产出，由此支持 Chronicle 对其持续性的判断。" } } ] }, "sources": [ { "id": "ams-notices-generative-ai-2024", "tier": "S2", "type": "official_announcement", "title": "Using Generative AI for Mathematics and Science", "url": "https://www.ams.org/notices/202401/rnoti-p93.pdf", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "ams-ai-advisory-governance", "tier": "S2", "type": "official_announcement", "title": "AMS Advisory Group on Artificial Intelligence and the Mathematical Community", "url": "https://www.ams.org/about-us/governance/committees/artificial-intelligence", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "ams-ai-publishing-white-paper-2024", "tier": "S2", "type": "other", "title": "Artificial Intelligence: Publishing in Mathematics", "url": "https://www.ams.org/about-us/CPub_AI-WhitePaper.pdf", "primary": false, "published_date": "2024-01-30", "accessed_at": "2026-09-14" }, { "id": "ams-white-paper-ai-2024", "tier": "S2", "type": "other", "title": "AMS White Paper on AI", "url": "https://www.ams.org/about-us/AMSWhitePaperonAI.pdf", "primary": false, "published_date": null, "accessed_at": "2026-09-14" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2026-leiden-declaration" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "american-mathematical-society", "ams", "field-building", "ai-governance", "publication-policy", "attribution", "research-integrity", "mathematical-community" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-leandojo", "slug": "leandojo-retrieval-augmented-theorem-proving", "title": { "en": "LeanDojo opens a reproducible environment for LLM theorem proving in Lean", "zh-CN": "LeanDojo 建立可复现的 Lean 大模型定理证明环境" }, "dates": { "event": "2023-06-27", "first_public_claim": "2023-06-27", "paper_release": "2023-06-27", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-15" }, "event_types": [ "infrastructure", "dataset", "system", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "LeanDojo lowered the reproducibility barrier for learning-based theorem proving by combining programmatic Lean interaction, extracted proof data, a large benchmark and an open retrieval-augmented prover.", "zh-CN": "LeanDojo 将可编程 Lean 交互、证明数据抽取、大规模基准和开放的检索增强证明器整合起来，显著降低了学习式定理证明的复现门槛。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "LeanDojo released an open toolkit and benchmark for interacting with Lean and training theorem provers, together with ReProver, a retrieval-augmented language-model prover evaluated on nearly one hundred thousand mathlib theorems.", "zh-CN": "LeanDojo 公开了用于与 Lean 交互和训练定理证明器的工具与基准，并发布检索增强语言模型证明器 ReProver，在近十万个 mathlib 定理构成的基准上进行评测。" }, "summary": { "en": "The project extracts proof states, tactics and premise information from Lean repositories and exposes a programmatic proof environment. ReProver retrieves relevant premises before generating tactics, directly addressing the library-scale premise-selection problem.", "zh-CN": "该项目从 Lean 仓库抽取证明状态、战术与前提信息，并提供可编程证明环境。ReProver 在生成战术前检索相关前提，直接处理大规模数学库中的前提选择问题。" }, "why_it_matters": { "en": "LeanDojo helped turn Lean theorem proving into an accessible machine-learning research platform and supplied infrastructure that later formal-math agents could reuse rather than rebuilding environment integration from scratch.", "zh-CN": "LeanDojo 推动 Lean 定理证明成为更易进入的机器学习研究平台，并提供了后续形式数学 Agent 可复用的基础设施，避免重复搭建证明环境集成。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "ReProver used retrieval and language-model generation to choose premises and propose Lean tactics, with the proof assistant determining whether generated proof steps were valid.", "zh-CN": "ReProver 使用检索与语言模型生成选择前提并提出 Lean 战术，由证明助手判断生成的证明步骤是否有效。" } }, "human_contribution": { "description": { "en": "Researchers engineered the Lean extraction and interaction tooling, built the benchmark, trained the retriever and generator, and designed reproducible evaluation splits.", "zh-CN": "研究者开发 Lean 数据抽取与交互工具、构建基准、训练检索器与生成器，并设计可复现的评测划分。" } }, "systems": [ "leandojo", "reprover", "lean" ], "organizations": [ "caltech", "nvidia" ], "people": [ "kaiyu-yang", "aidan-swope", "alex-gu", "anima-anandkumar" ], "problems": [ "lean-theorem-proving" ], "methods": [ "retrieval-augmented-generation", "premise-selection", "formal-theorem-proving", "language-modeling" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-06-27", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The paper described LeanDojo, ReProver and the benchmark methodology.", "zh-CN": "论文公开说明了 LeanDojo、ReProver 与基准方法。" } }, { "date": "2023-06-27", "status": "paper_released", "evidence_level": "E3", "note": { "en": "Open-source tooling, benchmark resources and prover code were released for reproduction and extension.", "zh-CN": "开源工具、基准资源与证明器代码被公开，可用于复现与扩展。" } } ] }, "sources": [ { "id": "arxiv-leandojo-2306.15626", "tier": "S1", "type": "paper", "title": "LeanDojo: Theorem Proving with Retrieval-Augmented Language Models", "url": "https://arxiv.org/abs/2306.15626", "primary": true, "published_date": "2023-06-27", "accessed_at": "2026-09-10" }, { "id": "github-lean-dojo", "tier": "S1", "type": "repository", "title": "LeanDojo repository", "url": "https://github.com/lean-dojo/LeanDojo", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "leandojo-repository", "kind": "code", "title": "LeanDojo theorem-proving toolkit", "url": "https://github.com/lean-dojo/LeanDojo" } ], "relationships": { "predecessors": [ "evt-2017-mathlib3", "evt-2019-coqgym", "evt-2020-gpt-f", "evt-2021-minif2f" ], "successors": [ "evt-2024-deepseek-prover-v1-5", "evt-2026-alphaproof-nexus" ], "related": [ "evt-2023-copra" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "theorem-proving", "retrieval", "infrastructure", "benchmark", "open-source" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-alphadev", "slug": "alphadev-sorting-algorithms", "title": { "en": "AlphaDev discovers faster sorting algorithms with deep reinforcement learning", "zh-CN": "AlphaDev 使用深度强化学习发现更快的排序算法" }, "dates": { "event": "2023-06-07", "first_public_claim": "2023-06-07", "paper_release": "2023-06-07", "artifact_release": "2023-06-07", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H2", "rationale": { "en": "AlphaDev extended reinforcement-learning-based algorithm discovery from mathematical search benchmarks into low-level computer-science routines whose discovered sorting algorithms were integrated into LLVM libc++, providing a deployed example of AI-generated exact algorithms.", "zh-CN": "AlphaDev 将基于强化学习的算法发现从数学搜索扩展到低层计算机算法，并使发现的排序算法进入 LLVM libc++，成为 AI 生成精确算法并实际部署的代表性案例。" } }, "mathematical_novelty": { "type": "new_algorithm" }, "interfaces": [ "symbolic", "numeric", "hybrid" ], "claim": { "en": "AlphaDev formulated low-level algorithm design as a reinforcement-learning game and discovered new sorting routines that outperformed prior human-designed benchmarks; fixed sort-3, sort-4 and sort-5 routines were integrated into the LLVM standard C++ library.", "zh-CN": "AlphaDev 将低层算法设计表述为强化学习游戏，并发现超过既有人类设计基准的新排序例程；其中固定长度的 sort-3、sort-4 与 sort-5 例程被集成进 LLVM 标准 C++ 库。" }, "summary": { "en": "The system searches directly over assembly instructions using an AlphaZero-style learning and search procedure. DeepMind reported speedups up to 70% for short sequences and about 1.7% for very long sequences, while releasing pseudocode and discovered assembly programs with correctness tests.", "zh-CN": "该系统使用类似 AlphaZero 的学习与搜索流程，直接在汇编指令空间中寻找算法。DeepMind 报告短序列最高约 70% 的加速、超长序列约 1.7% 的加速，并公开伪代码、发现的汇编程序及正确性测试。" }, "why_it_matters": { "en": "The result showed that AI-discovered algorithmic improvements could move from a research search space into widely used production software, connecting exact algorithm discovery with measurable real-world deployment.", "zh-CN": "该结果展示 AI 发现的算法改进可以从研究搜索空间进入广泛使用的生产软件，把精确算法发现与可测量的真实部署影响连接起来。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "AlphaDev searched the assembly-program space and discovered candidate sorting routines under correctness and latency rewards; the resulting algorithms were tested, translated and integrated by researchers and software maintainers.", "zh-CN": "AlphaDev 在汇编程序空间中搜索，并在正确性与延迟奖励下发现候选排序例程；研究者与软件维护者随后对算法进行测试、转换与集成。" } }, "human_contribution": { "description": { "en": "Researchers formulated AssemblyGame, designed the reinforcement-learning system and evaluation, analyzed the discovered routines and translated suitable discoveries into C++ for library integration.", "zh-CN": "研究者构造 AssemblyGame、设计强化学习系统与评测、分析发现的例程，并将适合部署的结果转换为 C++ 以集成到标准库。" } }, "systems": [ "alphadev" ], "organizations": [ "google-deepmind" ], "people": [ "daniel-j-mankowitz", "andrea-michi" ], "problems": [ "sorting-algorithms" ], "methods": [ "reinforcement-learning", "alphazero", "program-search", "assembly-search", "algorithm-discovery" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-06-07", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Nature published the AlphaDev algorithm-discovery results and Google DeepMind released an official technical account.", "zh-CN": "Nature 发表 AlphaDev 的算法发现结果，Google DeepMind 同日公开官方技术说明。" } }, { "date": "2023-06-07", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public AlphaDev repository exposes agent pseudocode, discovered assembly programs and correctness tests. E3 records inspectability rather than independent verification of every performance claim.", "zh-CN": "公开 AlphaDev 仓库提供 Agent 伪代码、发现的汇编程序与正确性测试。E3 表示产物可检查，并不等同于全部性能主张已经获得独立验证。" } } ] }, "sources": [ { "id": "nature-alphadev-2023", "tier": "S1", "type": "paper", "title": "Faster sorting algorithms discovered using deep reinforcement learning", "url": "https://www.nature.com/articles/s41586-023-06004-9", "primary": true, "published_date": "2023-06-07", "accessed_at": "2026-09-11" }, { "id": "deepmind-alphadev-2023", "tier": "S2", "type": "official_announcement", "title": "AlphaDev discovers faster sorting algorithms", "url": "https://deepmind.google/blog/alphadev-discovers-faster-sorting-algorithms/", "primary": false, "published_date": "2023-06-07", "accessed_at": "2026-09-11" }, { "id": "github-google-deepmind-alphadev", "tier": "S1", "type": "repository", "title": "AlphaDev accompanying repository", "url": "https://github.com/google-deepmind/alphadev", "primary": true, "published_date": "2023-06-07", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "alphadev-repository", "kind": "code", "title": "AlphaDev pseudocode, discovered assembly routines and correctness tests", "url": "https://github.com/google-deepmind/alphadev" } ], "relationships": { "predecessors": [ "evt-2022-alphatensor" ], "successors": [ "evt-2023-funsearch-cap-set" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "algorithm-discovery", "reinforcement-learning", "sorting", "program-search", "alphazero" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-process-supervision-prm800k", "slug": "process-supervision-prm800k", "title": { "en": "Process supervision and PRM800K establish step-level verification for math reasoning", "zh-CN": "过程监督与 PRM800K 建立数学推理的步骤级验证路线" }, "dates": { "event": "2023-05-31", "first_public_claim": "2023-05-31", "paper_release": "2023-05-31", "artifact_release": "2023-05-31", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "system", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "The work made step-level human feedback a concrete and scalable research object for mathematical reasoning, directly comparing process and outcome supervision and releasing PRM800K as a large process-supervision dataset that influenced later verifier and reward-model work.", "zh-CN": "该工作把步骤级人工反馈变成数学推理中可系统研究和扩展的对象，直接比较过程监督与结果监督，并发布大规模过程监督数据集 PRM800K，对后续验证器与奖励模型路线产生持续影响。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric" ], "claim": { "en": "OpenAI reported that process supervision significantly outperformed outcome supervision for training reward models on MATH solutions; its process-supervised model solved 78% of a representative held-out MATH subset, and the project released PRM800K with 800,000 step-level correctness labels.", "zh-CN": "OpenAI 报告称，在 MATH 解题上使用过程监督训练奖励模型显著优于结果监督；其过程监督模型在代表性的留出 MATH 子集上解出 78% 的问题，并发布包含 80 万个步骤级正确性标签的 PRM800K。" }, "summary": { "en": "Rather than rewarding only a final answer, the project collected human judgments on intermediate reasoning steps and trained process reward models from those labels. PRM800K exposes the annotations, labeling instructions and scored model samples used in the study.", "zh-CN": "该项目不只对最终答案给出奖励，而是收集中间推理步骤的人工判断，并据此训练过程奖励模型。PRM800K 公开了研究使用的标注、标注说明以及带评分的模型样本。" }, "why_it_matters": { "en": "Step-level verification became a durable component of later mathematical reasoning systems, providing training and selection signals that diagnose where a chain of reasoning first goes wrong rather than judging only its endpoint.", "zh-CN": "步骤级验证后来成为数学推理系统的重要组成部分：它可以定位推理链从何处开始出错，并为训练与候选选择提供比只判断最终答案更细粒度的信号。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Language models generated mathematical solution trajectories and learned reward models scored intermediate reasoning steps; the correctness labels used for process supervision were supplied by human annotators.", "zh-CN": "语言模型生成数学解题轨迹，学习式奖励模型对中间推理步骤进行评分；过程监督所需的正确性标签由人工标注者提供。" } }, "human_contribution": { "description": { "en": "Researchers designed the process-versus-outcome supervision comparison, data-collection and active-learning procedures, while human labelers supplied step-level judgments for PRM800K.", "zh-CN": "研究者设计过程监督与结果监督的比较、数据收集及主动学习流程，人工标注者则为 PRM800K 提供步骤级判断。" } }, "systems": [ "process-reward-model", "prm800k" ], "organizations": [ "openai" ], "people": [ "hunter-lightman", "vineet-kosaraju", "yura-burda", "harri-edwards", "bowen-baker", "teddy-lee", "jan-leike", "john-schulman", "ilya-sutskever", "karl-cobbe" ], "problems": [ "math-benchmark" ], "methods": [ "process-supervision", "process-reward-model", "outcome-supervision", "active-learning", "verification" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-05-31", "status": "paper_released", "evidence_level": "E2", "note": { "en": "OpenAI released the research paper and official description comparing process and outcome supervision on MATH.", "zh-CN": "OpenAI 公开研究论文与官方说明，报告在 MATH 上对过程监督和结果监督进行比较。" } }, { "date": "2023-05-31", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public PRM800K repository exposes 800,000 step-level labels, labeling instructions, data splits and evaluation samples. E3 records inspectability and does not imply independent verification of the reported model results.", "zh-CN": "公开的 PRM800K 仓库提供 80 万个步骤级标签、标注说明、数据划分与评测样本。E3 表示产物可直接检查，并不等同于论文报告的模型结果已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-lets-verify-step-by-step-2305.20050", "tier": "S1", "type": "paper", "title": "Let's Verify Step by Step", "url": "https://arxiv.org/abs/2305.20050", "primary": true, "published_date": "2023-05-31", "accessed_at": "2026-09-11" }, { "id": "openai-process-supervision-2023", "tier": "S2", "type": "official_announcement", "title": "Improving mathematical reasoning with process supervision", "url": "https://openai.com/index/improving-mathematical-reasoning-with-process-supervision/", "primary": true, "published_date": "2023-05-31", "accessed_at": "2026-09-11" }, { "id": "github-openai-prm800k", "tier": "S1", "type": "repository", "title": "PRM800K process supervision dataset", "url": "https://github.com/openai/prm800k", "primary": true, "published_date": "2023-05-31", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "prm800k-dataset", "kind": "dataset", "title": "PRM800K — 800,000 step-level correctness labels", "url": "https://github.com/openai/prm800k" } ], "relationships": { "predecessors": [ "evt-2021-gsm8k" ], "successors": [ "evt-2023-math-shepherd" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "process-supervision", "process-reward-model", "verifier", "math-reasoning", "dataset" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-baldur", "slug": "baldur-whole-proof-generation-repair", "title": { "en": "Baldur generates and repairs whole formal proofs with language models", "zh-CN": "Baldur 使用语言模型生成并修复完整形式证明" }, "dates": { "event": "2023-03-08", "first_public_claim": "2023-03-08", "paper_release": "2023-03-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Baldur established whole-proof generation plus checker-guided proof repair as a distinct alternative to step-by-step formal proof search, showing that a transformer could emit complete Isabelle/HOL proofs and use failed attempts and error messages as repair context.", "zh-CN": "Baldur 将“完整证明生成 + 检查器反馈修复”确立为逐步形式证明搜索之外的一条独立路线，展示 Transformer 可以一次生成完整 Isabelle/HOL 证明，并利用失败证明与错误信息进行修复。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "On a benchmark of 6,336 Isabelle/HOL theorems, Baldur generated whole proofs and repaired failed generations, proving an additional 8.7% of theorems beyond Thor; the paper reported that Baldur and Thor together proved 65.7% fully automatically.", "zh-CN": "在包含 6,336 个 Isabelle/HOL 定理的基准上，Baldur 生成完整证明并修复失败结果；论文报告它相较 Thor 额外证明了 8.7% 的定理，而 Baldur 与 Thor 合计可全自动证明 65.7%。" }, "summary": { "en": "Instead of predicting one proof step and searching over continuations, Baldur fine-tuned language models to generate an entire proof in one pass. A separate repair model then received a failed proof attempt together with proof-assistant error feedback and proposed a corrected proof.", "zh-CN": "与逐步预测证明动作并搜索后续路径不同，Baldur 微调语言模型一次生成完整证明；随后由独立的修复模型读取失败证明及证明助手的错误反馈，再提出修正后的证明。" }, "why_it_matters": { "en": "The work made complete-proof synthesis and feedback-driven repair a credible formal-reasoning pattern, complementing search-heavy theorem provers and anticipating later generate-check-revise workflows.", "zh-CN": "该工作使完整证明合成与反馈驱动修复成为可信的形式推理模式，补充了依赖搜索的定理证明路线，并预示了后来常见的“生成—检查—修订”工作流。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Fine-tuned language models generated complete candidate proofs and repaired failed attempts using checker feedback; Isabelle/HOL mechanically accepted or rejected the resulting proof text.", "zh-CN": "微调后的语言模型生成完整候选证明，并根据检查器反馈修复失败尝试；Isabelle/HOL 对最终证明文本进行机械接受或拒绝。" } }, "human_contribution": { "description": { "en": "Researchers designed the whole-proof and repair training setup, assembled the evaluation protocol, trained the models and analyzed performance against prior theorem-proving systems.", "zh-CN": "研究者设计完整证明与修复训练方案、构建评测流程、训练模型，并分析其相对既有定理证明系统的表现。" } }, "systems": [ "baldur", "isabelle-hol" ], "organizations": [], "people": [ "emily-first", "markus-n-rabe", "talia-ringer", "yuriy-brun" ], "problems": [ "automated-theorem-proving" ], "methods": [ "whole-proof-generation", "proof-repair", "language-models", "proof-assistant-feedback" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2023-03-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The public research record reports the whole-proof generation, repair method and Isabelle/HOL evaluation. This status records the paper and does not imply independent Chronicle verification or a public replay artifact.", "zh-CN": "公开研究记录报告了完整证明生成、修复方法及 Isabelle/HOL 评测。该状态仅记录论文已公开，不表示 Chronicle 已独立验证，也不表示存在可公开重放的完整产物。" } } ] }, "sources": [ { "id": "arxiv-baldur-2303.04910", "tier": "S1", "type": "paper", "title": "Baldur: Whole-Proof Generation and Repair with Large Language Models", "url": "https://arxiv.org/abs/2303.04910", "primary": true, "published_date": "2023-03-08", "accessed_at": "2026-09-11" }, { "id": "esec-fse-baldur-2023", "tier": "S1", "type": "other", "title": "Baldur: Whole-Proof Generation and Repair with Large Language Models", "url": "https://2023.esec-fse.org/details/fse-2023-research-papers/2/Baldur-Whole-Proof-Generation-and-Repair-with-Large-Language-Models", "primary": true, "published_date": "2023-12-06", "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2022-thor" ], "successors": [], "related": [ "evt-2023-leandojo", "evt-2023-copra" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "isabelle", "whole-proof-generation", "proof-repair", "language-model" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2023-proofnet", "slug": "proofnet-autoformalization-benchmark", "title": { "en": "ProofNet benchmarks autoformalization and proving of undergraduate mathematics", "zh-CN": "ProofNet 建立本科数学自动形式化与形式证明基准" }, "dates": { "event": "2023-02-24", "first_public_claim": "2023-02-24", "paper_release": "2023-02-24", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-14" }, "event_types": [ "benchmark", "dataset", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "ProofNet broadened evaluation beyond Olympiad statements to textbook-level undergraduate mathematics and paired informal statements, proofs and Lean formalizations.", "zh-CN": "ProofNet 把评测从奥赛题扩展到本科教材数学，并配对自然语言陈述、证明与 Lean 形式化。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "ProofNet introduced 371 undergraduate-level examples pairing natural-language theorem statements and proofs with Lean 3 formal statements.", "zh-CN": "ProofNet 引入 371 个本科层次样例，将自然语言定理陈述与证明和 Lean 3 形式陈述配对。" }, "summary": { "en": "The benchmark covers analysis, linear algebra, abstract algebra, topology and other textbook mathematics.", "zh-CN": "该基准覆盖分析、线性代数、抽象代数、拓扑等本科教材数学。" }, "why_it_matters": { "en": "It created a shared target for measuring whether models can translate ordinary mathematical prose into proof-assistant representations.", "zh-CN": "它为衡量模型能否把普通数学文本转化为证明助手表示建立了共享目标。" }, "ai_role": { "level": "computation_only", "description": { "en": "Models are evaluated on autoformalization and formal proving tasks built from the benchmark.", "zh-CN": "模型在该基准构建的自动形式化与形式证明任务上接受评测。" } }, "human_contribution": { "description": { "en": "Researchers curated textbook problems, natural-language proofs and corresponding Lean statements.", "zh-CN": "研究者整理教材题目、自然语言证明与对应 Lean 陈述。" } }, "systems": [ "proofnet", "lean" ], "organizations": [ "yale", "carnegie-mellon-university" ], "people": [], "problems": [ "undergraduate-mathematics" ], "methods": [ "benchmarking", "autoformalization" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2023-02-24", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-proofnet-2302.12433", "tier": "S1", "type": "paper", "title": "ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics", "url": "https://arxiv.org/abs/2302.12433", "primary": true, "published_date": "2023-02-24", "accessed_at": "2026-09-10" }, { "id": "github-proofnet", "tier": "S1", "type": "repository", "title": "ProofNet benchmark and replication repository", "url": "https://github.com/zhangir-azerbayev/ProofNet", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "proofnet-repository", "kind": "dataset", "title": "ProofNet benchmark and replication code", "url": "https://github.com/zhangir-azerbayev/ProofNet" } ], "relationships": { "predecessors": [ "evt-2021-minif2f", "evt-2022-draft-sketch-prove" ], "successors": [ "evt-2026-stochbench" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "autoformalization", "lean", "undergraduate-math" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-draft-sketch-prove", "slug": "draft-sketch-prove-informal-guidance", "title": { "en": "Draft, Sketch, and Prove uses informal proofs to guide formal proof search", "zh-CN": "Draft, Sketch, and Prove 用非形式证明引导形式证明搜索" }, "dates": { "event": "2022-10-21", "first_public_claim": "2022-10-21", "paper_release": "2022-10-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "formalization", "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "DSP made informal reasoning an explicit intermediate representation between language models and formal theorem provers.", "zh-CN": "DSP 将非形式推理显式作为语言模型与形式定理证明器之间的中间表示。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "DSP mapped informal proofs into formal sketches and raised automated proving performance from 20.9% to 39.3% on a competition-problem collection.", "zh-CN": "DSP 将非形式证明映射为形式 proof sketch，并在一组竞赛题上把自动证明性能从 20.9% 提升到 39.3%。" }, "summary": { "en": "Language models produce a high-level formal sketch whose subgoals are then discharged by an automated prover.", "zh-CN": "语言模型先生成高层形式证明草图，再由自动证明器完成其中的子目标。" }, "why_it_matters": { "en": "The architecture anticipated later systems that alternate natural-language decomposition with verifier-backed formal proof.", "zh-CN": "该架构预示了后来“自然语言分解 + 验证器支持的形式证明”交替执行的系统。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Language models draft and sketch proof structure; formal provers verify and complete subproblems.", "zh-CN": "语言模型负责起草和构造证明结构，形式证明器验证并完成子问题。" } }, "human_contribution": { "description": { "en": "Researchers designed the three-stage workflow and constructed evaluation problems and prompting procedures.", "zh-CN": "研究者设计三阶段工作流、评测问题与提示流程。" } }, "systems": [ "draft-sketch-prove" ], "organizations": [ "meta-ai", "university-of-cambridge" ], "people": [], "problems": [ "competition-mathematics" ], "methods": [ "autoformalization", "proof-sketch", "language-model" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2022-10-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-dsp-2210.12283", "tier": "S1", "type": "paper", "title": "Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs", "url": "https://arxiv.org/abs/2210.12283", "primary": true, "published_date": "2022-10-21", "accessed_at": "2026-09-10" }, { "id": "github-draft-sketch-prove", "tier": "S1", "type": "repository", "title": "Draft, Sketch, and Prove implementation and result artifacts", "url": "https://github.com/albertqjiang/draft_sketch_prove", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "draft-sketch-prove-code", "kind": "code", "title": "Draft, Sketch, and Prove implementation and result files", "url": "https://github.com/albertqjiang/draft_sketch_prove" } ], "relationships": { "predecessors": [ "evt-2022-thor", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "autoformalization", "proof-sketch", "lean", "language-model" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-alphatensor", "slug": "alphatensor-matrix-multiplication-algorithms", "title": { "en": "AlphaTensor discovers improved matrix multiplication algorithms", "zh-CN": "AlphaTensor 发现改进的矩阵乘法算法" }, "dates": { "event": "2022-10-05", "first_public_claim": "2022-10-05", "paper_release": "2022-10-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H1", "rationale": { "en": "AlphaTensor provided a prominent example of reinforcement learning discovering exact algorithms that improved long-standing matrix-multiplication records, including a finite-field 4-by-4 result reported as the first improvement over Strassen's two-level construction in that setting.", "zh-CN": "AlphaTensor 是强化学习发现精确算法的代表性案例：它改进了长期存在的矩阵乘法记录，其中有限域上的 4×4 结果被论文报告为该设定下首次超过 Strassen 两层构造。" } }, "mathematical_novelty": { "type": "new_algorithm" }, "interfaces": [ "symbolic", "numeric", "hybrid" ], "claim": { "en": "AlphaTensor discovered provably correct matrix multiplication algorithms that improved the best known multiplication counts for multiple matrix sizes, including a 4-by-4 construction over Z2 using 47 scalar multiplications instead of 49 from two-level Strassen.", "zh-CN": "AlphaTensor 发现了一批可证明正确的矩阵乘法算法，在多个矩阵尺寸上改进已知最佳乘法次数，其中在 Z2 上的 4×4 构造使用 47 次标量乘法，而两层 Strassen 构造需要 49 次。" }, "summary": { "en": "DeepMind represented matrix multiplication as a tensor-decomposition game and trained an AlphaZero-style reinforcement-learning agent to search the enormous space of factorizations. Released artifacts include discovered factorizations, benchmarking code and checks of algorithmic properties.", "zh-CN": "DeepMind 将矩阵乘法表示为张量分解游戏，并训练类似 AlphaZero 的强化学习智能体搜索巨大的分解空间。公开产物包括所发现的分解、基准代码以及算法性质检查工具。" }, "why_it_matters": { "en": "The work moved AI4Math beyond solving prepared exercises by demonstrating machine search that produced new exact algorithms with mathematical and computational significance.", "zh-CN": "该工作超越了求解预设习题的范式，展示了机器搜索能够产生具有数学与计算意义的新精确算法。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "AlphaTensor searched for tensor decompositions and discovered candidate algorithms; the resulting decompositions admit exact mathematical checking and were analyzed by the research team.", "zh-CN": "AlphaTensor 搜索张量分解并发现候选算法；所得分解可以进行精确数学检查，并由研究团队进一步分析。" } }, "human_contribution": { "description": { "en": "Researchers formulated TensorGame, designed the reinforcement-learning system and reward structures, chose target problems, verified outputs and interpreted their algorithmic consequences.", "zh-CN": "研究者构造 TensorGame、设计强化学习系统与奖励机制、选择目标问题、验证输出并解释其算法意义。" } }, "systems": [ "alphatensor" ], "organizations": [ "deepmind" ], "people": [ "alhussein-fawzi", "matej-balog", "aja-huang", "thomas-hubert", "pushmeet-kohli" ], "problems": [ "matrix-multiplication" ], "methods": [ "reinforcement-learning", "monte-carlo-tree-search", "tensor-decomposition", "algorithm-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2022-10-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Nature published the discovery results and their mathematical formulation.", "zh-CN": "Nature 发表了相关发现结果及其数学表述。" } }, { "date": "2022-10-05", "status": "paper_released", "evidence_level": "E3", "note": { "en": "DeepMind released discovered algorithms and supporting verification and benchmarking materials.", "zh-CN": "DeepMind 公开了所发现的算法以及配套验证与基准材料。" } } ] }, "sources": [ { "id": "nature-alphatensor-2022", "tier": "S1", "type": "paper", "title": "Discovering faster matrix multiplication algorithms with reinforcement learning", "url": "https://www.nature.com/articles/s41586-022-05172-4", "primary": true, "published_date": "2022-10-05", "accessed_at": "2026-09-10" }, { "id": "github-google-deepmind-alphatensor", "tier": "S1", "type": "repository", "title": "AlphaTensor accompanying repository", "url": "https://github.com/google-deepmind/alphatensor", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "alphatensor-results-repository", "kind": "code", "title": "AlphaTensor algorithms and verification materials", "url": "https://github.com/google-deepmind/alphatensor" } ], "relationships": { "predecessors": [], "successors": [ "evt-2025-alphaevolve" ], "related": [ "evt-2023-funsearch-cap-set" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "matrix-multiplication", "reinforcement-learning", "algorithm-discovery", "tensor-decomposition", "alphazero" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-minerva", "slug": "minerva-quantitative-reasoning-language-model", "title": { "en": "Minerva demonstrates large-scale language-model gains on quantitative reasoning", "zh-CN": "Minerva 展示大语言模型在定量推理上的规模化提升" }, "dates": { "event": "2022-06-29", "first_public_claim": "2022-06-29", "paper_release": "2022-06-29", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "system", "benchmark" ], "significance": { "tier": "H2", "rationale": { "en": "Minerva showed that a general language-model architecture further trained on technical content could make a large jump on mathematical and scientific quantitative reasoning benchmarks without external symbolic tools.", "zh-CN": "Minerva 展示了通用语言模型架构在技术内容上继续训练后，可以在不调用外部符号工具的情况下显著提升数学与科学定量推理基准表现。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "informal", "symbolic", "numeric" ], "claim": { "en": "Minerva achieved then-state-of-the-art performance on several quantitative reasoning benchmarks and correctly solved nearly one third of a separate set of more than two hundred undergraduate-level science problems evaluated by the researchers.", "zh-CN": "Minerva 在多个定量推理基准上取得当时的领先表现，并在研究团队另外评测的两百余道本科层次科学问题中正确解答了接近三分之一。" }, "summary": { "en": "Google Research continued pretraining a large language model on scientific papers and mathematical web content, then evaluated chain-of-thought-style solutions across mathematics, physics and other quantitative domains. The system operated in natural language rather than a proof assistant.", "zh-CN": "Google Research 在科学论文与数学网页内容上继续预训练大型语言模型，并在数学、物理等定量领域评测逐步推理式解答。该系统直接使用自然语言，而非证明助手。" }, "why_it_matters": { "en": "Minerva helped establish natural-language mathematical reasoning as a serious scaling target for large language models, providing an important precursor to later Olympiad-level end-to-end reasoning systems.", "zh-CN": "Minerva 推动自然语言数学推理成为大语言模型规模化研究的重要目标，并为后来的端到端奥赛级推理系统提供了关键前序参照。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The language model generated complete natural-language quantitative solutions; correctness was assessed against benchmark answers and researcher evaluation protocols.", "zh-CN": "语言模型自主生成完整的自然语言定量解答；正确性通过基准答案与研究者设计的评测流程判定。" } }, "human_contribution": { "description": { "en": "Researchers assembled the technical training mixture, designed prompting and evaluation procedures, curated additional undergraduate problems and analyzed model outputs.", "zh-CN": "研究者构建技术训练语料、设计提示与评测流程、整理额外本科问题，并分析模型输出。" } }, "systems": [ "minerva" ], "organizations": [ "google-research" ], "people": [ "aitor-lewkowycz", "anders-andreassen", "ethan-dyer", "guy-gur-ari" ], "problems": [ "math-benchmark", "quantitative-reasoning" ], "methods": [ "language-model-pretraining", "chain-of-thought", "quantitative-reasoning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2022-06-29", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The quantitative reasoning results and evaluation methodology were released in the research paper.", "zh-CN": "论文公开了定量推理结果与评测方法。" } } ] }, "sources": [ { "id": "arxiv-minerva-2206.14858", "tier": "S1", "type": "paper", "title": "Solving Quantitative Reasoning Problems with Language Models", "url": "https://arxiv.org/abs/2206.14858", "primary": true, "published_date": "2022-06-29", "accessed_at": "2026-09-10" }, { "id": "google-research-minerva-2022", "tier": "S2", "type": "official_announcement", "title": "Minerva: Solving Quantitative Reasoning Problems with Language Models", "url": "https://research.google/blog/minerva-solving-quantitative-reasoning-problems-with-language-models/", "primary": true, "published_date": "2022-06-30", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2025-gemini-imo-gold" ], "related": [ "evt-2020-gpt-f" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "language-model", "quantitative-reasoning", "math-benchmark", "natural-language", "scaling" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-autoformalization-llm", "slug": "autoformalization-large-language-models", "title": { "en": "Large language models show practical progress on mathematical autoformalization", "zh-CN": "大语言模型在数学自动形式化上展示实用进展" }, "dates": { "event": "2022-05-25", "first_public_claim": "2022-05-25", "paper_release": "2022-05-25", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system" ], "significance": { "tier": "H2", "rationale": { "en": "The work established an early large-language-model route from informal competition mathematics to proof-assistant specifications and showed that generated formal statements could improve downstream theorem proving, helping make autoformalization a concrete AI4Math research direction.", "zh-CN": "该工作较早建立了从非形式化竞赛数学到证明助手形式规范的大语言模型路线，并展示生成的形式陈述可以提升后续定理证明，使自动形式化成为更具体的 AI4Math 研究方向。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "The paper reported that large language models correctly translated 25.3% of sampled mathematical competition problems into Isabelle/HOL formal specifications, and that training a neural theorem prover on autoformalized theorems increased its miniF2F proof rate from 29.6% to 35.2%.", "zh-CN": "论文报告称，大语言模型能够将抽样数学竞赛题中的 25.3% 正确翻译为 Isabelle/HOL 形式规范；使用自动形式化生成的定理训练神经定理证明器后，其 miniF2F 证明率从 29.6% 提升到 35.2%。" }, "summary": { "en": "Researchers used few-shot prompting to ask large language models to translate informal mathematical statements into Isabelle/HOL. The generated formalizations were then used as additional training data for a neural theorem prover, linking informal-language translation with formal proof search in one pipeline.", "zh-CN": "研究者通过 few-shot prompting 让大语言模型把非形式化数学陈述翻译为 Isabelle/HOL，并将生成的形式化结果进一步作为神经定理证明器的训练数据，把自然语言翻译与形式证明搜索连接到同一流程中。" }, "why_it_matters": { "en": "The result provided an early empirical bridge between modern language models and proof assistants: autoformalization was not only evaluated as translation accuracy, but also shown to create training data that improved a downstream prover. This became an important precursor to later autoformalization benchmarks and synthetic formal-mathematics pipelines.", "zh-CN": "这一结果较早建立了现代语言模型与证明助手之间的经验性桥梁：自动形式化不仅以翻译准确率评估，而且被证明能够生成可提升下游证明器的数据，成为后来自动形式化基准与合成形式数学管线的重要前序。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The language model generated candidate Isabelle/HOL formal specifications from informal problem statements; those generated statements were also used to augment theorem-prover training.", "zh-CN": "语言模型从非形式化题目陈述生成候选 Isabelle/HOL 形式规范，并将这些生成的形式陈述用于扩充定理证明器训练数据。" } }, "human_contribution": { "description": { "en": "Researchers designed the prompting and evaluation protocol, assessed formalization correctness, integrated generated statements into theorem-prover training and measured the resulting miniF2F performance.", "zh-CN": "研究者设计提示与评测协议、判断形式化是否正确、将生成陈述接入定理证明器训练，并测量其在 miniF2F 上的表现。" } }, "systems": [ "isabelle-hol" ], "organizations": [ "google-research", "university-of-cambridge" ], "people": [ "yuhuai-wu", "albert-qiaochu-jiang", "wenda-li", "markus-rabe", "charles-staats", "mateja-jamnik", "christian-szegedy" ], "problems": [ "autoformalization", "minif2f" ], "methods": [ "large-language-model", "few-shot-prompting", "autoformalization", "synthetic-training-data" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2022-05-25", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The research paper publicly reported the Isabelle/HOL autoformalization and miniF2F results. E2 records a public research record and does not imply independent reproduction or verification.", "zh-CN": "研究论文公开报告了 Isabelle/HOL 自动形式化与 miniF2F 结果。E2 表示已有公开研究记录，并不意味着已经获得独立复现或验证。" } } ] }, "sources": [ { "id": "arxiv-autoformalization-2205.12615", "tier": "S1", "type": "paper", "title": "Autoformalization with Large Language Models", "url": "https://arxiv.org/abs/2205.12615", "primary": true, "published_date": "2022-05-25", "accessed_at": "2026-09-11" }, { "id": "neurips-autoformalization-2022", "tier": "S1", "type": "paper", "title": "Autoformalization with Large Language Models — NeurIPS 2022", "url": "https://proceedings.neurips.cc/paper_files/paper/2022/hash/d0c6bc641a56bebee9d985b937307367-Abstract-Conference.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "google-research-autoformalization-2022", "tier": "S2", "type": "official_announcement", "title": "Autoformalization with Large Language Models", "url": "https://research.google/pubs/autoformalization-with-large-language-models/", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2018-neural-mizar-autoformalization", "evt-2021-minif2f" ], "successors": [ "evt-2023-proofnet" ], "related": [ "evt-2022-draft-sketch-prove" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "autoformalization", "large-language-model", "isabelle", "miniF2F", "formal-mathematics" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-naturalprover", "slug": "naturalprover-grounded-proof-generation", "title": { "en": "NaturalProver grounds language-model proof generation in mathematical references", "zh-CN": "NaturalProver 以数学参考资料约束语言模型证明生成" }, "dates": { "event": "2022-05-25", "first_public_claim": "2022-05-25", "paper_release": "2022-05-25", "artifact_release": "2022-06-03", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "NaturalProver made next-step and full-proof generation in ordinary mathematical language an explicit language-model task and paired generation with retrieved or human-provided mathematical references, anticipating later retrieval-grounded mathematical reasoning systems.", "zh-CN": "NaturalProver 将普通数学语言中的下一步证明与完整证明生成明确建模为语言模型任务，并使用检索或人工提供的数学参考资料约束生成，成为后来检索增强数学推理系统的重要前序。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal" ], "claim": { "en": "The paper reported that NaturalProver improved next-step suggestions and full-proof generation over fine-tuned GPT-3 on NaturalProofs, generated some short 2–6 step proofs, and produced next-step suggestions judged correct and useful more than 40% of the time in human evaluation.", "zh-CN": "论文报告称，NaturalProver 在 NaturalProofs 上的下一步建议与完整证明生成质量优于微调 GPT-3，能够生成部分 2–6 步的短证明，并在人工评测中使超过 40% 的下一步建议被判断为正确且有用。" }, "summary": { "en": "NaturalProver conditions language-model proof generation on mathematical background references such as definitions and theorems, either retrieved automatically or supplied by humans. The project studied both next-step suggestion and full-proof generation and released the NaturalProofs-Gen data, training and generation code, evaluation tooling and model assets.", "zh-CN": "NaturalProver 在证明生成时让语言模型条件化于定义、定理等数学背景资料，这些资料可以自动检索或由人类提供。项目同时研究下一步证明建议与完整证明生成，并公开 NaturalProofs-Gen 数据、训练与生成代码、评测工具和模型资源。" }, "why_it_matters": { "en": "The work helped establish natural-language theorem proving as a generative-model problem distinct from answer-only quantitative reasoning and formal proof search. Its grounding mechanism also made mathematical references explicit rather than leaving proof generation entirely inside an ungrounded language model.", "zh-CN": "该工作推动自然语言定理证明成为区别于仅输出答案的定量推理和形式证明搜索的生成模型任务；其 grounding 机制还显式引入数学参考资料，而不是把证明生成完全留在无外部依据的语言模型内部。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The language model generated proof steps and complete natural-language proofs conditioned on mathematical references, with optional constrained decoding to enforce reference use.", "zh-CN": "语言模型在数学参考资料条件下生成证明步骤和完整自然语言证明，并可通过约束解码强化对参考资料的使用。" } }, "human_contribution": { "description": { "en": "Researchers designed the grounding and decoding methods, assembled the generation datasets and evaluation setup, and university-level mathematics students evaluated proof quality and next-step usefulness.", "zh-CN": "研究者设计 grounding 与解码方法、构建生成数据与评测流程，并由具有大学数学背景的学生评估证明质量和下一步建议的有效性。" } }, "systems": [ "naturalprover", "naturalproofs" ], "organizations": [ "university-of-washington", "allen-institute-for-ai" ], "people": [ "sean-welleck", "jiacheng-liu", "ximing-lu", "hannaneh-hajishirzi", "yejin-choi" ], "problems": [ "natural-language-theorem-proving", "proof-step-generation" ], "methods": [ "language-model-generation", "retrieval-augmented-generation", "constrained-decoding", "reference-grounding" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2022-05-25", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The paper publicly reported the grounded proof-generation tasks, model and evaluation results. This research record alone does not imply independent verification of generated proofs.", "zh-CN": "论文公开报告了 grounded proof generation 任务、模型与评测结果；该研究记录本身不表示生成证明已获得独立验证。" } }, { "date": "2022-06-03", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The authors released a public repository containing NaturalProofs-Gen data, training and generation code, evaluation tooling and model assets. E3 records artifact inspectability, not mathematical certification of the generated proofs.", "zh-CN": "作者公开仓库，包含 NaturalProofs-Gen 数据、训练与生成代码、评测工具和模型资源。E3 表示产物可检查，并不等同于对生成证明的数学正确性认证。" } } ] }, "sources": [ { "id": "arxiv-naturalprover-2205.12910", "tier": "S1", "type": "paper", "title": "NaturalProver: Grounded Mathematical Proof Generation with Language Models", "url": "https://arxiv.org/abs/2205.12910", "primary": true, "published_date": "2022-05-25", "accessed_at": "2026-09-11" }, { "id": "neurips-naturalprover-2022", "tier": "S1", "type": "paper", "title": "NaturalProver: Grounded Mathematical Proof Generation with Language Models — NeurIPS 2022", "url": "https://proceedings.neurips.cc/paper_files/paper/2022/hash/1fc548a8243ad06616eee731e0572927-Abstract-Conference.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-naturalprover", "tier": "S1", "type": "repository", "title": "NaturalProver code, data, evaluation and model repository", "url": "https://github.com/wellecks/naturalprover", "primary": true, "published_date": "2022-06-03", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "naturalprover-repository", "kind": "code", "title": "NaturalProver code, NaturalProofs-Gen data and released model assets", "url": "https://github.com/wellecks/naturalprover" } ], "relationships": { "predecessors": [ "evt-2020-nl-premise-selection" ], "successors": [], "related": [ "evt-2022-minerva" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "natural-language-proof", "language-model", "retrieval", "grounded-generation", "theorem-proving" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-htps", "slug": "hypertree-proof-search", "title": { "en": "HyperTree Proof Search introduces online self-improvement for neural theorem proving", "zh-CN": "HyperTree Proof Search 引入神经定理证明的在线自我改进" }, "dates": { "event": "2022-05-23", "first_public_claim": "2022-05-23", "paper_release": "2022-05-23", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "HTPS coupled AlphaZero-inspired search with online learning and substantially advanced both Metamath and Lean theorem-proving performance.", "zh-CN": "HTPS 将 AlphaZero 式搜索与在线学习结合，在 Metamath 与 Lean 定理证明上均取得显著提升。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "HTPS plus online training reached 82.6% on held-out Metamath theorems and improved miniF2F-curriculum performance to 42%.", "zh-CN": "HTPS 配合在线训练在留出 Metamath 定理上达到 82.6%，并将 miniF2F-curriculum 的证明率提升到 42%。" }, "summary": { "en": "The system learns from its own proof searches and uses a hyper-tree search algorithm inspired by Monte Carlo tree search and AlphaZero.", "zh-CN": "系统从自身证明搜索中继续学习，并使用受蒙特卡洛树搜索与 AlphaZero 启发的超树搜索算法。" }, "why_it_matters": { "en": "It foreshadowed the verifier-guided self-improvement loops that became common in later formal reasoning systems.", "zh-CN": "它预示了后来形式推理系统中广泛采用的“验证器反馈 + 自我改进”训练循环。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The prover searches, learns from successful and failed search trajectories, and iteratively improves its policy.", "zh-CN": "证明器执行搜索、从成功与失败的轨迹中学习，并迭代改进策略。" } }, "human_contribution": { "description": { "en": "Researchers designed HTPS, training environments and benchmark protocols.", "zh-CN": "研究者设计 HTPS、训练环境与基准协议。" } }, "systems": [ "htps" ], "organizations": [ "meta-ai" ], "people": [], "problems": [ "metamath", "minif2f" ], "methods": [ "online-training", "tree-search", "expert-iteration" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2022-05-23", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-htps-2205.11491", "tier": "S1", "type": "paper", "title": "HyperTree Proof Search for Neural Theorem Proving", "url": "https://arxiv.org/abs/2205.11491", "primary": true, "published_date": "2022-05-23", "accessed_at": "2026-09-10" }, { "id": "github-evariste-htps", "tier": "S1", "type": "repository", "title": "Evariste code accompanying HyperTree Proof Search", "url": "https://github.com/facebookresearch/Evariste", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "htps-evariste-code", "kind": "code", "title": "Evariste HyperTree Proof Search research artifact", "url": "https://github.com/facebookresearch/Evariste" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "tree-search", "formal-proof", "online-learning", "alphazero" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-thor", "slug": "thor-language-model-hammer-integration", "title": { "en": "Thor integrates language models with automated theorem-prover hammers", "zh-CN": "Thor 将语言模型与自动定理证明器 Hammer 集成" }, "dates": { "event": "2022-05-22", "first_public_claim": "2022-05-22", "paper_release": "2022-05-22", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Thor was an early explicit neuro-symbolic architecture in which language models delegated premise-selection bottlenecks to classical automated provers.", "zh-CN": "Thor 是较早明确采用神经符号分工的架构之一：语言模型把前提选择瓶颈交给传统自动定理证明器处理。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic", "hybrid" ], "claim": { "en": "Thor increased a language model's success on the PISA dataset from 39% to 57% and matched leading miniF2F methods with less compute.", "zh-CN": "Thor 将语言模型在 PISA 数据集上的成功率从 39% 提升到 57%，并以更少算力在 miniF2F 上达到当时领先方法水平。" }, "summary": { "en": "The framework uses theorem-prover hammers for premise selection while leaving other proof decisions to the language model.", "zh-CN": "该框架使用定理证明器 hammer 进行前提选择，其余证明决策由语言模型完成。" }, "why_it_matters": { "en": "It highlighted a durable design principle: use symbolic tools where exhaustive reliability is strong and learned models where generation is needed.", "zh-CN": "它体现了一条长期有效的设计原则：把符号工具用于可靠的结构化搜索，把学习模型用于需要生成与启发式判断的环节。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The language model generated proof actions while automated provers supplied premise-search assistance.", "zh-CN": "语言模型生成证明动作，自动定理证明器负责提供前提搜索支持。" } }, "human_contribution": { "description": { "en": "Researchers designed the integration protocol and evaluation across theorem-proving environments.", "zh-CN": "研究者设计集成协议并在多个定理证明环境中进行评测。" } }, "systems": [ "thor" ], "organizations": [ "university-of-cambridge", "microsoft-research" ], "people": [], "problems": [ "pisa", "minif2f" ], "methods": [ "hammer", "premise-selection", "language-model" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2022-05-22", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "arxiv-thor-2205.10893", "tier": "S1", "type": "paper", "title": "Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers", "url": "https://arxiv.org/abs/2205.10893", "primary": true, "published_date": "2022-05-22", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2021-pact", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "neuro-symbolic", "hammer", "premise-selection" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2022-statement-curriculum-learning", "slug": "lean-statement-curriculum-learning", "title": { "en": "OpenAI's Lean prover uses expert iteration to solve formal Olympiad problems", "zh-CN": "OpenAI Lean 证明器通过专家迭代求解形式化奥赛题" }, "dates": { "event": "2022-02-02", "first_public_claim": "2022-02-02", "paper_release": "2022-02-03", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "system", "competition" ], "significance": { "tier": "H2", "rationale": { "en": "The work showed that proof search interleaved with learning could create its own curriculum and reach a new state of the art on miniF2F.", "zh-CN": "该工作展示了证明搜索与学习交替进行可以形成自举式课程，并在 miniF2F 上取得当时领先结果。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "OpenAI reported 41.2% on miniF2F and automatic proofs of challenging AMC/AIME and two IMO-adapted problems using statement curriculum learning in Lean.", "zh-CN": "OpenAI 报告其基于 Lean 的 statement curriculum learning 在 miniF2F 上达到 41.2%，并自动证明若干 AMC/AIME 及两道改编 IMO 问题。" }, "summary": { "en": "The prover alternated proof search with retraining on newly discovered proofs over statements of varied difficulty.", "zh-CN": "该证明器在不同难度的形式命题上交替执行证明搜索与基于新发现证明的再训练。" }, "why_it_matters": { "en": "It connected language-model theorem proving with expert-iteration ideas that later became central to formal reasoning systems.", "zh-CN": "它把语言模型定理证明与专家迭代结合，后者后来成为形式推理系统中的核心训练范式之一。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The neural prover searched for Lean proofs and used successful proofs as new training data.", "zh-CN": "神经证明器搜索 Lean 证明，并把成功证明作为新的训练数据。" } }, "human_contribution": { "description": { "en": "Researchers curated statements, designed the expert-iteration loop and evaluated generated formal proofs.", "zh-CN": "研究者整理命题、设计专家迭代训练循环并评测生成的形式证明。" } }, "systems": [ "lean-statement-curriculum-prover", "lean" ], "organizations": [ "openai" ], "people": [], "problems": [ "minif2f", "olympiad-mathematics" ], "methods": [ "expert-iteration", "proof-search", "language-model" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2022-02-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } } ] }, "sources": [ { "id": "openai-formal-math-2022", "tier": "S2", "type": "official_announcement", "title": "Solving (some) formal math olympiad problems", "url": "https://openai.com/index/formal-math/", "primary": true, "published_date": "2022-02-02", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2021-pact", "evt-2021-minif2f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "expert-iteration", "olympiad", "formal-proof" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-her-prover", "slug": "her-incremental-first-order-theorem-prover", "title": { "en": "Incremental learning and hindsight replay reduce handcrafted guidance in first-order theorem proving", "zh-CN": "增量学习与 hindsight replay 减少一阶定理证明中的手工搜索启发式" }, "dates": { "event": "2021-12-20", "first_public_claim": "2021-12-20", "paper_release": "2021-12-20", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "This work showed that a learned first-order prover could replace much of a strong prover's handcrafted clause-selection guidance with an incrementally trained neural scorer, using hindsight experience replay to learn from unsuccessful searches and reaching competitive performance on standard theorem-proving benchmarks.", "zh-CN": "该工作展示了学习式一阶证明器可以用增量训练的神经评分器替代强自动证明器中大量手工 clause-selection 启发式，并借助 hindsight experience replay 从失败搜索中学习，在标准定理证明基准上达到具有竞争力的性能。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The authors trained a first-order logic prover around a basic given-clause algorithm, replacing handcrafted clause-scoring heuristics with a learned neural scorer and using hindsight experience replay so training could extract useful supervision even from failed proof searches; the resulting prover matched or surpassed strong traditional baselines on several TPTP-derived benchmarks.", "zh-CN": "作者以基础 given-clause 算法构建一阶逻辑证明器，用学习式神经评分器替代手工 clause-scoring 启发式，并利用 hindsight experience replay 从失败证明搜索中提取训练信号；所得证明器在多个源自 TPTP 的基准上达到或超过强传统基线。" }, "summary": { "en": "Clauses are encoded as graphs and scored by transformer-based models. Training proceeds incrementally, while hindsight replay turns intermediate states from unsuccessful searches into additional learning targets instead of discarding those trajectories.", "zh-CN": "系统把 clause 编码为图并交由基于 Transformer 的模型评分。训练以增量方式推进，同时使用 hindsight replay 将失败搜索中的中间状态转化为额外学习目标，而不是丢弃这些轨迹。" }, "why_it_matters": { "en": "The system is an early example of self-generated proof-search experience replacing brittle hand-designed search knowledge, a pattern that later became central to self-improving neural theorem provers and reasoning agents.", "zh-CN": "该系统较早展示了如何用证明搜索过程中自产生的经验替代脆弱的手工搜索知识，这一模式后来成为自我改进神经证明器和推理智能体的重要组成部分。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The learned clause scorer guided proof search and was iteratively improved from search experience, including trajectories that did not initially find a proof.", "zh-CN": "学习式 clause scorer 负责引导证明搜索，并从搜索经验中迭代改进，其中也包括最初未找到证明的轨迹。" } }, "human_contribution": { "description": { "en": "Researchers designed the given-clause environment, graph representation, transformer scorer, hindsight-replay training scheme and benchmark evaluation.", "zh-CN": "研究者设计 given-clause 环境、图表示、Transformer 评分器、hindsight replay 训练方案与基准评测。" } }, "systems": [ "her-theorem-prover" ], "organizations": [ "deepmind" ], "people": [], "problems": [ "first-order-theorem-proving" ], "methods": [ "incremental-learning", "hindsight-experience-replay", "learned-clause-selection", "transformer", "proof-search" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2021-12-20", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records the system and reported theorem-proving results from the public research paper. No directly linked public code or independently replayed artifact is used here to raise the evidence level.", "zh-CN": "Chronicle 根据公开研究论文记录该系统及其报告的定理证明结果；本记录未使用可直接链接的公开代码或独立 replay artifact 来提高证据等级。" } } ] }, "sources": [ { "id": "arxiv-her-prover-2112.10664", "tier": "S1", "type": "paper", "title": "Proving Theorems using Incremental Learning and Hindsight Experience Replay", "url": "https://arxiv.org/abs/2112.10664", "primary": true, "published_date": "2021-12-20", "accessed_at": "2026-09-11" }, { "id": "pmlr-her-prover-icml-2022", "tier": "S1", "type": "paper", "title": "Proving Theorems using Incremental Learning and Hindsight Experience Replay", "url": "https://proceedings.mlr.press/v162/aygun22a.html", "primary": true, "published_date": "2022-06-28", "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2022-htps" ], "related": [ "evt-2021-tacticzero", "evt-2021-pact" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "first-order-logic", "reinforcement-learning", "hindsight-replay", "proof-search" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-deepmind-math-discovery", "slug": "deepmind-ml-guided-pure-math-discovery", "title": { "en": "DeepMind and mathematicians use machine learning to guide new discoveries in pure mathematics", "zh-CN": "DeepMind 与数学家利用机器学习引导纯数学新发现" }, "dates": { "event": "2021-12-01", "first_public_claim": "2021-11-30", "paper_release": "2021-12-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H1", "rationale": { "en": "This work is a candidate Historical Milestone because it provided an early, high-profile demonstration that modern machine learning could make a substantive intellectual contribution to frontier pure-mathematics research rather than only solve benchmark problems or automate formal proof search. In two distinct fields, learned models exposed relationships that guided mathematicians toward new research-level results: a theorem-level relationship in hyperbolic knot theory and a new formula and conjectural route for Kazhdan-Lusztig combinatorial invariance. The Nature paper explicitly proposed this workflow as a model for human-AI mathematical discovery.", "zh-CN": "该工作被建议列为 Historical Milestone，因为它较早且高影响力地展示了现代机器学习能够对前沿纯数学研究作出实质性智力贡献，而不仅是解决基准题或自动执行形式证明搜索。在两个不同领域中，学习模型揭示的关系引导数学家得到研究级新成果：双曲纽结理论中的定理级关系，以及 Kazhdan-Lusztig 组合不变性方向的新公式与猜想性解决路线。Nature 主论文还明确把这一流程提出为人机协作数学发现的一种范式。" } }, "mathematical_novelty": { "type": "new_result" }, "interfaces": [ "informal", "numeric" ], "claim": { "en": "A DeepMind–mathematician collaboration reported that machine-learning models helped identify previously unnoticed structures in two pure-mathematics research programs. In knot theory, ML-guided feature analysis contributed to the discovery of a relationship between knot signature and hyperbolic cusp geometry that the mathematicians then proved in a companion paper. In representation theory, the collaboration derived a new Bruhat-graph-based formula for Kazhdan-Lusztig polynomials of symmetric groups that suggested a route toward the combinatorial invariance conjecture.", "zh-CN": "DeepMind 与数学家的合作工作报告称，机器学习模型帮助在两个纯数学研究方向中识别此前未被注意的结构。在纽结理论中，ML 引导的特征分析参与发现了纽结 signature 与双曲 cusp geometry 之间的关系，随后数学家在配套论文中给出了证明；在表示论中，合作团队得到一个基于 Bruhat graph 的对称群 Kazhdan-Lusztig 多项式新公式，并据此提出通向组合不变性猜想的研究路线。" }, "summary": { "en": "The project used supervised machine learning to search large mathematical datasets for predictive relationships and attribution methods to expose which variables drove those predictions. Mathematicians then interpreted the signals, reformulated them as mathematical statements, tested counterexamples and supplied conventional mathematical arguments. The Nature article demonstrated the workflow on hyperbolic knots and Kazhdan-Lusztig polynomials, alongside public notebooks and datasets for both case studies.", "zh-CN": "该项目利用监督式机器学习在大型数学数据集中寻找预测关系，再利用 attribution 方法揭示哪些变量驱动模型预测。数学家随后解释这些信号，将其重新表述为数学命题、寻找反例并给出传统数学论证。Nature 论文以双曲纽结和 Kazhdan-Lusztig 多项式为两个案例展示这一流程，并公开了相应 notebook 与数据。" }, "why_it_matters": { "en": "The historical importance is the research workflow rather than autonomous theorem proving: AI acted as a pattern-finding instrument inside live pure-mathematics research, while mathematicians retained problem selection, interpretation, conjecture formulation and proof. This human-AI discovery pattern anticipated later systems aimed explicitly at research-level mathematical discovery.", "zh-CN": "其历史意义主要在研究工作流而非自主定理证明：AI 作为模式发现工具进入真实纯数学研究过程，而数学家仍负责问题选择、解释、猜想形成和证明。这种人机协作发现模式预示了后来明确面向研究级数学发现的 AI 系统。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Machine-learning models searched mathematical datasets for predictive structure and attribution analyses highlighted candidate relationships that redirected or sharpened human mathematical investigation; the AI did not autonomously produce the final rigorous proofs.", "zh-CN": "机器学习模型在数学数据集中寻找预测结构，attribution 分析突出潜在关系，从而改变或聚焦人类数学家的研究方向；AI 并未自主完成最终严格证明。" } }, "human_contribution": { "description": { "en": "Mathematicians selected research questions, generated and interpreted domain data, judged which learned signals were mathematically meaningful, constructed counterexamples, formulated precise conjectures and supplied rigorous mathematical arguments. DeepMind researchers designed and trained the ML pipeline and collaborated on interpreting the learned structure.", "zh-CN": "数学家选择研究问题、生成和解释领域数据、判断哪些学习信号具有数学意义、构造反例、形成精确猜想并给出严格数学论证；DeepMind 研究者设计并训练机器学习流程，并共同解释模型发现的结构。" } }, "systems": [ "ml-guided-mathematical-discovery" ], "organizations": [ "deepmind", "university-of-oxford", "university-of-sydney" ], "people": [ "alex-davies", "petar-velickovic", "andras-juhasz", "marc-lackenby", "geordie-williamson", "pushmeet-kohli" ], "problems": [ "hyperbolic-knot-invariants", "kazhdan-lusztig-combinatorial-invariance" ], "methods": [ "supervised-learning", "attribution", "pattern-discovery", "conjecture-generation", "human-ai-collaboration" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2021-12-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Nature research article and companion mathematical preprints publicly documented the ML-guided discovery workflow and the resulting knot-theory and representation-theory contributions.", "zh-CN": "Nature 研究论文与配套数学预印本公开记录了 ML 引导的发现流程，以及由此形成的纽结理论和表示论研究贡献。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The Chronicle review linked DeepMind's public notebooks and datasets for both mathematical case studies, making the computational discovery artifacts directly inspectable. E3 records artifact availability and does not by itself constitute independent verification of every mathematical interpretation or priority claim.", "zh-CN": "Chronicle 本轮审核链接了 DeepMind 针对两个数学案例公开的 notebook 与数据，使计算发现产物可以直接检查。E3 表示 artifact 可检查，并不单独构成对全部数学解释或历史优先权主张的独立验证。" } } ] }, "sources": [ { "id": "nature-ai-guided-math-2021", "tier": "S1", "type": "paper", "title": "Advancing mathematics by guiding human intuition with AI", "url": "https://www.nature.com/articles/s41586-021-04086-x", "primary": true, "published_date": "2021-12-01", "accessed_at": "2026-09-11" }, { "id": "arxiv-hyperbolic-knots-2111.15323", "tier": "S1", "type": "paper", "title": "The signature and cusp geometry of hyperbolic knots", "url": "https://arxiv.org/abs/2111.15323", "primary": true, "published_date": "2021-11-30", "accessed_at": "2026-09-11" }, { "id": "arxiv-kl-invariance-2111.15161", "tier": "S1", "type": "paper", "title": "Towards combinatorial invariance for Kazhdan-Lusztig polynomials", "url": "https://arxiv.org/abs/2111.15161", "primary": true, "published_date": "2021-11-30", "accessed_at": "2026-09-11" }, { "id": "deepmind-pure-math-blog-2021", "tier": "S2", "type": "official_announcement", "title": "Exploring the beauty of pure mathematics in novel ways", "url": "https://deepmind.google/blog/exploring-the-beauty-of-pure-mathematics-in-novel-ways/", "primary": true, "published_date": "2021-12-01", "accessed_at": "2026-09-11" }, { "id": "github-deepmind-mathematics-conjectures", "tier": "S1", "type": "repository", "title": "DeepMind mathematics conjectures notebooks and datasets", "url": "https://github.com/google-deepmind/mathematics_conjectures", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "nature-news-deepmind-math-2021", "tier": "S4", "type": "media", "title": "DeepMind's AI helps untangle the mathematics of knots", "url": "https://www.nature.com/articles/d41586-021-03593-1", "primary": false, "published_date": "2021-12-01", "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "deepmind-mathematics-conjectures-notebooks", "kind": "code", "title": "Reproducible knot-theory and representation-theory notebooks and data", "url": "https://github.com/google-deepmind/mathematics_conjectures" } ], "relationships": { "predecessors": [], "successors": [ "evt-2022-alphatensor" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mathematical-discovery", "pure-mathematics", "knot-theory", "representation-theory", "machine-learning", "human-ai-collaboration" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-gsm8k", "slug": "gsm8k-verifier-math-reasoning", "title": { "en": "GSM8K and learned verifiers establish a durable benchmark for language-model math reasoning", "zh-CN": "GSM8K 与学习式验证器建立语言模型数学推理的长期基准" }, "dates": { "event": "2021-10-27", "first_public_claim": "2021-10-27", "paper_release": "2021-10-27", "artifact_release": "2021-10-29", "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "dataset", "system" ], "significance": { "tier": "H2", "rationale": { "en": "GSM8K became a durable benchmark for multi-step language-model mathematical reasoning, while the accompanying learned-verifier method established an influential generate-and-rank pattern for improving solution accuracy. Both the dataset and verification idea remained central reference points as reasoning models evolved.", "zh-CN": "GSM8K 成为衡量语言模型多步数学推理能力的长期基准；同期提出的学习式验证器则确立了具有持续影响的“生成多个候选解并由验证器排序”路线。随着推理模型发展，数据集与验证思想都长期保持为重要参照。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "numeric" ], "claim": { "en": "OpenAI introduced GSM8K, a dataset of roughly 8,500 grade-school mathematics word problems, and showed that a learned verifier selecting among multiple generated solutions substantially improved large-model accuracy over finetuning alone.", "zh-CN": "OpenAI 发布约 8,500 道小学数学文字题组成的 GSM8K 数据集，并展示学习式验证器从多个模型生成解中选择候选，可以相较单纯微调显著提升大模型准确率。" }, "summary": { "en": "The work paired a human-written math reasoning dataset with a generator-verifier pipeline. A language model generated many candidate solutions, while a separately trained verifier scored those solutions and selected the most promising answer.", "zh-CN": "该工作把人工编写的数学推理数据集与生成器—验证器流程结合：语言模型生成多个候选解，另一个单独训练的验证器对候选进行评分并选择最有希望的答案。" }, "why_it_matters": { "en": "GSM8K became one of the most reused small-scale mathematical reasoning benchmarks, and its verifier-based inference pattern anticipated later outcome- and process-verification methods used throughout LLM reasoning research.", "zh-CN": "GSM8K 此后成为使用最广泛的小规模数学推理基准之一，而其基于验证器的推理流程也预示了后来 LLM 推理研究中广泛采用的结果验证与过程验证方法。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Language models generated candidate mathematical solutions and a learned verifier ranked their correctness; the benchmark questions and reference solutions were written and curated by humans.", "zh-CN": "语言模型生成候选数学解，学习式验证器对其正确性进行排序；基准题目与参考解答由人工编写和整理。" } }, "human_contribution": { "description": { "en": "Researchers designed the benchmark and verifier methodology, commissioned and curated the human-written problems and solutions, trained the models, and evaluated scaling behavior.", "zh-CN": "研究者设计基准与验证器方法，组织并整理人工编写的题目和解答，训练模型并评测其扩展规律。" } }, "systems": [ "gsm8k", "learned-verifier" ], "organizations": [ "openai" ], "people": [], "problems": [ "grade-school-math-word-problems" ], "methods": [ "language-modeling", "verifier-ranking", "generate-and-rank", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2021-10-27", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record introduced GSM8K and the verifier-based solution-selection method.", "zh-CN": "arXiv 研究记录发布了 GSM8K，并提出基于验证器的候选解选择方法。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The canonical record links the archived official OpenAI dataset repository, making the benchmark data and example evaluation code directly inspectable. E3 does not imply independent verification of every reported model result.", "zh-CN": "canonical record 直接链接 OpenAI 已归档的官方数据集仓库，使基准数据与示例评测代码可直接检查。E3 并不表示论文报告的全部模型结果都已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-gsm8k-2110.14168", "tier": "S1", "type": "paper", "title": "Training Verifiers to Solve Math Word Problems", "url": "https://arxiv.org/abs/2110.14168", "primary": true, "published_date": "2021-10-27", "accessed_at": "2026-09-11" }, { "id": "openai-solving-math-word-problems-2021", "tier": "S2", "type": "official_announcement", "title": "Solving math word problems", "url": "https://openai.com/index/solving-math-word-problems/", "primary": true, "published_date": "2021-10-29", "accessed_at": "2026-09-11" }, { "id": "github-openai-grade-school-math", "tier": "S1", "type": "repository", "title": "OpenAI Grade School Math dataset and example code", "url": "https://github.com/openai/grade-school-math", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "gsm8k-dataset-repository", "kind": "dataset", "title": "GSM8K dataset and example model-solution code", "url": "https://github.com/openai/grade-school-math" } ], "relationships": { "predecessors": [ "evt-2021-math-benchmark" ], "successors": [ "evt-2022-minerva" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "gsm8k", "benchmark", "dataset", "math-reasoning", "verifier", "language-model" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-minif2f", "slug": "minif2f-formal-olympiad-benchmark", "title": { "en": "miniF2F establishes a cross-system benchmark for formal Olympiad mathematics", "zh-CN": "miniF2F 建立跨形式系统的奥赛数学基准" }, "dates": { "event": "2021-08-31", "first_public_claim": "2021-08-31", "paper_release": "2021-08-31", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "benchmark", "dataset", "infrastructure", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "miniF2F created a shared set of Olympiad-level statements across formal systems, making progress in neural theorem proving easier to compare and helping establish a durable evaluation target used by later Lean provers.", "zh-CN": "miniF2F 将奥赛级题目整理为多个形式系统中的共享题集，使神经定理证明方法更容易直接比较，并成为后来多种 Lean 证明器长期使用的评测目标。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "miniF2F introduced 488 formal Olympiad-level problem statements spanning Metamath, Lean and additional proof assistants, with held-out splits intended for cross-system theorem-proving evaluation.", "zh-CN": "miniF2F 引入了 488 个形式化的奥赛级数学题目陈述，覆盖 Metamath、Lean 等证明助手，并提供用于跨系统定理证明评测的留出划分。" }, "summary": { "en": "The benchmark translated problems from AIME, AMC, IMO and educational sources into formal languages. Its goal was not a new mathematical theorem but a reproducible common target on which learned theorem provers could be trained and compared.", "zh-CN": "该基准把 AIME、AMC、IMO 及教学来源中的问题翻译为形式语言。其贡献不是新的数学定理，而是为学习式定理证明器提供可复现、可训练和可比较的共同目标。" }, "why_it_matters": { "en": "miniF2F became part of the evaluation backbone for formal AI4Math, allowing later systems such as LeanDojo, COPRA and DeepSeek-Prover to report progress against a recognizable shared task.", "zh-CN": "miniF2F 成为形式化 AI4Math 的核心评测基础之一，使 LeanDojo、COPRA、DeepSeek-Prover 等后续系统能够在一个可识别的共享任务上报告进展。" }, "ai_role": { "level": "computation_only", "description": { "en": "AI systems were benchmarked on the dataset, but the benchmark construction and formal statement curation were human-led rather than an AI mathematical discovery.", "zh-CN": "AI 系统在该数据集上接受评测，但基准构建与形式化题目整理主要由人类完成，并非 AI 数学发现事件。" } }, "human_contribution": { "description": { "en": "The authors selected source problems, translated and curated formal statements, designed benchmark splits and maintained the cross-system evaluation resource.", "zh-CN": "作者选择原始问题、翻译并整理形式化陈述、设计评测划分，并维护跨系统评测资源。" } }, "systems": [ "minif2f", "lean", "metamath", "isabelle", "hol-light" ], "organizations": [ "openai", "formal-mathematics-community" ], "people": [ "kunhao-zheng", "jesse-michael-han", "stanislas-polu" ], "problems": [ "olympiad-mathematics" ], "methods": [ "benchmarking", "formalization", "theorem-proving" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2021-08-31", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The benchmark was documented in an arXiv paper and released as a public formal-mathematics repository.", "zh-CN": "该基准通过 arXiv 论文公开说明，并以形式数学公共仓库的形式发布。" } } ] }, "sources": [ { "id": "arxiv-minif2f-2109.00110", "tier": "S1", "type": "paper", "title": "MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics", "url": "https://arxiv.org/abs/2109.00110", "primary": true, "published_date": "2021-08-31", "accessed_at": "2026-09-10" }, { "id": "github-openai-minif2f", "tier": "S1", "type": "benchmark", "title": "OpenAI miniF2F repository", "url": "https://github.com/openai/miniF2F", "primary": true, "published_date": null, "accessed_at": "2026-09-10" } ], "artifacts": [ { "id": "minif2f-repository", "kind": "benchmark", "title": "miniF2F benchmark repository", "url": "https://github.com/openai/miniF2F" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f" ], "successors": [ "evt-2023-leandojo", "evt-2023-copra", "evt-2024-deepseek-prover-v1-5" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "olympiad", "lean", "metamath", "theorem-proving", "formalization" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-math-ai-workshop", "slug": "math-ai-workshop-series", "title": { "en": "MATH-AI begins a recurring workshop series on mathematical reasoning and AI", "zh-CN": "MATH-AI 开启数学推理与 AI 的持续性 workshop 系列" }, "dates": { "event": "2021-05-07", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "MATH-AI is a field-building milestone because its 2021 inaugural ICLR workshop created a dedicated, reviewed forum around mathematical reasoning as an AI research problem, with explicit participation from machine learning, automated theorem proving, cognitive science and mathematics. The series then continued through five held editions from 2021 to 2025, with a sixth NeurIPS workshop accepted and scheduled for 2026, demonstrating durable community continuity rather than a one-off meeting.", "zh-CN": "MATH-AI 构成领域建构里程碑，因为其 2021 年首届 ICLR workshop 建立了一个专门讨论“数学推理作为 AI 研究问题”的投稿评审论坛，并明确连接机器学习、自动定理证明、认知科学与数学共同体。该系列随后在 2021–2025 年连续举办五届，第六届也已被 NeurIPS 2026 接收并排期，体现出持续性的共同体建设而非一次性会议。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The first MATH-AI workshop, The Role of Mathematical Reasoning in General Artificial Intelligence, was held at ICLR on 7 May 2021. Its double-blind call for papers sought work on mathematical reasoning, theorem proving, informal and formal mathematics, datasets and related reasoning problems. Official MATH-AI records document successive editions at NeurIPS in 2022, 2023, 2024 and 2025, and a sixth edition accepted for NeurIPS 2026.", "zh-CN": "首届 MATH-AI workshop“ The Role of Mathematical Reasoning in General Artificial Intelligence”于 2021 年 5 月 7 日在 ICLR 举行。其双盲征稿面向数学推理、定理证明、非形式与形式数学、数据集及相关推理问题。MATH-AI 官方记录显示，该系列随后于 2022、2023、2024、2025 年连续在 NeurIPS 举办，并已有第六届获得 NeurIPS 2026 接收。" }, "summary": { "en": "MATH-AI began as a cross-disciplinary workshop asking how mathematical reasoning could illuminate general AI. The inaugural program combined invited talks, contributed papers, poster sessions and a discussion panel, while its review process used anonymized submissions. Across later editions the series evolved with the field toward large language models, theorem proving, autoformalization, mathematical discovery and agentic AI while retaining a dedicated mathematical-reasoning identity.", "zh-CN": "MATH-AI 最初以跨学科 workshop 形式讨论数学推理如何帮助理解一般人工智能。首届议程结合邀请报告、投稿论文、poster session 与讨论 panel，并采用匿名投稿评审。随着领域演化，后续各届逐步覆盖大语言模型、定理证明、自动形式化、数学发现与 Agentic AI，同时保持以数学推理为核心的专门学术身份。" }, "why_it_matters": { "en": "A durable workshop series is evidence that AI4Math had begun to organize as a recurring scholarly community before the current wave of frontier research claims. MATH-AI also links an earlier theorem-proving and mathematical-reasoning community to the later LLM-centered AI4Math ecosystem, making its inaugural edition a useful institutional milestone in the field's recent history.", "zh-CN": "一个持续举办的专门 workshop 系列表明，在当前前沿 AI4Math 研究 claim 大量出现之前，AI4Math 已开始形成重复运作的学术共同体。MATH-AI 还连接了较早的定理证明 / 数学推理社区与后来以 LLM 为中心的 AI4Math 生态，因此其首届会议具有明确的领域制度史意义。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records the formation of a recurring scholarly venue rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是持续性学术 venue 的形成，而不是某个 AI 系统执行数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "Human organizers established the workshop, recruited speakers and program-committee members, ran a double-blind submission process, selected contributed work and sustained the series across successive ICLR and NeurIPS editions.", "zh-CN": "人类组织者建立 workshop、邀请报告人与 program committee 成员、运行双盲投稿评审、筛选投稿成果，并在 ICLR 与后续 NeurIPS 多届会议中持续维护该系列。" } }, "systems": [], "organizations": [ "iclr", "neurips" ], "people": [], "problems": [], "methods": [ "scholarly-venue", "mathematical-reasoning-community" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2021-05-07", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official ICLR 2021 MATH-AI pages establish the inaugural workshop date, mathematical-reasoning scope, organizers, program committee, accepted papers and double-blind review process.", "zh-CN": "ICLR 2021 MATH-AI 官方页面记录了首届 workshop 日期、数学推理主题范围、组织者、program committee、录用论文与双盲评审流程。" } }, { "date": "2026-09-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official sixth-workshop site lists the five earlier editions from 2021 through 2025 and records the accepted NeurIPS 2026 edition, supporting the Chronicle's durability assessment without treating future attendance or impact as already observed.", "zh-CN": "第六届 workshop 官方网站列出了 2021–2025 年五届既有会议，并记录已获接收的 NeurIPS 2026 第六届，由此支持 Chronicle 对系列持续性的判断；该记录不把尚未发生的 2026 参会情况或影响视为既成事实。" } } ] }, "sources": [ { "id": "math-ai-2021-official", "tier": "S2", "type": "official_announcement", "title": "MATH-AI: The Role of Mathematical Reasoning in General Artificial Intelligence", "url": "https://mathai-iclr.github.io/", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "math-ai-2021-cfp", "tier": "S2", "type": "official_announcement", "title": "MATH-AI ICLR 2021 Call for Papers", "url": "https://mathai-iclr.github.io/cfp/", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "math-ai-2026-series", "tier": "S2", "type": "official_announcement", "title": "6th MATH-AI Workshop at NeurIPS 2026", "url": "https://mathai-2026.github.io/", "primary": false, "published_date": null, "accessed_at": "2026-09-14" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2016-aitp" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "math-ai", "field-building", "workshop-series", "mathematical-reasoning", "theorem-proving", "autoformalization", "iclr", "neurips" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-math-benchmark", "slug": "math-competition-problem-benchmark", "title": { "en": "MATH makes competition mathematics a standard language-model benchmark", "zh-CN": "MATH 将竞赛数学确立为语言模型标准基准之一" }, "dates": { "event": "2021-03-05", "first_public_claim": "2021-03-05", "paper_release": "2021-03-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "MATH became a durable benchmark for measuring multi-step competition-level mathematical reasoning and later exposed saturation as reasoning models improved.", "zh-CN": "MATH 成为衡量多步竞赛级数学推理的长期基准，并在后续推理模型快速提升后反过来显示出基准饱和问题。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "The MATH dataset introduced 12,500 challenging competition mathematics problems with step-by-step solutions for training and evaluation.", "zh-CN": "MATH 数据集引入了 12,500 道具有逐步解答的高难度竞赛数学问题，用于训练与评测。" }, "summary": { "en": "The benchmark covered algebra, geometry, number theory, probability and other competition topics and provided full solution derivations.", "zh-CN": "该基准覆盖代数、几何、数论、概率等竞赛数学主题，并提供完整解题过程。" }, "why_it_matters": { "en": "For several years, progress on MATH served as one of the clearest quantitative signals of LLM mathematical reasoning.", "zh-CN": "此后数年，MATH 上的进展成为观察 LLM 数学推理能力变化的主要量化信号之一。" }, "ai_role": { "level": "computation_only", "description": { "en": "AI systems are evaluated and trained on the benchmark; the benchmark itself is a human-curated research artifact.", "zh-CN": "AI 系统在该基准上训练与评测；基准本身由研究者构建。" } }, "human_contribution": { "description": { "en": "Researchers collected problems and solutions, designed the dataset and evaluated scaling behavior.", "zh-CN": "研究者收集题目与解答、设计数据集并研究模型扩展规律。" } }, "systems": [ "math-benchmark" ], "organizations": [ "uc-berkeley" ], "people": [], "problems": [ "competition-mathematics" ], "methods": [ "benchmarking", "dataset-curation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2021-03-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-math-2103.03874", "tier": "S1", "type": "paper", "title": "Measuring Mathematical Problem Solving With the MATH Dataset", "url": "https://arxiv.org/abs/2103.03874", "primary": true, "published_date": "2021-03-05", "accessed_at": "2026-09-10" }, { "id": "github-math-dataset", "tier": "S1", "type": "repository", "title": "MATH dataset repository and evaluation code", "url": "https://github.com/hendrycks/math", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "math-dataset-repository", "kind": "dataset", "title": "MATH dataset loaders and evaluation code", "url": "https://github.com/hendrycks/math" } ], "relationships": { "predecessors": [ "evt-2019-mathematics-dataset" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "competition-math", "language-model", "reasoning" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-tacticzero", "slug": "tacticzero-deep-rl-theorem-proving", "title": { "en": "TacticZero learns interactive theorem proving from scratch with deep reinforcement learning", "zh-CN": "TacticZero 以深度强化学习从零学习交互式定理证明" }, "dates": { "event": "2021-02-19", "first_public_claim": "2021-02-19", "paper_release": "2021-02-19", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "TacticZero established a distinct reinforcement-learning route for proof-assistant-native theorem proving: an end-to-end agent learned proof search, tactic selection and tactic arguments without relying on an imitation dataset of expert proofs, and the work became a representative early neural ITP system.", "zh-CN": "TacticZero 建立了一条具有代表性的强化学习定理证明路线：端到端智能体直接在证明助手环境中学习证明搜索、tactic 选择及参数，而不依赖专家证明的模仿学习数据，成为早期神经交互式定理证明的重要系统之一。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "TacticZero formulated HOL4 interactive theorem proving as a Markov decision process and trained a deep reinforcement-learning agent to learn search, tactic and argument prediction from scratch; the authors reported that it outperformed the existing HOL4 hammers on held-out problems.", "zh-CN": "TacticZero 将 HOL4 交互式定理证明建模为马尔可夫决策过程，并以深度强化学习从零训练搜索、tactic 与参数预测智能体；作者报告该系统在留出问题上优于 HOL4 中已有的 hammer 自动证明器。" }, "summary": { "en": "The system represents proof search as an end-to-end reinforcement-learning problem and introduces backtracking that lets the agent abandon predicted dead ends and resume from promising alternatives. The resulting proofs are constructed inside HOL4 and therefore remain subject to the proof assistant's kernel checking.", "zh-CN": "该系统把证明搜索整体表述为端到端强化学习问题，并引入回溯机制，使智能体能够放弃预测为死路的推导并从更有希望的分支继续搜索。最终证明在 HOL4 内构造，因此仍接受证明助手内核检查。" }, "why_it_matters": { "en": "It demonstrated that reinforcement learning could jointly learn proof-search control and proof actions inside a mature interactive theorem prover, providing an early precursor to later self-improving and search-driven neural theorem-proving systems.", "zh-CN": "它展示了强化学习能够在成熟交互式证明器内部同时学习证明搜索控制与证明动作，为后续自我改进和搜索驱动的神经定理证明系统提供了早期范式。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The learned agent selected proof-search branches, tactics and tactic arguments; HOL4 mechanically checked proof steps accepted by the environment.", "zh-CN": "学习式智能体负责选择证明搜索分支、tactic 及其参数；HOL4 对环境接受的证明步骤进行机械检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the reinforcement-learning formulation, search and backtracking mechanism, HOL4 integration, training protocol and evaluation.", "zh-CN": "研究者设计强化学习表述、搜索与回溯机制、HOL4 集成、训练流程与评测方案。" } }, "systems": [ "tacticzero", "hol4" ], "organizations": [ "australian-national-university", "csiro-data61" ], "people": [ "minchao-wu", "michael-norrish", "christian-walder", "amir-dezfouli" ], "problems": [], "methods": [ "deep-reinforcement-learning", "proof-search", "tactic-prediction", "backtracking" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2021-02-19", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The public research record documents the HOL4 system and its reported held-out theorem-proving results. Machine checking refers to proofs constructed inside HOL4 and does not imply independent reproduction of the reported benchmark performance.", "zh-CN": "公开研究记录描述了 HOL4 系统及其留出定理证明结果。machine_checked 仅指在 HOL4 内构造的证明接受内核检查，并不表示论文所报告的基准性能已经得到独立复现。" } } ] }, "sources": [ { "id": "arxiv-tacticzero-2102.09756", "tier": "S1", "type": "paper", "title": "TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning", "url": "https://arxiv.org/abs/2102.09756", "primary": true, "published_date": "2021-02-19", "accessed_at": "2026-09-11" }, { "id": "neurips-tacticzero-2021", "tier": "S1", "type": "paper", "title": "TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning", "url": "https://proceedings.neurips.cc/paper/2021/hash/4dea382d82666332fb564f2e711cbc71-Abstract.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2018-tactictoe", "evt-2019-holist", "evt-2020-gpt-f" ], "successors": [ "evt-2022-htps" ], "related": [ "evt-2021-pact", "evt-2021-minif2f" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "hol4", "theorem-proving", "reinforcement-learning", "proof-search", "tactics" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2021-pact", "slug": "pact-proof-artifact-cotraining", "title": { "en": "PACT uses proof artifacts to scale language-model theorem proving", "zh-CN": "PACT 利用证明产物扩展语言模型定理证明" }, "dates": { "event": "2021-02-11", "first_public_claim": "2021-02-11", "paper_release": "2021-02-11", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "PACT established proof-term-derived self-supervision as a practical way to alleviate data scarcity in neural theorem proving.", "zh-CN": "PACT 将证明项衍生的自监督数据用于缓解神经定理证明中的数据稀缺问题，形成了重要的训练路线。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "PACT co-trained a Transformer theorem prover on Lean proof artifacts and improved held-out theorem-proving success from 32% to 48%.", "zh-CN": "PACT 使用 Lean 证明产物对 Transformer 定理证明器进行协同训练，将留出定理的证明成功率从 32% 提升至 48%。" }, "summary": { "en": "The method extracts self-supervised objectives from kernel-level proof terms and trains them alongside tactic prediction.", "zh-CN": "该方法从内核级证明项中提取自监督目标，并与 tactic prediction 一起训练。" }, "why_it_matters": { "en": "It helped establish that formal libraries contain much more learnable signal than only the next tactic labels exposed at the surface.", "zh-CN": "它说明形式数学库中可学习的信息远多于表层的下一步 tactic 标签，为后续大规模形式证明训练提供了基础。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "The language model predicts proof tactics using representation learned from both tactic labels and proof-artifact objectives.", "zh-CN": "语言模型利用 tactic 标签和证明产物目标共同学习的表示来预测证明步骤。" } }, "human_contribution": { "description": { "en": "Researchers designed the artifact objectives, instrumented Lean, and curated the evaluation setting.", "zh-CN": "研究者设计证明产物训练目标、接入 Lean 并构建评测设置。" } }, "systems": [ "pact", "lean" ], "organizations": [ "openai" ], "people": [], "problems": [], "methods": [ "proof-artifact-cotraining", "transformer", "tactic-prediction" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2021-02-11", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records this event from the cited primary or official source; the status does not imply independent Chronicle verification.", "zh-CN": "Chronicle 依据所引 primary / official source 记录该事件；该状态不表示 Chronicle 已完成独立验证。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "This corpus refresh added a directly inspectable public artifact maintained by the authors or releasing organization. E3 records artifact-level inspectability and does not imply independent verification of the underlying scientific or mathematical claim.", "zh-CN": "本轮 corpus 刷新增补了由作者或发布机构维护、可直接检查的公开产物。E3 表示证据已达到可检查 artifact 层级，并不等同于底层科学或数学主张已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-pact-2102.06203", "tier": "S1", "type": "paper", "title": "Proof Artifact Co-training for Theorem Proving with Language Models", "url": "https://arxiv.org/abs/2102.06203", "primary": true, "published_date": "2021-02-11", "accessed_at": "2026-09-10" }, { "id": "github-pact-lean-step-public", "tier": "S1", "type": "repository", "title": "PACT LeanStep proof-artifact extraction code", "url": "https://github.com/jesse-michael-han/lean-step-public", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "pact-lean-step-public", "kind": "code", "title": "LeanStep proof-artifact extraction code used for PACT", "url": "https://github.com/jesse-michael-han/lean-step-public" } ], "relationships": { "predecessors": [ "evt-2020-gpt-f" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "theorem-proving", "self-supervision", "language-model" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-gpt-f", "slug": "gpt-f-metamath-theorem-proving", "title": { "en": "GPT-f brings generative language modeling to formal theorem proving", "zh-CN": "GPT-f 将生成式语言模型引入形式定理证明" }, "dates": { "event": "2020-09-07", "first_public_claim": "2020-09-07", "paper_release": "2020-09-07", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-10", "last_updated": "2026-09-10" }, "event_types": [ "proof", "formalization", "system" ], "significance": { "tier": "H2", "rationale": { "en": "GPT-f was an early demonstration that transformer language models could generate formal proof steps rather than only score or classify them, and its authors reported new shorter proofs accepted into the Metamath library.", "zh-CN": "GPT-f 是较早展示 Transformer 语言模型能够直接生成形式证明步骤、而非仅进行评分或分类的系统之一；作者还报告其找到的新短证明被 Metamath 主库接收。" } }, "mathematical_novelty": { "type": "new_proof" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "GPT-f used a generative transformer model to search for proofs in Metamath and found new shorter proofs that were accepted into the main Metamath library.", "zh-CN": "GPT-f 使用生成式 Transformer 模型在 Metamath 中搜索证明，并找到被 Metamath 主库接收的新短证明。" }, "summary": { "en": "OpenAI researchers Stanislas Polu and Ilya Sutskever trained generative models over formal mathematical text and integrated them into proof search for the Metamath language. The work framed theorem proving as sequence generation and showed that learned generation could contribute usable proof artifacts to an established formal library.", "zh-CN": "OpenAI 研究者 Stanislas Polu 与 Ilya Sutskever 在形式数学文本上训练生成模型，并将其整合进 Metamath 的证明搜索。该工作把定理证明表述为序列生成任务，并展示了学习式生成模型可以向既有形式数学库贡献可用的证明产物。" }, "why_it_matters": { "en": "The result is a useful starting point for the later LLM-plus-proof-assistant line of AI4Math, where language models propose proof actions and formal systems provide exact feedback.", "zh-CN": "这一结果可视为后来“LLM + 证明助手”AI4Math 路线的重要起点：语言模型提出证明动作，形式系统提供精确反馈。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "The model generated candidate proof steps and proof searches; Metamath mechanically checked resulting proofs before they could be accepted.", "zh-CN": "模型生成候选证明步骤并执行证明搜索；所得证明在被接收前由 Metamath 进行机械检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the model and search procedure, selected the formal corpus and evaluation, and the Metamath community maintained the target library and reviewed contributions.", "zh-CN": "研究者设计模型与搜索流程、选择形式语料和评测方式；Metamath 社区维护目标证明库并审核贡献。" } }, "systems": [ "gpt-f", "metamath" ], "organizations": [ "openai", "metamath-community" ], "people": [ "stanislas-polu", "ilya-sutskever" ], "problems": [], "methods": [ "transformer-language-modeling", "formal-theorem-proving", "proof-search" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2020-09-07", "status": "paper_released", "evidence_level": "E2", "note": { "en": "OpenAI and the arXiv paper reported the Metamath prover and the adoption of generated shorter proofs into the library.", "zh-CN": "OpenAI 与 arXiv 论文报告了该 Metamath 证明器，以及生成的更短证明被主库接收的情况。" } } ] }, "sources": [ { "id": "openai-gpt-f-2020", "tier": "S2", "type": "official_announcement", "title": "Generative language modeling for automated theorem proving", "url": "https://openai.com/index/generative-language-modeling-for-automated-theorem-proving/", "primary": true, "published_date": "2020-09-07", "accessed_at": "2026-09-10" }, { "id": "arxiv-gpt-f-2009.03393", "tier": "S1", "type": "paper", "title": "Generative Language Modeling for Automated Theorem Proving", "url": "https://arxiv.org/abs/2009.03393", "primary": true, "published_date": "2020-09-07", "accessed_at": "2026-09-10" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2021-minif2f", "evt-2023-leandojo", "evt-2023-copra", "evt-2024-deepseek-prover-v1-5" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "metamath", "theorem-proving", "transformers", "formal-mathematics", "proof-search" ], "editorial": { "created_at": "2026-09-10", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-tactician", "slug": "tactician-coq-tactic-learning", "title": { "en": "Tactician integrates adaptive tactic learning and proof synthesis into Coq", "zh-CN": "Tactician 将自适应 tactic 学习与证明合成直接集成进 Coq" }, "dates": { "event": "2020-07-31", "first_public_claim": "2020-07-31", "paper_release": "2020-07-31", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "proof", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Tactician turned learned tactic prediction into an integrated, interactive Coq workflow that could learn from existing developments, suggest the next tactic or synthesize a proof, and continue adapting as users worked across package dependencies.", "zh-CN": "Tactician 将学习式 tactic 预测发展为直接嵌入 Coq 的交互工作流：它可以从既有开发中学习、建议下一步 tactic 或自动合成证明，并在跨 package dependency 的实际使用中持续适应。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Tactician provided a Coq plugin that learns from previously written tactic scripts and can either recommend the next tactic interactively or perform automated tactic-level proof synthesis, with tooling designed to learn across installed Coq developments.", "zh-CN": "Tactician 提供 Coq 插件，从已有 tactic script 中学习，既能交互式推荐下一步 tactic，也能执行 tactic 层面的自动证明合成，并支持从已安装的 Coq 开发中持续学习。" }, "summary": { "en": "The project combines online tactic learning, proof search and package-aware instrumentation so machine-learning assistance lives inside the proof assistant rather than as a detached benchmark-only experiment.", "zh-CN": "该项目把在线 tactic 学习、证明搜索与 package-aware instrumentation 结合起来，使机器学习辅助直接存在于证明助手工作流中，而不是停留在独立的 benchmark 实验里。" }, "why_it_matters": { "en": "It is an early example of a maintained proof-assistant-native learning platform, anticipating later AI theorem-proving infrastructure that exposes interactive proof states to continuously improving learned agents.", "zh-CN": "它是较早的、持续维护的 proof-assistant-native 学习平台之一，预示了后来把交互式证明状态暴露给持续改进学习 Agent 的 AI 定理证明基础设施路线。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Learned models rank tactic choices and drive tactic-level proof search while remaining embedded in a human-controlled Coq proof-development loop.", "zh-CN": "学习模型对 tactic 选择进行排序并驱动 tactic 层面的证明搜索，同时仍嵌入由人控制的 Coq 证明开发循环。" } }, "human_contribution": { "description": { "en": "Researchers designed the learning and search machinery, implemented the Coq plugin and dependency-aware instrumentation, and human Coq developments provide the tactic traces from which the system learns.", "zh-CN": "研究者设计学习与搜索机制、实现 Coq 插件及 dependency-aware instrumentation；人工编写的 Coq 开发则提供系统学习所需的 tactic 轨迹。" } }, "systems": [ "tactician", "coq" ], "organizations": [], "people": [ "lasse-blaauwbroek", "josef-urban", "herman-geuvers" ], "problems": [], "methods": [ "tactic-learning", "proof-search", "online-learning", "proof-synthesis" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2020-07-31", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv extended paper and CICM publication record establish the Tactician system and its integration model for Coq.", "zh-CN": "arXiv 扩展论文与 CICM 正式发表记录确立了 Tactician 系统及其 Coq 集成方式。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The Chronicle linked the maintained public Tactician repository as a directly inspectable implementation artifact. E3 denotes artifact availability and does not imply independent verification of research-performance claims.", "zh-CN": "Chronicle 补入持续维护的 Tactician 公开仓库作为可直接检查的实现产物。E3 表示 artifact 可用，并不等同于对研究性能主张的独立验证。" } } ] }, "sources": [ { "id": "arxiv-tactician-2008.00120", "tier": "S1", "type": "paper", "title": "The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq", "url": "https://arxiv.org/abs/2008.00120", "primary": true, "published_date": "2020-07-31", "accessed_at": "2026-09-11" }, { "id": "doi-tactician-cicm2020", "tier": "S1", "type": "paper", "title": "The Tactician: A Seamless, Interactive Tactic Learner and Prover for Coq — CICM 2020", "url": "https://doi.org/10.1007/978-3-030-53518-6_17", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-coq-tactician", "tier": "S1", "type": "repository", "title": "Tactician Coq plugin and prover repository", "url": "https://github.com/coq-tactician/coq-tactician", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "coq-tactician-repository", "kind": "code", "title": "Tactician Coq plugin, tests and proof-learning implementation", "url": "https://github.com/coq-tactician/coq-tactician" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2023-leandojo", "evt-2023-copra" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "coq", "theorem-proving", "tactic-learning", "proof-assistant", "interactive-proving" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-int", "slug": "int-generalization-theorem-proving", "title": { "en": "INT makes systematic generalization a first-class theorem-proving benchmark", "zh-CN": "INT 将系统化泛化能力确立为定理证明基准的核心对象" }, "dates": { "event": "2020-07-06", "first_public_claim": "2020-07-06", "paper_release": "2020-07-06", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-11" }, "event_types": [ "benchmark", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "INT reframed theorem-proving evaluation around controlled generalization rather than only aggregate proof success, using a theorem generator to expose distinct distribution shifts and providing a lightweight environment for learning-based prover research.", "zh-CN": "INT 不再只用总体证明成功率评价定理证明器，而是借助定理生成器系统构造不同分布偏移，把受控泛化能力作为核心评测对象，并提供轻量级学习式证明研究环境。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "INT introduced an inequality theorem-proving benchmark with a theoretically unbounded theorem-and-proof generator, six controlled generalization settings, and fast sequence- and graph-based interfaces for training and evaluating proof agents.", "zh-CN": "INT 引入不等式定理证明基准，提供理论上可无限生成定理与证明的生成器、六类受控泛化设置，以及用于训练和评测证明 Agent 的快速序列与图接口。" }, "summary": { "en": "The benchmark generates synthetic inequality proofs from axioms and varies properties of training and test distributions so researchers can distinguish memorization-like success from different forms of out-of-distribution theorem-proving generalization.", "zh-CN": "该基准从公理出发生成合成不等式证明，并系统改变训练与测试分布的属性，使研究者能够区分近似记忆式成功与不同形式的分布外定理证明泛化。" }, "why_it_matters": { "en": "It supplied an early controlled testbed for a problem that remains central to learned theorem proving: whether a prover can transfer beyond theorem shapes and proof patterns seen during training.", "zh-CN": "它较早为学习式定理证明中的核心问题提供了受控试验场：证明器能否超越训练阶段见过的定理形态和证明模式进行迁移。" }, "ai_role": { "level": "computation_only", "description": { "en": "Learning-based proof agents are trained and evaluated inside the generated theorem-proving environment; the benchmark itself is a researcher-designed evaluation artifact.", "zh-CN": "学习式证明 Agent 在生成的定理证明环境中训练与评测；基准本身是研究者设计的评测产物。" } }, "human_contribution": { "description": { "en": "Researchers designed the inequality axioms, theorem generator, six generalization regimes, interfaces, baselines and evaluation protocol.", "zh-CN": "研究者设计不等式公理、定理生成器、六类泛化设置、交互接口、基线和评测协议。" } }, "systems": [ "int-benchmark" ], "organizations": [ "university-of-toronto", "vector-institute" ], "people": [ "yuhuai-wu", "albert-qiaochu-jiang", "jimmy-ba", "roger-grosse" ], "problems": [ "inequality-theorem-proving" ], "methods": [ "theorem-generation", "benchmarking", "systematic-generalization", "graph-neural-networks", "transformers" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2020-07-06", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record established the INT benchmark, theorem generator and reported generalization experiments.", "zh-CN": "arXiv 研究记录公开了 INT 基准、定理生成器及其报告的泛化实验。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The Chronicle linked the ICLR 2021 research record and the authors' public INT repository containing the proving environment, generator and training code. E3 denotes inspectable artifacts, not independent verification of benchmark conclusions.", "zh-CN": "Chronicle 补入 ICLR 2021 研究记录以及作者公开的 INT 仓库，其中包含证明环境、生成器和训练代码。E3 表示存在可检查产物，并不等同于对基准结论的独立验证。" } } ] }, "sources": [ { "id": "arxiv-int-2007.02924", "tier": "S1", "type": "paper", "title": "INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving", "url": "https://arxiv.org/abs/2007.02924", "primary": true, "published_date": "2020-07-06", "accessed_at": "2026-09-11" }, { "id": "openreview-int-iclr2021", "tier": "S1", "type": "paper", "title": "INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving — ICLR 2021", "url": "https://openreview.net/forum?id=O6LPudowNQm", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-int", "tier": "S1", "type": "repository", "title": "INT theorem-proving benchmark and environment", "url": "https://github.com/albertqjiang/INT", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "int-repository", "kind": "code", "title": "INT theorem generator, proving environment and training code", "url": "https://github.com/albertqjiang/INT" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2021-minif2f" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "benchmark", "theorem-proving", "generalization", "synthetic-data", "inequalities" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-11", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-isarstep", "slug": "isarstep-high-level-reasoning", "title": { "en": "IsarStep benchmarks high-level mathematical reasoning from human-written Isabelle proofs", "zh-CN": "IsarStep 以人工 Isabelle 证明建立高层数学推理基准" }, "dates": { "event": "2020-06-13", "first_public_claim": "2020-06-13", "paper_release": "2020-06-13", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "IsarStep created a large non-synthetic benchmark from human-written Isabelle proofs and focused evaluation on recovering missing intermediate propositions rather than only predicting low-level tactics. It helped establish high-level proof-step generation over real formal mathematics as a distinct learning problem before later language-model theorem-proving systems scaled similar ideas.", "zh-CN": "IsarStep 从人工编写的 Isabelle 证明中构建大规模非合成 benchmark，并把评测重点放在恢复缺失的中间命题，而不只是预测低层 tactic。它推动“在真实形式数学中生成高层证明步骤”成为独立学习问题，早于后来语言模型定理证明系统对类似路线的扩展。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Wenda Li, Lei Yu, Yuhuai Wu and Lawrence C. Paulson introduced IsarStep, a benchmark mined from Isabelle's Archive of Formal Proofs in which models must predict a missing intermediate proposition from surrounding proof context, covering undergraduate- and research-level mathematics and computer science material.", "zh-CN": "Wenda Li、Lei Yu、Yuhuai Wu 与 Lawrence C. Paulson 提出 IsarStep：一个从 Isabelle Archive of Formal Proofs 中抽取的 benchmark，要求模型根据周围证明上下文预测缺失的中间命题，覆盖本科与研究级数学及计算机科学形式化内容。" }, "summary": { "en": "IsarStep converts declarative Isar proofs into sequence-to-sequence examples where a proof fragment has an intermediate proposition removed. The task tests whether a model can reconstruct a semantically useful bridge between surrounding proof states, and the authors evaluated Transformer-based baselines including a hierarchical architecture designed for long proof context.", "zh-CN": "IsarStep 将声明式 Isar 证明转换为序列到序列样本，并移除其中的中间命题。任务要求模型重建连接前后证明状态的语义桥梁；作者评测了 Transformer 类基线，并设计面向长证明上下文的分层架构。" }, "why_it_matters": { "en": "The benchmark shifted part of learned theorem proving toward human-readable intermediate reasoning over real proof corpora. Together with contemporaneous formal-math pretraining work, it supplied an important pre-LLM testbed for learning reusable mathematical representations and proof steps from mature proof-assistant libraries.", "zh-CN": "该 benchmark 将部分学习式定理证明研究从低层动作预测推进到真实证明语料上的可读中间推理。它与同期形式数学预训练研究一起，为后来的 LLM 时代之前从成熟证明助手数学库学习可复用数学表示与证明步骤提供了重要试验场。" }, "ai_role": { "level": "computation_only", "description": { "en": "Neural sequence models were trained and evaluated to predict missing formal propositions from proof context; the underlying Isabelle developments, benchmark extraction and evaluation protocol were human-authored or researcher-designed.", "zh-CN": "神经序列模型被训练和评测，用于根据证明上下文预测缺失的形式命题；底层 Isabelle 证明、benchmark 抽取和评测协议由人类编写或研究者设计。" } }, "human_contribution": { "description": { "en": "Researchers mined and processed the Isabelle proof corpus, defined the missing-proposition task and data splits, designed sequence-to-sequence and hierarchical Transformer baselines, and evaluated model generalization on held-out proofs.", "zh-CN": "研究者抽取并处理 Isabelle 证明语料、定义缺失命题任务与数据划分、设计序列到序列及分层 Transformer 基线，并在留出证明上评估模型泛化能力。" } }, "systems": [ "isarstep", "isabelle" ], "organizations": [ "university-of-cambridge" ], "people": [ "wenda-li", "lei-yu", "yuhuai-wu", "lawrence-c-paulson" ], "problems": [ "high-level-mathematical-reasoning", "missing-proposition-generation" ], "methods": [ "sequence-to-sequence-learning", "hierarchical-transformer", "proof-corpus-mining", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2020-06-13", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record establishes the IsarStep task, Isabelle-derived dataset and reported neural sequence-model experiments.", "zh-CN": "arXiv 研究记录确认了 IsarStep 任务、源自 Isabelle 的数据集以及论文报告的神经序列模型实验。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public IsarStep repository exposes the code and links to the released dataset, hierarchical Transformer implementation and test suite. E3 records artifact-level inspectability rather than independent reproduction of every reported result.", "zh-CN": "公开 IsarStep 仓库提供代码，并链接已发布的数据集、分层 Transformer 实现与测试集。E3 表示 artifact 可直接检查，并不代表论文报告的全部结果已获得独立复现。" } } ] }, "sources": [ { "id": "arxiv-isarstep-2006.09265", "tier": "S1", "type": "paper", "title": "IsarStep: a Benchmark for High-level Mathematical Reasoning", "url": "https://arxiv.org/abs/2006.09265", "primary": true, "published_date": "2020-06-13", "accessed_at": "2026-09-15" }, { "id": "openreview-isarstep-iclr2021", "tier": "S1", "type": "paper", "title": "IsarStep: a Benchmark for High-level Mathematical Reasoning — ICLR 2021", "url": "https://openreview.net/forum?id=Pzj6fzU6wkj", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-isarstep", "tier": "S1", "type": "repository", "title": "IsarStep code, dataset and HAT resources", "url": "https://github.com/Wenda302/IsarStep", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "isarstep-repository", "kind": "benchmark", "title": "IsarStep benchmark code, dataset links and hierarchical Transformer resources", "url": "https://github.com/Wenda302/IsarStep" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2020-skip-tree" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "isarstep", "isabelle", "theorem-proving", "mathematical-reasoning", "benchmark", "dataset", "transformer", "formal-mathematics" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-skip-tree", "slug": "skip-tree-self-supervised-math", "title": { "en": "Skip-tree training brings structure-aware self-supervision to formal mathematical reasoning", "zh-CN": "Skip-tree 将结构感知的自监督训练引入形式数学推理" }, "dates": { "event": "2020-06-08", "first_public_claim": "2020-06-08", "paper_release": "2020-06-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Skip-tree training was an early structure-aware self-supervised objective for formal mathematics, showing that language-model pretraining over mathematical expression trees could support several downstream reasoning tasks and useful conjecture generation.", "zh-CN": "Skip-tree training 是较早面向形式数学结构设计的自监督目标之一，展示了对数学表达式树进行语言模型预训练可以支持多类下游推理任务，并生成具有可证明性和可用性的 conjecture。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The authors introduced the skip-tree pretraining task for formal mathematical expressions and reported that skip-tree-trained models outperformed standard skip-sequence training on tasks including type inference, missing-assumption prediction and equality completion, while also producing conjectures evaluated for provability and usefulness.", "zh-CN": "作者提出面向形式数学表达式的 skip-tree 预训练任务，并报告该方法在类型推断、缺失假设预测和等式补全等任务上优于标准 skip-sequence 训练，同时还能生成并按可证明性与可用性评估 conjecture。" }, "summary": { "en": "Rather than masking only a flat token span, skip-tree training removes a subtree from a structured mathematical expression and trains a model to reconstruct it, encouraging representations that reflect the compositional structure of formal mathematics.", "zh-CN": "Skip-tree 不只遮蔽扁平 token 序列，而是从结构化数学表达式中移除一个子树并要求模型重建，从而促使表示学习利用形式数学的组合结构。" }, "why_it_matters": { "en": "The work helped establish self-supervised pretraining on formal mathematical corpora as a distinct route to reusable reasoning representations before later large-scale formal-math language models and proof-oriented pretraining pipelines.", "zh-CN": "该工作在后续大规模形式数学语言模型与证明导向预训练管线出现之前，较早展示了在形式数学语料上进行自监督预训练、学习可复用推理表示的技术路线。" }, "ai_role": { "level": "computation_only", "description": { "en": "Language models learn representations from self-supervised reconstruction of formal expressions and are evaluated on mathematical reasoning and conjecture-generation tasks.", "zh-CN": "语言模型通过对形式表达式进行自监督重建来学习表示，并在数学推理与 conjecture generation 任务上接受评测。" } }, "human_contribution": { "description": { "en": "Researchers designed the skip-tree objective, downstream tasks, formal-mathematics corpus processing and evaluation methodology.", "zh-CN": "研究者设计 skip-tree 目标、下游任务、形式数学语料处理和评测方法。" } }, "systems": [ "skip-tree" ], "organizations": [ "google-research" ], "people": [ "markus-n-rabe", "dennis-lee", "kshitij-bansal", "christian-szegedy" ], "problems": [], "methods": [ "self-supervised-learning", "skip-tree-training", "formal-math-pretraining", "conjecture-generation" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2020-06-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Chronicle records the method and reported results from the arXiv research record, later accepted at ICLR 2021; no directly inspectable public implementation artifact is recorded here.", "zh-CN": "Chronicle 根据 arXiv 研究记录及其后 ICLR 2021 接收记录记载该方法与报告结果；本记录目前未收录可直接检查的公开实现产物。" } } ] }, "sources": [ { "id": "arxiv-skip-tree-2006.04757", "tier": "S1", "type": "paper", "title": "Mathematical Reasoning via Self-supervised Skip-tree Training", "url": "https://arxiv.org/abs/2006.04757", "primary": true, "published_date": "2020-06-08", "accessed_at": "2026-09-11" }, { "id": "openreview-skip-tree-iclr2021", "tier": "S1", "type": "paper", "title": "Mathematical Reasoning via Self-supervised Skip-tree Training — ICLR 2021", "url": "https://openreview.net/forum?id=YmqAnY0CMEy", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "google-iclr-2021-skip-tree", "tier": "S2", "type": "official_announcement", "title": "Google at ICLR 2021", "url": "https://research.google/blog/google-at-iclr-2021/", "primary": false, "published_date": "2021-05-03", "accessed_at": "2026-09-11" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2020-isarstep", "evt-2021-pact" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "formal-mathematics", "self-supervision", "mathematical-reasoning", "pretraining", "conjecture-generation" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-nl-premise-selection", "slug": "natural-language-premise-selection", "title": { "en": "Natural-language premise selection turns mathematical reference retrieval into a benchmark task", "zh-CN": "自然语言前提选择将数学参考资料检索转化为基准任务" }, "dates": { "event": "2020-04-30", "first_public_claim": "2020-04-30", "paper_release": "2020-04-30", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "Natural Language Premise Selection made retrieval of supporting definitions and propositions from ordinary mathematical text an explicit machine-learning task and released a ProofWiki-derived dataset for evaluating it. This supplied an early benchmark for reasoning over mixed prose and formulae before later natural-language theorem-proving datasets and grounded proof-generation systems.", "zh-CN": "Natural Language Premise Selection 将从普通数学文本中检索相关定义与命题明确建模为机器学习任务，并发布源自 ProofWiki 的评测数据集。它为同时处理数学自然语言与公式的推理提供了较早 benchmark，并早于后来的自然语言定理证明数据集与 grounded proof generation 系统。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic" ], "claim": { "en": "Deborah Ferreira and André Freitas introduced the natural-language premise-selection task, in which a system receives a mathematical conjecture expressed through prose and formulae and must retrieve definitions or propositions likely to support a proof, together with a ProofWiki-derived dataset and reproducible extraction pipeline.", "zh-CN": "Deborah Ferreira 与 André Freitas 提出自然语言前提选择任务：系统接收由数学文字与公式共同表达的 conjecture，并检索最可能支持其证明的定义或命题；作者同时发布源自 ProofWiki 的数据集与可复现的数据抽取流程。" }, "summary": { "en": "The work treated mathematical discourse as a retrieval problem rather than only an answer-generation problem. Its dataset captures links among conjectures, definitions and supporting propositions in ProofWiki, while accompanying baselines and later graph-based experiments measured how effectively models could recover proof-relevant references.", "zh-CN": "该工作把数学语篇理解明确表述为检索问题，而不仅是答案生成问题。其数据集记录 ProofWiki 中 conjecture、定义与支持命题之间的关系，并通过基线方法及后续图模型实验衡量模型恢复证明相关参考资料的能力。" }, "why_it_matters": { "en": "Reference selection is a core bottleneck in both informal and formal mathematical reasoning. By defining a benchmark directly on human-facing mathematical text, this work provided a bridge from earlier formal premise-selection research toward later NaturalProofs-style retrieval and reference-grounded proof generation.", "zh-CN": "参考资料选择是非形式与形式数学推理中的共同瓶颈。该工作直接在面向人类的数学文本上定义 benchmark，为更早的形式化 premise selection 研究通向后来 NaturalProofs 式检索与参考资料约束的证明生成提供了桥梁。" }, "ai_role": { "level": "computation_only", "description": { "en": "Machine-learning and retrieval models were trained and evaluated to rank proof-relevant mathematical statements; the task definition, ProofWiki extraction and relevance labels were constructed by researchers from existing human-authored mathematical material.", "zh-CN": "机器学习与检索模型被训练和评测，用于排序与证明相关的数学陈述；任务定义、ProofWiki 数据抽取与相关性关系由研究者从既有人工数学材料中构建。" } }, "human_contribution": { "description": { "en": "Researchers defined the task, built the ProofWiki-derived corpus and extraction pipeline, designed evaluation splits and baselines, and analyzed the difficulty of retrieving mathematically relevant premises from mixed prose and formulae.", "zh-CN": "研究者定义任务、构建源自 ProofWiki 的语料与抽取管线、设计评测划分和基线，并分析从数学文字与公式混合语篇中检索相关前提的难点。" } }, "systems": [ "nl-ps", "ps-proofwiki" ], "organizations": [ "university-of-manchester" ], "people": [ "deborah-ferreira", "andre-freitas" ], "problems": [ "natural-language-premise-selection" ], "methods": [ "premise-selection", "information-retrieval", "mathematical-language-processing", "dataset-construction" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2020-04-30", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and LREC research records establish the natural-language premise-selection task and the released ProofWiki-derived dataset.", "zh-CN": "arXiv 与 LREC 研究记录确认了自然语言前提选择任务以及公开的 ProofWiki 衍生数据集。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public nl-ps repository exposes the dataset, extraction pipeline and baseline tooling. E3 records artifact-level inspectability rather than independent validation of every reported retrieval result.", "zh-CN": "公开 nl-ps 仓库提供数据集、抽取管线与基线工具。E3 表示 artifact 可直接检查，并不代表论文报告的全部检索结果已获得独立验证。" } } ] }, "sources": [ { "id": "arxiv-nl-premise-selection-2004.14959", "tier": "S1", "type": "paper", "title": "Natural Language Premise Selection: Finding Supporting Statements for Mathematical Text", "url": "https://arxiv.org/abs/2004.14959", "primary": true, "published_date": "2020-04-30", "accessed_at": "2026-09-15" }, { "id": "acl-lrec-nl-premise-selection-2020", "tier": "S1", "type": "paper", "title": "Natural Language Premise Selection: Finding Supporting Statements for Mathematical Text — LREC 2020", "url": "https://aclanthology.org/2020.lrec-1.266/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "acl-premise-selection-math-texts-2020", "tier": "S1", "type": "paper", "title": "Premise Selection in Natural Language Mathematical Texts — ACL 2020", "url": "https://aclanthology.org/2020.acl-main.657/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-nl-ps", "tier": "S1", "type": "repository", "title": "PS-ProofWiki dataset generation and baseline repository", "url": "https://github.com/debymf/nl-ps", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "nl-ps-repository", "kind": "dataset", "title": "PS-ProofWiki dataset, extraction pipeline and baselines", "url": "https://github.com/debymf/nl-ps" } ], "relationships": { "predecessors": [], "successors": [ "evt-2022-naturalprover" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "natural-language-premise-selection", "proofwiki", "premise-selection", "mathematical-language-processing", "benchmark", "dataset", "retrieval" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2020-metagen", "slug": "metagen-synthetic-theorem-generation", "title": { "en": "MetaGen learns to generate synthetic theorems and proofs for theorem-prover training", "zh-CN": "MetaGen 学习生成合成定理与证明，用于训练定理证明器" }, "dates": { "event": "2020-02-17", "first_public_claim": "2020-02-17", "paper_release": "2020-02-17", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-11", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "MetaGen made learned generation of synthetic formal theorems and proofs a practical data-augmentation strategy for neural theorem proving, addressing the scarcity of human-written formal proof data and improving a Metamath prover on real tasks.", "zh-CN": "MetaGen 将学习式生成合成形式定理与证明发展为神经定理证明中的实用数据增强路线，用于缓解人工形式证明数据稀缺，并提升 Metamath 真实任务上的证明器表现。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "MetaGen trained a neural generator to synthesize Metamath theorems together with proofs and used those generated examples to improve a neural theorem prover, with the authors reporting state-of-the-art automated theorem-proving performance on their Metamath evaluation.", "zh-CN": "MetaGen 训练神经生成器合成带有证明的 Metamath 定理，并用这些生成样本改进神经定理证明器；作者报告其在所用 Metamath 评测上取得当时领先的自动定理证明表现。" }, "summary": { "en": "The system learns from existing formal mathematics, generates additional theorem-proof pairs, and feeds the synthetic corpus back into prover training rather than relying only on scarce human-authored proof traces.", "zh-CN": "该系统从既有形式数学中学习，生成额外的定理—证明对，再把合成语料反馈到证明器训练中，而不是仅依赖稀缺的人工证明轨迹。" }, "why_it_matters": { "en": "It established an early neural data-generation route for formal mathematics that complements later proof-artifact, synthetic-formalization and self-training pipelines.", "zh-CN": "它较早确立了面向形式数学的神经数据生成路线，并与后来利用证明产物、合成形式化和自训练的数据管线形成历史上的连续技术脉络。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "A learned generator produces synthetic formal theorem-proof pairs, while a learned prover is trained on the augmented corpus to search for proofs of target theorems.", "zh-CN": "学习式生成器产生合成形式定理—证明对，学习式证明器再利用扩充后的语料训练并搜索目标定理的证明。" } }, "human_contribution": { "description": { "en": "Researchers designed the generator-prover training loop, formal data pipeline and evaluation, and the Metamath library supplied the human-authored formal corpus and proof checker.", "zh-CN": "研究者设计生成器—证明器训练循环、形式数据管线与评测；Metamath 库提供人工编写的形式语料和证明检查器。" } }, "systems": [ "metagen", "metamath" ], "organizations": [ "princeton-university" ], "people": [ "mingzhe-wang", "jia-deng" ], "problems": [], "methods": [ "synthetic-theorem-generation", "synthetic-proof-generation", "data-augmentation", "neural-theorem-proving" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2020-02-17", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record established the synthetic theorem-and-proof generation method and its reported Metamath theorem-proving results.", "zh-CN": "arXiv 研究记录公开了合成定理与证明生成方法及其报告的 Metamath 定理证明结果。" } }, { "date": "2026-09-11", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The Chronicle linked the peer-reviewed NeurIPS 2020 record and the authors' public MetaGen repository. E3 records inspectable research artifacts and does not imply independent verification of the reported performance claim.", "zh-CN": "Chronicle 补入 NeurIPS 2020 同行评议记录以及作者公开的 MetaGen 仓库。E3 表示存在可检查研究产物，并不等同于对所报告性能主张的独立验证。" } } ] }, "sources": [ { "id": "arxiv-metagen-2002.07019", "tier": "S1", "type": "paper", "title": "Learning to Prove Theorems by Learning to Generate Theorems", "url": "https://arxiv.org/abs/2002.07019", "primary": true, "published_date": "2020-02-17", "accessed_at": "2026-09-11" }, { "id": "neurips-metagen-2020", "tier": "S1", "type": "paper", "title": "Learning to Prove Theorems by Learning to Generate Theorems — NeurIPS 2020", "url": "https://proceedings.neurips.cc/paper/2020/hash/d2a27e83d429f0dcae6b937cf440aeb1-Abstract.html", "primary": true, "published_date": null, "accessed_at": "2026-09-11" }, { "id": "github-princeton-metagen", "tier": "S1", "type": "repository", "title": "MetaGen code and reproduction repository", "url": "https://github.com/princeton-vl/MetaGen", "primary": true, "published_date": null, "accessed_at": "2026-09-11" } ], "artifacts": [ { "id": "metagen-repository", "kind": "code", "title": "MetaGen code, models and reproduction resources", "url": "https://github.com/princeton-vl/MetaGen" } ], "relationships": { "predecessors": [ "evt-2016-holophrasm" ], "successors": [], "related": [ "evt-2020-gpt-f", "evt-2021-pact" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "metamath", "theorem-proving", "synthetic-data", "formal-mathematics", "data-generation" ], "editorial": { "created_at": "2026-09-11", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2019-coqgym", "slug": "coqgym-astactic-theorem-proving", "title": { "en": "CoqGym and ASTactic scale learning-based interaction with the Coq proof assistant", "zh-CN": "CoqGym 与 ASTactic 扩展基于学习的 Coq 交互式定理证明" }, "dates": { "event": "2019-05-21", "first_public_claim": "2019-05-21", "paper_release": "2019-05-21", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "benchmark", "dataset", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "CoqGym turned a large collection of real Coq developments into an interactive machine-learning environment containing tens of thousands of human proofs, while ASTactic generated structured tactics rather than choosing only from a fixed tactic vocabulary. The environment became an important early template for later proof-assistant learning infrastructure.", "zh-CN": "CoqGym 将大量真实 Coq 工程转化为包含数万条人工证明的交互式机器学习环境；ASTactic 则生成结构化 tactic，而不是只从固定 tactic 集合中选择。该环境成为后来证明助手学习基础设施的重要早期范式之一。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Kaiyu Yang and Jia Deng released CoqGym, a dataset and interactive environment built from 71,000 human-written proofs across 123 Coq projects, together with ASTactic, a deep-learning model that generates tactics as abstract syntax trees and was reported to prove held-out theorems beyond the reach of the compared built-in automated tactics.", "zh-CN": "Kaiyu Yang 与 Jia Deng 发布 CoqGym：一个由 123 个 Coq 项目、约 71,000 条人工证明构成的数据集与交互环境，并提出 ASTactic 深度学习模型，以抽象语法树形式生成 tactics；论文报告其能够证明部分比较基线中的内置自动 tactic 无法证明的留出定理。" }, "summary": { "en": "CoqGym extracted proof states, environments, goals, tactics and proof trees from open-source Coq projects and exposed them through a programmatic interaction layer. ASTactic learned proof-step generation from this corpus and composed tactics from runtime syntax rather than relying only on a predetermined list of complete tactics.", "zh-CN": "CoqGym 从开源 Coq 项目中抽取证明状态、环境、目标、tactics 与证明树，并通过可编程交互层暴露这些信息。ASTactic 从该语料学习生成证明步骤，并基于运行时语法组合 tactics，而不是仅依赖预先固定的完整 tactic 列表。" }, "why_it_matters": { "en": "CoqGym made learning-based theorem proving on a mature interactive proof assistant substantially more data-rich and reproducible. Its environment-and-corpus design anticipated later projects such as LeanDojo that similarly expose large proof-assistant libraries as reusable machine-learning infrastructure.", "zh-CN": "CoqGym 使成熟交互式证明助手上的学习式定理证明获得更丰富、可复现的数据与交互基础。其“环境 + 大型证明语料”设计预示了 LeanDojo 等后来项目把证明助手数学库封装为可复用机器学习基础设施的路线。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "ASTactic generated structured Coq tactics from proof states and searched for proof scripts, while Coq checked whether generated tactic sequences produced valid formal proofs.", "zh-CN": "ASTactic 根据证明状态生成结构化 Coq tactics 并搜索证明脚本，由 Coq 检查生成的 tactic 序列是否构成有效形式证明。" } }, "human_contribution": { "description": { "en": "Researchers assembled and instrumented the Coq projects, designed the data extraction and interaction environment, defined train/validation/test splits, built ASTactic and evaluated it against automated tactics and theorem provers.", "zh-CN": "研究者整理并改造 Coq 工程、设计数据抽取与交互环境、定义训练 / 验证 / 测试划分、构建 ASTactic，并将其与自动 tactics 和定理证明器进行评测比较。" } }, "systems": [ "coqgym", "astactic", "coq" ], "organizations": [ "princeton-university" ], "people": [ "kaiyu-yang", "jia-deng" ], "problems": [ "coq-theorem-proving" ], "methods": [ "tactic-generation", "abstract-syntax-tree-generation", "interactive-theorem-proving", "supervised-learning", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2019-05-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and ICML research records establish CoqGym, ASTactic, the dataset scale and the reported held-out theorem-proving experiments. Machine checking refers to proofs accepted by Coq and does not imply independent reproduction of the reported success rates.", "zh-CN": "arXiv 与 ICML 研究记录确认了 CoqGym、ASTactic、数据规模及论文报告的留出定理证明实验。machine_checked 仅指生成证明通过 Coq 检查，并不表示论文报告的成功率已得到独立复现。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public CoqGym repository exposes the interaction environment, extraction pipeline, proof corpus tooling and ASTactic implementation. E3 denotes artifact-level inspectability rather than independent verification of every experimental claim.", "zh-CN": "公开 CoqGym 仓库提供交互环境、数据抽取管线、证明语料工具与 ASTactic 实现。E3 表示存在可直接检查的 artifacts，而非对全部实验结论的独立验证。" } } ] }, "sources": [ { "id": "arxiv-coqgym-1905.09381", "tier": "S1", "type": "paper", "title": "Learning to Prove Theorems via Interacting with Proof Assistants", "url": "https://arxiv.org/abs/1905.09381", "primary": true, "published_date": "2019-05-21", "accessed_at": "2026-09-15" }, { "id": "pmlr-coqgym-icml2019", "tier": "S1", "type": "paper", "title": "Learning to Prove Theorems via Interacting with Proof Assistants — ICML 2019", "url": "https://proceedings.mlr.press/v97/yang19a.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-princeton-coqgym", "tier": "S1", "type": "repository", "title": "CoqGym learning environment and ASTactic implementation", "url": "https://github.com/princeton-vl/CoqGym", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "coqgym-repository", "kind": "code", "title": "CoqGym environment, proof-corpus tooling and ASTactic code", "url": "https://github.com/princeton-vl/CoqGym" } ], "relationships": { "predecessors": [ "evt-2018-gamepad" ], "successors": [ "evt-2023-leandojo" ], "related": [ "evt-2019-holist" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "coqgym", "astactic", "coq", "theorem-proving", "proof-assistant", "dataset", "tactic-generation", "machine-learning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2019-holist", "slug": "holist-deephol-theorem-proving", "title": { "en": "HOList and DeepHOL open a reinforcement-learning environment for higher-order theorem proving", "zh-CN": "HOList 与 DeepHOL 建立高阶逻辑强化学习定理证明环境" }, "dates": { "event": "2019-04-05", "first_public_claim": "2019-04-05", "paper_release": "2019-04-05", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "benchmark", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "HOList combined an open HOL Light interaction environment, a benchmark drawn from a substantial formal mathematics library, and the DeepHOL neural prover in one reproducible research stack. It became an important early reference point for reinforcement-learning and neural proof guidance inside interactive theorem provers, preceding later systems that learned more of search and tactic selection end to end.", "zh-CN": "HOList 将开放的 HOL Light 交互环境、源自大型形式数学库的 benchmark 与 DeepHOL 神经证明器整合为统一研究栈，成为强化学习与神经证明引导进入交互式定理证明的重要早期参照，并为后来更端到端地学习搜索与 tactic 选择的系统提供前史。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Google Research and collaborators released HOList, an open-source reinforcement-learning environment and benchmark built on HOL Light, together with DeepHOL, a deep-learning-driven tactic-based prover trained on human and synthesized proofs and evaluated on theorem corpora including Flyspeck-derived material.", "zh-CN": "Google Research 与合作研究者发布 HOList：一个基于 HOL Light 的开源强化学习环境与 benchmark，并配套发布 DeepHOL 深度学习 tactic 证明器；该系统利用人工与合成证明训练，并在包含 Flyspeck 相关内容的定理语料上进行评测。" }, "summary": { "en": "HOList instrumented HOL Light so learning systems could interact with proof states and tactics through a machine-learning environment. The benchmark packaged theorem statements from core, complex and Flyspeck corpora with train, validation and test labels, while DeepHOL supplied a neural prover and reinforcement-learning loop for generating additional successful proof traces.", "zh-CN": "HOList 对 HOL Light 进行工程化封装，使学习系统能够通过机器学习环境与证明状态和 tactics 交互。其 benchmark 将 core、complex 与 Flyspeck 语料中的定理陈述整理为训练、验证和测试划分；DeepHOL 则提供神经证明器与强化学习循环，用于持续生成新的成功证明轨迹。" }, "why_it_matters": { "en": "The release showed how a mature proof assistant and a substantial mathematical library could be exposed as a learning environment rather than only as a static corpus. That environment-plus-benchmark pattern became central to later neural theorem-proving infrastructure and made proof-assistant-native reinforcement learning a concrete experimental program.", "zh-CN": "该工作展示了如何把成熟证明助手与大型数学库转化为可交互的学习环境，而不仅是静态语料。此后“环境 + benchmark”的模式成为神经定理证明基础设施的重要范式，并使证明助手原生的强化学习成为可重复研究路线。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "DeepHOL used learned models to guide tactic choice, premise selection and proof search, including reinforcement from synthesized successful proofs; candidate proofs were ultimately checked through the HOL Light environment.", "zh-CN": "DeepHOL 使用学习模型引导 tactic 选择、前提选择与证明搜索，并利用合成成功证明进行强化训练；候选证明最终通过 HOL Light 环境接受机械检查。" } }, "human_contribution": { "description": { "en": "Researchers built the HOL Light interface, benchmark extraction, training pipeline, proof-search machinery, neural models, reinforcement-learning loop and evaluation protocol.", "zh-CN": "研究者构建 HOL Light 交互接口、benchmark 抽取流程、训练管线、证明搜索机制、神经模型、强化学习循环与评测协议。" } }, "systems": [ "holist", "deephol", "hol-light" ], "organizations": [ "google-research" ], "people": [ "kshitij-bansal", "sarah-loos", "markus-n-rabe", "christian-szegedy", "stewart-wilcox" ], "problems": [ "higher-order-logic-theorem-proving" ], "methods": [ "reinforcement-learning", "tactic-prediction", "premise-selection", "proof-search", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2019-04-05", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and ICML research records establish HOList, its benchmark and the reported DeepHOL experiments. Machine checking refers to proof traces accepted through HOL Light and does not imply independent reproduction of the reported benchmark performance.", "zh-CN": "arXiv 与 ICML 研究记录确认了 HOList、其 benchmark 以及论文报告的 DeepHOL 实验。machine_checked 仅指证明轨迹通过 HOL Light 检查，并不表示论文报告的 benchmark 性能已得到独立复现。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public Deepmath codebase and HOList benchmark site expose the prover code, benchmark definition, model resources and proof-checking workflow. E3 denotes inspectable artifacts rather than independent confirmation of all experimental claims.", "zh-CN": "公开的 Deepmath 代码库与 HOList benchmark 网站提供证明器代码、benchmark 定义、模型资源与证明检查流程。E3 表示存在可直接检查的 artifacts，而非对全部实验结论的独立确认。" } } ] }, "sources": [ { "id": "arxiv-holist-1904.03241", "tier": "S1", "type": "paper", "title": "HOList: An Environment for Machine Learning of Higher-Order Theorem Proving", "url": "https://arxiv.org/abs/1904.03241", "primary": true, "published_date": "2019-04-05", "accessed_at": "2026-09-15" }, { "id": "pmlr-holist-icml2019", "tier": "S1", "type": "paper", "title": "HOList: An Environment for Machine Learning of Higher Order Logic Theorem Proving — ICML 2019", "url": "https://proceedings.mlr.press/v97/bansal19a.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "google-research-holist", "tier": "S2", "type": "official_announcement", "title": "HOList — Google Research publication record", "url": "https://research.google/pubs/holist-an-environment-for-machine-learning-of-higher-order-logic-theorem-proving/", "primary": false, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-deepmath-deephol", "tier": "S1", "type": "repository", "title": "Deepmath repository containing DeepHOL", "url": "https://github.com/tensorflow/deepmath", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "holist-benchmark-site", "tier": "S2", "type": "benchmark", "title": "HOList benchmark and DeepHOL resources", "url": "https://sites.google.com/view/holist/home", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "deephol-code", "kind": "code", "title": "DeepHOL neural theorem prover code", "url": "https://github.com/tensorflow/deepmath" }, { "id": "holist-benchmark", "kind": "benchmark", "title": "HOList higher-order theorem-proving benchmark", "url": "https://sites.google.com/view/holist/home" } ], "relationships": { "predecessors": [ "evt-2017-holstep" ], "successors": [ "evt-2021-tacticzero" ], "related": [ "evt-2019-coqgym" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "holist", "deephol", "hol-light", "theorem-proving", "reinforcement-learning", "benchmark", "proof-search", "formal-mathematics" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2019-mathematics-dataset", "slug": "mathematics-dataset-neural-reasoning", "title": { "en": "Mathematics Dataset establishes a large synthetic benchmark for neural mathematical reasoning", "zh-CN": "Mathematics Dataset 建立大规模合成神经数学推理基准" }, "dates": { "event": "2019-04-02", "first_public_claim": "2019-04-02", "paper_release": "2019-04-02", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "Mathematics Dataset was an early large-scale benchmark built specifically to measure neural mathematical reasoning across arithmetic, algebra, calculus, probability and related school-level domains. Its generated training data and explicit interpolation/extrapolation tests made mathematical generalization a concrete evaluation target before later language-model benchmarks such as MATH and GSM8K.", "zh-CN": "Mathematics Dataset 是较早专门用于衡量神经网络数学推理能力的大规模基准之一，覆盖算术、代数、微积分、概率等学校数学领域。它通过大规模生成式训练数据以及明确的插值 / 外推测试，把数学泛化能力转化为可系统评测的研究目标，并早于后来的 MATH、GSM8K 等语言模型数学基准。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "symbolic", "numeric" ], "claim": { "en": "DeepMind researchers released a task suite and generator for free-form textual mathematics questions spanning arithmetic, algebra, calculus, comparison, measurement, number theory-like elementary tasks, polynomials and probability, together with interpolation and extrapolation tests designed to measure both in-distribution performance and generalization beyond training difficulty.", "zh-CN": "DeepMind 研究者发布了一套以自由文本问答表示的数学任务与生成器，覆盖算术、代数、微积分、比较、度量、初等数论类任务、多项式和概率，并设计插值与外推测试，用于同时衡量分布内表现以及超出训练难度的泛化能力。" }, "summary": { "en": "The original release provided millions of generated question-answer pairs per module and evaluated contemporary sequence-to-sequence neural architectures on both ordinary test splits and extrapolation settings. The accompanying open-source generator made it possible to reproduce and extend the task distribution rather than treating the benchmark as a fixed static question list.", "zh-CN": "原始版本为每个模块提供数百万规模的生成式问答样本，并在常规测试划分与外推设置上评估当时的序列到序列神经网络。配套开源生成器使研究者能够复现并扩展任务分布，而不仅依赖固定的静态题目列表。" }, "why_it_matters": { "en": "The benchmark helped establish mathematical reasoning as a distinct neural-model evaluation problem with controlled difficulty and generalization tests. It provides an important pre-LLM reference point for the later progression from synthetic school mathematics to human-written word problems and competition mathematics.", "zh-CN": "该基准推动数学推理成为具有受控难度和泛化测试的独立神经模型评测问题，并为后来从合成学校数学走向人工编写文字题和竞赛数学的 benchmark 演化提供了重要的前 LLM 历史参照。" }, "ai_role": { "level": "computation_only", "description": { "en": "Neural sequence models were trained and evaluated on generated mathematics questions; the benchmark generator, task design, splits and evaluation methodology were created by researchers rather than discovered by an AI system.", "zh-CN": "神经序列模型在生成式数学问题上训练与评测；基准生成器、任务设计、数据划分和评测方法由研究者构建，并非 AI 自主发现的数学成果。" } }, "human_contribution": { "description": { "en": "Researchers designed the mathematical modules and generators, constructed interpolation and extrapolation regimes, released the code and data, and analyzed model performance and failure modes.", "zh-CN": "研究者设计数学模块与生成器、构建插值和外推设置、发布代码与数据，并分析模型表现及失效模式。" } }, "systems": [ "mathematics-dataset" ], "organizations": [ "deepmind" ], "people": [ "david-saxton", "edward-grefenstette", "felix-hill", "pushmeet-kohli" ], "problems": [ "school-level-mathematical-reasoning" ], "methods": [ "synthetic-data-generation", "sequence-to-sequence-learning", "benchmarking", "extrapolation-testing" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2019-04-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and ICLR research records establish the task suite, evaluation design and reported neural-model experiments.", "zh-CN": "arXiv 与 ICLR 研究记录确认了任务套件、评测设计以及论文报告的神经模型实验。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The maintained public DeepMind repository exposes the dataset generator, pre-generated-data references and version-1.0 task structure. E3 records artifact-level inspectability rather than independent reproduction of every reported model result.", "zh-CN": "持续公开的 DeepMind 仓库提供数据生成器、预生成数据入口与 Version 1.0 任务结构。E3 表示存在可直接检查的 artifact，并不代表论文报告的全部模型结果都已获得独立复现。" } } ] }, "sources": [ { "id": "arxiv-mathematics-dataset-1904.01557", "tier": "S1", "type": "paper", "title": "Analysing Mathematical Reasoning Abilities of Neural Models", "url": "https://arxiv.org/abs/1904.01557", "primary": true, "published_date": "2019-04-02", "accessed_at": "2026-09-15" }, { "id": "openreview-mathematics-dataset-iclr2019", "tier": "S1", "type": "paper", "title": "Analysing Mathematical Reasoning Abilities of Neural Models — ICLR 2019", "url": "https://openreview.net/forum?id=H1gR5iR5FX", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-deepmind-mathematics-dataset", "tier": "S1", "type": "repository", "title": "DeepMind Mathematics Dataset generator and release", "url": "https://github.com/google-deepmind/mathematics_dataset", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "mathematics-dataset-repository", "kind": "dataset", "title": "Mathematics Dataset generator and pre-generated-data release", "url": "https://github.com/google-deepmind/mathematics_dataset" } ], "relationships": { "predecessors": [], "successors": [ "evt-2021-math-benchmark" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mathematics-dataset", "benchmark", "dataset", "mathematical-reasoning", "synthetic-data", "generalization", "neural-networks" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2018-gamepad", "slug": "gamepad-coq-learning-environment", "title": { "en": "GamePad exposes Coq proof traces and interaction as a machine-learning environment", "zh-CN": "GamePad 将 Coq 证明轨迹与交互封装为机器学习环境" }, "dates": { "event": "2018-06-02", "first_public_claim": "2018-06-02", "paper_release": "2018-06-02", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "GamePad was an early proof-assistant machine-learning environment that exposed Coq proof states, steps, trees and interactive tactic execution through Python. Its environment-plus-proof-trace design directly preceded larger-scale Coq learning infrastructure such as CoqGym, whose paper identifies GamePad as its closest prior work.", "zh-CN": "GamePad 是较早面向证明助手机器学习的交互环境之一，通过 Python 暴露 Coq 的证明状态、步骤、证明树与 tactic 交互执行。其“交互环境 + 证明轨迹”设计直接早于更大规模的 Coq 学习基础设施 CoqGym；后者论文明确将 GamePad 称为最接近的前序工作。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Daniel Huang, Prafulla Dhariwal, Dawn Song and Ilya Sutskever released GamePad, a Python environment for extracting and manipulating Coq proof traces and interacting with Coq. The paper used the environment to synthesize proofs for a simple algebraic rewrite task and to train baseline models for position evaluation and tactic prediction on a formalization of the Feit–Thompson theorem.", "zh-CN": "Daniel Huang、Prafulla Dhariwal、Dawn Song 与 Ilya Sutskever 发布 GamePad：一个用于抽取和操作 Coq 证明轨迹并与 Coq 交互的 Python 环境。论文使用该环境在简单代数重写任务上合成证明，并基于 Feit–Thompson 定理形式化训练 position evaluation 与 tactic prediction 基线模型。" }, "summary": { "en": "GamePad instruments Coq so proof states, proof steps, mid-level and kernel-level terms and proof trees can be represented as Python data structures. A lightweight coqtop wrapper lets learning code send tactics and receive parsed proof states, while released tooling supports extracting data from the Mathematical Components odd-order development.", "zh-CN": "GamePad 对 Coq 进行工程化封装，使证明状态、证明步骤、中层与内核级项以及证明树都能表示为 Python 数据结构。轻量级 coqtop wrapper 允许学习代码发送 tactics 并接收解析后的证明状态，公开工具还支持从 Mathematical Components 的 odd-order 工程中抽取数据。" }, "why_it_matters": { "en": "The project helped establish proof assistants as interactive machine-learning environments rather than only sources of static theorem corpora. That interface pattern became important for later systems that train models by repeatedly observing proof states and acting inside a trusted prover.", "zh-CN": "该项目推动证明助手从静态定理语料来源转变为可供机器学习系统交互的环境。这种接口范式随后成为许多系统的重要基础：模型能够反复观察证明状态，并在可信证明器内部执行动作。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Machine-learning models predicted proof progress and tactics, and the environment supported automated proof synthesis on a simple rewrite task; the main historical contribution was the reusable Coq interaction and trace infrastructure rather than a new mathematical proof.", "zh-CN": "机器学习模型预测证明进度与 tactics，环境也支持在简单重写任务上自动合成证明；其主要历史贡献是可复用的 Coq 交互与轨迹基础设施，而不是新的数学证明。" } }, "human_contribution": { "description": { "en": "Researchers instrumented Coq, designed the Python representations and interaction API, prepared the Feit–Thompson-derived data workflow, implemented baseline learning tasks and evaluated the environment.", "zh-CN": "研究者改造 Coq、设计 Python 表示与交互 API、准备源自 Feit–Thompson 形式化的数据流程、实现基线学习任务并评测该环境。" } }, "systems": [ "gamepad", "coq" ], "organizations": [ "university-of-california-berkeley", "openai" ], "people": [ "daniel-huang", "prafulla-dhariwal", "dawn-song", "ilya-sutskever" ], "problems": [ "coq-theorem-proving" ], "methods": [ "interactive-theorem-proving", "tactic-prediction", "proof-state-representation", "proof-trace-extraction", "machine-learning-environment" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2018-06-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record establishes GamePad, its Coq interaction design and the reported proof-synthesis and prediction experiments.", "zh-CN": "arXiv 研究记录确认了 GamePad、其 Coq 交互设计以及论文报告的证明合成与预测实验。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public GamePad repository exposes the Coq tracing setup, Python interaction library, examples and data/model workflow. E3 records artifact-level inspectability rather than independent reproduction of every experiment.", "zh-CN": "公开 GamePad 仓库提供 Coq tracing 配置、Python 交互库、示例以及数据 / 模型流程。E3 表示 artifact 可直接检查，并不代表论文报告的全部实验已获得独立复现。" } } ] }, "sources": [ { "id": "arxiv-gamepad-1806.00608", "tier": "S1", "type": "paper", "title": "GamePad: A Learning Environment for Theorem Proving", "url": "https://arxiv.org/abs/1806.00608", "primary": true, "published_date": "2018-06-02", "accessed_at": "2026-09-15" }, { "id": "github-gamepad", "tier": "S1", "type": "repository", "title": "GamePad Coq learning environment", "url": "https://github.com/ml4tp/gamepad", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "gamepad-repository", "kind": "code", "title": "GamePad Coq learning environment and proof-trace tooling", "url": "https://github.com/ml4tp/gamepad" } ], "relationships": { "predecessors": [], "successors": [ "evt-2019-coqgym" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "gamepad", "coq", "theorem-proving", "machine-learning-environment", "proof-traces", "tactic-prediction", "infrastructure" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2018-rl-theorem-proving", "slug": "reinforcement-learning-theorem-proving", "title": { "en": "Reinforcement learning guides large-scale automated theorem-proving search", "zh-CN": "强化学习用于引导大规模自动定理证明搜索" }, "dates": { "event": "2018-05-19", "first_public_claim": "2018-05-19", "paper_release": "2018-05-19", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "Reinforcement Learning of Theorem Proving established a prominent large-scale route in which an automated prover improves search guidance from its own previous proof attempts rather than relying primarily on hand-built domain heuristics. It helped make reinforcement learning over broad formal-theorem corpora a concrete AI4Math research program before later proof-assistant-native RL systems.", "zh-CN": "Reinforcement Learning of Theorem Proving 建立了一条具有代表性的大规模路线：自动证明器从此前的证明尝试中学习搜索引导，而不是主要依赖人工编写的领域启发式。它在后续证明助手原生强化学习系统出现之前，推动面向大规模形式定理语料的强化学习成为具体的 AI4Math 研究方向。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Cezary Kaliszyk, Josef Urban, Henryk Michalewski and Mirek Olšák introduced a connection-style theorem prover whose Monte Carlo simulations were guided by reinforcement learning from previous proof attempts. The paper reported that its strongest trained configuration solved more than 40% more previously unseen problems than a baseline prover under the same inference budget.", "zh-CN": "Cezary Kaliszyk、Josef Urban、Henryk Michalewski 与 Mirek Olšák 提出一种 connection-style 定理证明器，使用从此前证明尝试中学习的强化学习策略引导蒙特卡洛模拟。论文报告称，在相同推理预算下，最强训练配置在此前未见问题上比基线证明器多解决超过 40% 的问题。" }, "summary": { "en": "The system repeatedly performs proof-search simulations, turns successful and failed attempts into learning signals, and retrains guidance used in subsequent searches. The approach was evaluated over a large formal-mathematics problem corpus, emphasizing learned search control rather than theorem-specific handwritten heuristics.", "zh-CN": "该系统反复执行证明搜索模拟，把成功与失败的尝试转化为学习信号，并重新训练后续搜索所使用的引导策略。方法在大型形式数学问题语料上进行评测，重点是学习式搜索控制，而非针对具体定理手写启发式规则。" }, "why_it_matters": { "en": "The work showed that theorem proving could be organized as an iterative learning-and-search loop at substantial corpus scale. This helped connect automated theorem proving with modern reinforcement-learning methodology and supplied historical context for later self-improving and interactive proof-search agents.", "zh-CN": "该工作展示了定理证明可以在相当规模的语料上组织为“学习—搜索—再学习”的迭代循环，推动自动定理证明与现代强化学习方法结合，并为后来的自我改进式和交互式证明搜索智能体提供历史前序。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The learned policy guided proof-search simulations and was updated from prior proof attempts; the automated prover carried out the search and produced successful formal derivations without human step-by-step tactic selection.", "zh-CN": "学习式策略引导证明搜索模拟，并根据此前证明尝试持续更新；自动证明器执行搜索并产生成功的形式推导，不需要人类逐步选择证明动作。" } }, "human_contribution": { "description": { "en": "Researchers designed the connection-style prover, reinforcement-learning loop, search features, training/evaluation corpus and experimental protocol.", "zh-CN": "研究者设计 connection-style 证明器、强化学习循环、搜索特征、训练与评测语料以及实验协议。" } }, "systems": [ "rl-theorem-prover" ], "organizations": [ "university-of-innsbruck" ], "people": [ "cezary-kaliszyk", "josef-urban", "henryk-michalewski", "mirek-olsak" ], "problems": [ "automated-theorem-proving" ], "methods": [ "reinforcement-learning", "monte-carlo-search", "connection-tableaux", "proof-search" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2018-05-19", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and NeurIPS research records establish the reinforcement-learning proof-search algorithm and the reported large-corpus evaluation. The Chronicle does not record a directly inspectable proof artifact or independent replay for this event, so formal assurance remains `none`.", "zh-CN": "arXiv 与 NeurIPS 研究记录确认了强化学习证明搜索算法及论文报告的大规模语料评测。Chronicle 当前未记录可直接检查的证明 artifact 或独立 replay，因此 formal assurance 保持为 `none`。" } } ] }, "sources": [ { "id": "arxiv-rl-theorem-proving-1805.07563", "tier": "S1", "type": "paper", "title": "Reinforcement Learning of Theorem Proving", "url": "https://arxiv.org/abs/1805.07563", "primary": true, "published_date": "2018-05-19", "accessed_at": "2026-09-15" }, { "id": "neurips-rl-theorem-proving-2018", "tier": "S1", "type": "paper", "title": "Reinforcement Learning of Theorem Proving — NeurIPS 2018", "url": "https://proceedings.neurips.cc/paper/2018/hash/55acf8539596d25624059980986aaa78-Abstract.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2017-deep-network-guided-proof-search" ], "successors": [], "related": [ "evt-2018-tactictoe" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "reinforcement-learning", "automated-theorem-proving", "monte-carlo-search", "proof-search", "formal-mathematics" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2018-neural-mizar-autoformalization", "slug": "neural-mizar-autoformalization", "title": { "en": "Neural translation establishes an early route from informalized mathematics to formal Mizar", "zh-CN": "神经翻译建立从非形式化数学文本到形式 Mizar 的早期路线" }, "dates": { "event": "2018-05-10", "first_public_claim": "2018-05-10", "paper_release": "2018-05-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "These experiments were an early neural autoformalization milestone: instead of assuming a formal theorem statement as input, a neural machine-translation model was trained to map natural-looking mathematical text into Mizar statements. The work became an explicit predecessor in later autoformalization research, including the 2022 large-language-model route.", "zh-CN": "这些实验是较早具有代表性的神经自动形式化里程碑：系统不再假设输入已经是形式定理陈述，而是训练神经机器翻译模型，把接近自然数学语言的文本映射为 Mizar 形式陈述。后来的自动形式化研究，包括 2022 年的大语言模型路线，也明确把该工作列为前序研究。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "Qingxiang Wang, Cezary Kaliszyk and Josef Urban trained neural machine-translation models on aligned informalized-LaTeX and formal Mizar statements. The paper reported 65.73% exact generation for the best model configuration on its inference data, with the union of evaluated models covering 79.17%.", "zh-CN": "Qingxiang Wang、Cezary Kaliszyk 与 Josef Urban 在对齐的 informalized-LaTeX 文本与形式 Mizar 陈述上训练神经机器翻译模型。论文报告称，最佳模型配置在推理数据上的精确生成率为 65.73%，多种评测模型结果的并集覆盖率达到 79.17%。" }, "summary": { "en": "The authors constructed a large aligned corpus by informalizing Mizar statements into LaTeX-like mathematical text and trained sequence-to-sequence translation models to reconstruct the formal language. The study evaluated multiple neural translation configurations and used case studies to examine which mathematical structures could be recovered correctly.", "zh-CN": "作者通过将 Mizar 陈述 informalize 为类似 LaTeX 的数学文本，构建大规模对齐语料，并训练序列到序列翻译模型重建形式语言。研究比较多种神经翻译配置，并通过案例分析模型能够正确恢复哪些数学结构。" }, "why_it_matters": { "en": "Autoformalization is a key interface problem between human mathematical writing and machine-checkable formal mathematics. This work showed, before the modern LLM era, that learned translation could make the informal-to-formal direction a concrete empirical research problem rather than only a long-term aspiration.", "zh-CN": "自动形式化是连接人类数学书写与机器可检查形式数学的关键接口问题。该工作在现代 LLM 时代之前就展示了学习式翻译能够把 informal-to-formal 方向转化为可实验评测的具体研究问题，而不仅是长期愿景。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Neural sequence-to-sequence models generated candidate formal Mizar statements from informalized mathematical input; the models performed the central translation task evaluated in the study.", "zh-CN": "神经序列到序列模型从 informalized 数学输入生成候选 Mizar 形式陈述，并承担研究所评测的核心翻译任务。" } }, "human_contribution": { "description": { "en": "Researchers created the aligned informal/formal corpus, designed the translation experiments and evaluation methodology, selected model configurations and analyzed generated statements.", "zh-CN": "研究者构建 informal / formal 对齐语料、设计翻译实验与评测方法、选择模型配置，并分析生成的形式陈述。" } }, "systems": [ "mizar" ], "organizations": [ "university-of-innsbruck" ], "people": [ "qingxiang-wang", "cezary-kaliszyk", "josef-urban" ], "problems": [ "mathematical-autoformalization" ], "methods": [ "neural-machine-translation", "sequence-to-sequence-learning", "aligned-corpus-construction", "autoformalization" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2018-05-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and CICM research records establish the neural informal-to-formal translation experiments and the reported Mizar results. E2 records a public research record and does not imply independent reproduction or semantic validation of every generated statement.", "zh-CN": "arXiv 与 CICM 研究记录确认了神经 informal-to-formal 翻译实验及论文报告的 Mizar 结果。E2 表示已有公开研究记录，并不意味着全部生成陈述都获得了独立复现或语义验证。" } } ] }, "sources": [ { "id": "arxiv-neural-mizar-autoformalization-1805.06502", "tier": "S1", "type": "paper", "title": "First Experiments with Neural Translation of Informal to Formal Mathematics", "url": "https://arxiv.org/abs/1805.06502", "primary": true, "published_date": "2018-05-10", "accessed_at": "2026-09-15" }, { "id": "doi-cicm-neural-mizar-autoformalization-2018", "tier": "S1", "type": "paper", "title": "First Experiments with Neural Translation of Informal to Formal Mathematics — CICM 2018", "url": "https://doi.org/10.1007/978-3-319-96812-4_22", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2016-semantic-parsing-math" ], "successors": [ "evt-2022-autoformalization-llm" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "autoformalization", "mizar", "neural-machine-translation", "informal-mathematics", "formal-mathematics", "sequence-to-sequence" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2017-mathlib3", "slug": "mathlib3-formal-mathematics-library", "title": { "en": "Mathlib3 creates a shared Lean library for collaborative formal mathematics", "zh-CN": "Mathlib3 建立面向协作式形式数学的共享 Lean 数学库" }, "dates": { "event": "2017-07-21", "first_public_claim": null, "paper_release": null, "artifact_release": "2017-07-21", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-27" }, "event_types": [ "formalization", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Mathlib transformed Lean from a proof-assistant platform into a growing shared corpus of reusable formal mathematics. The library's scale, collaborative development model and machine-readable theorem/proof data later made it central infrastructure for Lean-based AI theorem proving and benchmark construction.", "zh-CN": "Mathlib 把 Lean 从证明助手平台进一步发展为持续增长、可复用的共享形式数学语料库；其规模、协作开发模式以及机器可读的定理与证明数据，后来使其成为基于 Lean 的 AI 定理证明和基准构建的核心基础设施。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The preserved leanprover-community/mathlib3 repository was created on GitHub on 21 July 2017, providing the exact artifact anchor used for this Event. The later mathlib community paper documents the project as a community-driven effort to build a unified library of mathematics formalized in Lean and explains its mathematical, automation and organizational architecture.", "zh-CN": "保留至今的 leanprover-community/mathlib3 GitHub 仓库创建于 2017 年 7 月 21 日，因此本 Event 以该精确 artifact 时间作为 canonical 锚点。后来由 mathlib 社群发表的论文将该项目描述为在 Lean 中构建统一形式数学库的社区协作工程，并系统说明其数学结构、自动化与组织架构。" }, "summary": { "en": "Mathlib organized community-authored Lean definitions, theorems, proofs and tactics into a common mathematical library spanning algebra, analysis, topology, number theory and other areas. Shared APIs and review practices made formal developments composable rather than isolated project artifacts.", "zh-CN": "Mathlib 将社群编写的 Lean 定义、定理、证明与 tactics 组织为共享数学库，逐步覆盖代数、分析、拓扑、数论等领域；统一 API 与协作审查实践使形式化成果能够相互复用，而非停留在彼此隔离的项目中。" }, "why_it_matters": { "en": "Modern learning-based theorem provers need not only a proof checker but also large libraries of formal statements, proof states and dependencies. Mathlib became precisely that substrate for Lean, later underpinning environments and datasets such as LeanDojo and a wide range of LLM-based formal-math systems.", "zh-CN": "现代学习式定理证明不仅需要证明检查器，也需要大规模形式陈述、证明状态与依赖关系语料。Mathlib 正是 Lean 生态中的这一基础层，后来直接支撑 LeanDojo 等环境、数据集以及大量基于 LLM 的形式数学系统。" }, "ai_role": { "level": "computation_only", "description": { "en": "The mathematical library was primarily authored and reviewed by humans, while Lean mechanically checked the formal content; the Event concerns creation of machine-readable proof infrastructure rather than autonomous AI discovery.", "zh-CN": "数学库内容主要由人类编写与审查，Lean 负责机械检查；本 Event 记录的是机器可读证明基础设施的形成，而非自主 AI 数学发现。" } }, "human_contribution": { "description": { "en": "The Lean mathematical community collaboratively developed, reviewed and maintained reusable formal definitions, theorems, proofs and automation in a shared repository.", "zh-CN": "Lean 数学社群以协作方式在共享仓库中开发、审查并维护可复用的形式定义、定理、证明与自动化工具。" } }, "systems": [ "lean", "mathlib3" ], "organizations": [ "leanprover-community" ], "people": [], "problems": [ "formal-mathematical-knowledge" ], "methods": [ "mathematical-library", "collaborative-formalization", "proof-checking", "interactive-theorem-proving" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "2017-07-21", "status": "claimed", "evidence_level": "E3", "note": { "en": "The preserved public repository provides an exact GitHub creation timestamp and directly inspectable formal artifact; the later mathlib paper documents the library's community-driven architecture and scope.", "zh-CN": "保留的公开仓库提供精确 GitHub 创建时间戳以及可直接检查的形式化 artifact；后来的 mathlib 论文记录了该数学库的社区协作架构与覆盖范围。" } } ] }, "sources": [ { "id": "github-mathlib3-repository", "tier": "S1", "type": "repository", "title": "leanprover-community/mathlib3 repository", "url": "https://github.com/leanprover-community/mathlib3", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "arxiv-lean-mathematical-library-2019", "tier": "S1", "type": "paper", "title": "The Lean mathematical library", "url": "https://arxiv.org/abs/1910.09336", "primary": false, "published_date": "2019-10-21", "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "mathlib3-repository", "kind": "code", "title": "Lean 3 mathlib repository", "url": "https://github.com/leanprover-community/mathlib3" } ], "relationships": { "predecessors": [ "evt-2015-lean" ], "successors": [ "evt-2023-leandojo", "evt-2026-lean-pool" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "mathlib", "formal-mathematics", "mathematical-library", "proof-assistant", "open-source" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-27", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2018-tactictoe", "slug": "tactictoe-hol4-tactic-learning", "title": { "en": "TacticToe learns tactic-level proof search from human HOL4 proofs", "zh-CN": "TacticToe 从人工 HOL4 证明中学习 tactic 级证明搜索" }, "dates": { "event": "2017-05-04", "first_public_claim": "2017-05-04", "paper_release": "2017-05-04", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "TacticToe was an important early proof-assistant-native learning system that used recorded human HOL4 proofs to guide tactic-level proof search directly inside a mature interactive theorem prover. The initial LPAR-21 publication combined learned tactic and premise selection with modified A* search; an expanded 2018 study developed the same system further with Monte Carlo tree search. Together the work established a line later continued by reinforcement-learning systems such as TacticZero.", "zh-CN": "TacticToe 是较早具有代表性的证明助手原生学习系统之一，利用既有人工 HOL4 证明，在成熟交互式定理证明器内部直接引导 tactic 级证明搜索。LPAR-21 的初始版本将学习式 tactic / premise selection 与改进 A* 搜索结合，2018 年扩展研究又进一步以蒙特卡洛树搜索发展同一系统；这一路线后来由 TacticZero 等强化学习系统继续推进。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Thibault Gauthier, Cezary Kaliszyk and Josef Urban introduced TacticToe in the LPAR-21 proceedings published on 4 May 2017. The system learned tactic and premise choices from previous HOL4 proofs and used modified A* search to explore tactic-level proof paths, re-proving 39% of 7,902 HOL4 theorems within five seconds in the reported evaluation. A later expanded study published in 2018 replaced the search with Monte Carlo tree search and reported stronger results on the HOL4 standard library.", "zh-CN": "Thibault Gauthier、Cezary Kaliszyk 与 Josef Urban 在 2017 年 5 月 4 日发布的 LPAR-21 proceedings 中提出 TacticToe。系统从既有 HOL4 证明中学习 tactic 与前提选择，并使用改进 A* 搜索探索 tactic 级证明路径；论文报告在五秒限制下重新证明了 7,902 个 HOL4 定理中的 39%。2018 年发布的扩展研究进一步把搜索机制发展为蒙特卡洛树搜索，并在 HOL4 标准库上报告了更强结果。" }, "summary": { "en": "TacticToe records tactic-level proof information from HOL4, learns which proof actions are promising in a new goal state, and searches over complete tactic sequences directly in higher-order logic rather than translating every problem to first-order logic. The 2017 system used a modified A*-style search with tactic prediction and small-scale hammering; the later expanded implementation developed the search machinery further and remains available in the HOL4 repository.", "zh-CN": "TacticToe 从 HOL4 中记录 tactic 级证明信息，学习在新目标状态下哪些证明动作更有希望，并直接在高阶逻辑环境中搜索完整 tactic 序列，而不是把每个问题都翻译到一阶逻辑。2017 年系统采用改进 A* 风格搜索并结合 tactic prediction 与小规模 hammering；后续扩展实现进一步发展搜索机制，相关代码至今仍可在 HOL4 仓库中检查。" }, "why_it_matters": { "en": "The work demonstrated that machine learning could guide proof-assistant-native tactic search rather than only premise filtering for an external automated prover. This combination of learned action prediction, search and kernel-checked proof construction became a recurring design pattern in later neural interactive theorem proving.", "zh-CN": "该工作展示了机器学习可以直接引导证明助手原生的 tactic 搜索，而不仅仅为外部自动证明器筛选前提。“学习式动作预测 + 搜索 + 内核检查证明”的组合后来成为神经交互式定理证明中反复出现的设计范式。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "Learned predictors ranked tactics and supporting premises while the search algorithm explored proof paths; successful proof scripts were constructed and checked inside HOL4.", "zh-CN": "学习式预测器负责排序 tactics 与支持前提，搜索算法负责探索证明路径；成功的证明脚本最终在 HOL4 内构造并接受检查。" } }, "human_contribution": { "description": { "en": "Researchers designed the proof-trace recording, learned predictors, tactic-level search procedure, HOL4 integration and evaluation protocol, while the learning signal came from existing human-written HOL4 proofs.", "zh-CN": "研究者设计证明轨迹记录、学习式预测器、tactic 级搜索机制、HOL4 集成与评测协议；学习信号来自既有人工编写的 HOL4 证明。" } }, "systems": [ "tactictoe", "hol4" ], "organizations": [], "people": [ "thibault-gauthier", "cezary-kaliszyk", "josef-urban", "ramana-kumar", "michael-norrish" ], "problems": [ "hol4-theorem-proving" ], "methods": [ "tactic-prediction", "premise-selection", "a-star-search", "monte-carlo-tree-search", "proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2017-05-04", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The LPAR-21 proceedings establish the initial public TacticToe system, its learned tactic-level proof search and the reported HOL4 evaluation. Machine checking refers to proof scripts accepted by HOL4 and does not imply independent reproduction of the reported success rate.", "zh-CN": "LPAR-21 proceedings 确认了首次公开的 TacticToe 系统、其学习式 tactic 级证明搜索以及论文报告的 HOL4 评测。machine_checked 仅指证明脚本通过 HOL4 检查，并不表示论文报告的成功率已获得独立复现。" } }, { "date": "2018-04-02", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The expanded 2018 research record documents the later Monte Carlo tree-search version and stronger HOL4 standard-library evaluation without changing the identity of the underlying TacticToe milestone.", "zh-CN": "2018 年扩展研究记录描述了后续蒙特卡洛树搜索版本及更强的 HOL4 标准库评测，但并未构成另一个独立的 TacticToe 历史事件。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The maintained public HOL4 repository contains the TacticToe implementation, recording workflow, evaluation support and usage instructions. E3 denotes inspectable artifacts rather than independent verification of every experimental claim.", "zh-CN": "持续维护的 HOL4 公开仓库包含 TacticToe 实现、证明记录流程、评测支持与使用说明。E3 表示存在可直接检查的 artifacts，而非对全部实验结论的独立验证。" } } ] }, "sources": [ { "id": "easychair-tactictoe-lpar2017", "tier": "S1", "type": "paper", "title": "TacticToe: Learning to Reason with HOL4 Tactics — LPAR-21", "url": "https://easychair.org/publications/paper/WsM", "primary": true, "published_date": "2017-05-04", "accessed_at": "2026-09-15" }, { "id": "arxiv-tactictoe-1804.00596", "tier": "S1", "type": "paper", "title": "TacticToe: Learning to Prove with Tactics", "url": "https://arxiv.org/abs/1804.00596", "primary": true, "published_date": "2018-04-02", "accessed_at": "2026-09-15" }, { "id": "github-hol4-tactictoe", "tier": "S1", "type": "repository", "title": "HOL4 TacticToe implementation", "url": "https://github.com/HOL-Theorem-Prover/HOL/tree/develop/src/tactictoe", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "tactictoe-hol4-code", "kind": "code", "title": "TacticToe implementation in the HOL4 repository", "url": "https://github.com/HOL-Theorem-Prover/HOL/tree/develop/src/tactictoe" } ], "relationships": { "predecessors": [], "successors": [ "evt-2021-tacticzero" ], "related": [ "evt-2018-rl-theorem-proving" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "tactictoe", "hol4", "theorem-proving", "tactic-learning", "premise-selection", "proof-search", "machine-learning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [ { "date": "2026-09-15", "summary": { "en": "Corrected the canonical event date from 2018-04-02 to 2017-05-04 after locating the LPAR-21 proceedings publication of the initial TacticToe system, and revised the record to distinguish the 2017 A*-guided version from the expanded 2018 Monte Carlo tree-search study while preserving the stable Event ID.", "zh-CN": "在确认 LPAR-21 proceedings 已于 2017-05-04 公开初始 TacticToe 系统后，将 canonical event date 从 2018-04-02 纠正为 2017-05-04，并区分 2017 年 A* 引导版本与 2018 年蒙特卡洛树搜索扩展研究，同时保留稳定 Event ID。" }, "source_ids": [ "easychair-tactictoe-lpar2017", "arxiv-tactictoe-1804.00596" ] } ] }, { "schema_version": 1, "id": "evt-2017-holstep", "slug": "holstep-machine-learning-dataset", "title": { "en": "HolStep establishes a large machine-learning benchmark from real HOL Light proofs", "zh-CN": "HolStep 从真实 HOL Light 证明中建立大规模机器学习基准" }, "dates": { "event": "2017-03-01", "first_public_claim": "2017-03-01", "paper_release": "2017-03-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "HolStep turned large-scale HOL Light proof traces into a public machine-learning dataset and benchmark with millions of labeled proof-step examples. By making premise usefulness and proof-step relevance measurable on real higher-order-logic mathematics, it supplied an early common substrate for neural theorem-proving research and directly enabled later work such as FormulaNet while anticipating richer HOL Light learning environments such as HOList.", "zh-CN": "HolStep 将大规模 HOL Light 证明轨迹整理为公开机器学习数据集与 benchmark，包含数百万个带标签的证明步骤样本。它把真实高阶逻辑数学中的前提有用性与证明步骤相关性转化为可统一评测的问题，为早期神经定理证明研究提供了公共基础，并直接支撑 FormulaNet 等后续工作，也预示了 HOList 这类更完整的 HOL Light 学习环境。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Cezary Kaliszyk, François Chollet and Christian Szegedy released HolStep, a BSD-licensed dataset derived from 11,400 HOL Light proofs with more than two million labeled training and test proof-step examples, together with benchmark tasks and baseline logistic-regression, convolutional and recurrent neural models for classifying useful proof steps.", "zh-CN": "Cezary Kaliszyk、François Chollet 与 Christian Szegedy 发布 HolStep：一个基于 11,400 条 HOL Light 证明构建、采用 BSD 许可的数据集，包含超过两百万个带标签的训练与测试证明步骤样本，并配套定义证明步骤有用性等 benchmark 任务以及逻辑回归、卷积网络和循环神经网络基线。" }, "summary": { "en": "HolStep extracts intermediate statements and conjectures from HOL Light proofs, canonicalizes their textual representation and pairs useful proof steps with negative examples. The release defines conditioned and unconditioned proof-step classification tasks and provides baseline code so researchers can compare learned representations and relevance models on a common formal-mathematics corpus.", "zh-CN": "HolStep 从 HOL Light 证明中抽取中间陈述与 conjecture，对文本表示进行规范化，并把实际使用的证明步骤与负样本配对。该发布定义 conditioned 与 unconditioned proof-step classification 等任务，并提供基线代码，使研究者能够在统一的形式数学语料上比较学习式表示与相关性模型。" }, "why_it_matters": { "en": "The project helped shift machine learning for theorem proving from small bespoke experiments toward reusable datasets and reproducible evaluation. HolStep subsequently became a benchmark for neural architectures and an important historical precursor to later environment-plus-benchmark systems for formal mathematics.", "zh-CN": "该项目推动定理证明机器学习从小规模、定制化实验走向可复用数据集与可复现评测。HolStep 随后成为多种神经架构的 benchmark，并成为后来“交互环境 + benchmark”形式数学系统的重要历史前序。" }, "ai_role": { "level": "computation_only", "description": { "en": "Machine-learning models were trained to classify proof-step usefulness and related tasks on the extracted HOL corpus; the historical milestone is the benchmark and dataset rather than an AI-generated mathematical result.", "zh-CN": "机器学习模型在抽取的 HOL 语料上训练，用于判断证明步骤有用性等任务；该历史节点的核心贡献是 benchmark 与数据集，而不是 AI 生成的新数学结果。" } }, "human_contribution": { "description": { "en": "Researchers extracted and normalized the HOL Light proof corpus, designed positive and negative examples, defined benchmark tasks, released the dataset and implemented baseline models and evaluation.", "zh-CN": "研究者抽取并规范化 HOL Light 证明语料、设计正负样本、定义 benchmark 任务、发布数据集，并实现基线模型与评测流程。" } }, "systems": [ "holstep", "hol-light" ], "organizations": [ "university-of-innsbruck", "google-research" ], "people": [ "cezary-kaliszyk", "francois-chollet", "christian-szegedy" ], "problems": [ "higher-order-logic-theorem-proving", "premise-selection" ], "methods": [ "proof-trace-extraction", "proof-step-classification", "premise-selection", "convolutional-neural-network", "recurrent-neural-network", "benchmarking" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2017-03-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and ICLR research records establish the HolStep dataset, benchmark tasks and reported baseline experiments.", "zh-CN": "arXiv 与 ICLR 研究记录确认了 HolStep 数据集、benchmark 任务以及论文报告的基线实验。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public Deepmath repository retains HolStep baseline code and the original research record identifies the public dataset release. E3 records artifact-level inspectability rather than independent reproduction of every reported baseline result.", "zh-CN": "公开 Deepmath 仓库仍保留 HolStep 基线代码，原始研究记录也明确给出公开数据集入口。E3 表示 artifact 可直接检查，并不代表论文报告的全部基线结果已获得独立复现。" } } ] }, "sources": [ { "id": "arxiv-holstep-1703.00426", "tier": "S1", "type": "paper", "title": "HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving", "url": "https://arxiv.org/abs/1703.00426", "primary": true, "published_date": "2017-03-01", "accessed_at": "2026-09-15" }, { "id": "openreview-holstep-iclr2017", "tier": "S1", "type": "paper", "title": "HolStep: A Machine Learning Dataset for Higher-order Logic Theorem Proving — ICLR 2017", "url": "https://openreview.net/pdf?id=ryuxYmvel", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "google-research-holstep", "tier": "S2", "type": "official_announcement", "title": "HolStep — Google Research publication record", "url": "https://research.google/pubs/holstep-a-machine-learning-dataset-for-higher-order-logic-theorem-proving/", "primary": false, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-deepmath-holstep", "tier": "S1", "type": "repository", "title": "Deepmath HolStep baseline implementation", "url": "https://github.com/tensorflow/deepmath/tree/master/deepmath/holstep_baselines", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "holstep-dataset", "kind": "dataset", "title": "HolStep higher-order-logic theorem-proving dataset", "url": "http://cl-informatik.uibk.ac.at/cek/holstep/" }, { "id": "holstep-baseline-code", "kind": "code", "title": "HolStep baseline models in Deepmath", "url": "https://github.com/tensorflow/deepmath/tree/master/deepmath/holstep_baselines" } ], "relationships": { "predecessors": [], "successors": [ "evt-2019-holist" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "holstep", "hol-light", "theorem-proving", "benchmark", "dataset", "premise-selection", "proof-steps", "machine-learning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2017-deep-network-guided-proof-search", "slug": "deep-network-guided-proof-search", "title": { "en": "Deep networks are integrated directly into automated theorem-prover search", "zh-CN": "深度网络被直接接入自动定理证明器的内部搜索" }, "dates": { "event": "2017-01-24", "first_public_claim": "2017-01-24", "paper_release": "2017-01-24", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "Deep Network Guided Proof Search was an important early step from learned premise selection toward learned control inside the proof search itself. By training neural models on Mizar-derived proof traces and inserting their predictions into E prover's processed-clause selection, the work established a concrete deep-learning route for internal automated-theorem-prover guidance before later reinforcement-learning and proof-assistant-native systems.", "zh-CN": "Deep Network Guided Proof Search 是从“学习式前提选择”进一步走向“直接学习证明器内部搜索控制”的重要早期节点。该工作从 Mizar 衍生的证明轨迹训练神经模型，并把预测直接接入 E prover 的 processed-clause selection，在后来的强化学习与证明助手原生系统出现之前，建立了深度学习引导自动定理证明内部搜索的具体路线。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Sarah Loos, Geoffrey Irving, Christian Szegedy and Cezary Kaliszyk trained deep neural networks on existing automated proofs of Mizar statements and used them to guide processed-clause selection inside E prover. The paper reported finding first-order proofs for a subset of translated Mizar theorems that previously lacked ATP-generated proofs, increasing the corpus coverage with ATP proofs from about 56% to 59%.", "zh-CN": "Sarah Loos、Geoffrey Irving、Christian Szegedy 与 Cezary Kaliszyk 使用既有 Mizar 自动证明轨迹训练深度神经网络，并将其用于引导 E prover 内部的 processed-clause selection。论文报告称，该方法为一部分此前没有 ATP 证明的 Mizar 翻译定理找到了新的 first-order proofs，使语料中具有 ATP 证明的覆盖率从约 56% 提升到 59%。" }, "summary": { "en": "The system learns from clause-level traces of successful automated proofs and ranks generated clauses during saturation-style proof search. Because neural evaluation is slower than hand-engineered heuristics, the authors used hybrid guidance and a two-phase search strategy that lets the learned model improve the search trajectory before faster conventional heuristics finish the proof attempt.", "zh-CN": "该系统从成功自动证明的 clause-level 轨迹中学习，并在 saturation-style proof search 中对生成的 clauses 进行排序。由于神经网络评估慢于人工设计启发式，作者采用混合引导与 two-phase search：先利用学习模型改善搜索轨迹，再由更快的传统启发式完成后续证明尝试。" }, "why_it_matters": { "en": "The work demonstrated that neural models could influence the inner loop of a mature automated theorem prover rather than acting only as an upstream filter. That distinction became important in later work on learned clause guidance, reinforcement-learning proof search and search-in-the-loop theorem proving.", "zh-CN": "该工作展示了神经模型不仅可以作为上游过滤器，还可以直接影响成熟自动定理证明器的内部搜索循环。这一区别后来成为学习式 clause guidance、强化学习证明搜索以及 search-in-the-loop theorem proving 的重要技术前史。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Learned neural models ranked processed clauses during automated proof search, while E prover carried out the symbolic inference and constructed successful first-order proofs without human step-by-step intervention.", "zh-CN": "学习式神经模型在自动证明搜索中排序 processed clauses，由 E prover 执行符号推理并构造成功的一阶逻辑证明，不需要人类逐步干预证明动作。" } }, "human_contribution": { "description": { "en": "Researchers designed the neural clause-guidance models, proof-trace training data, hybrid and two-phase search strategy, E-prover integration and evaluation over Mizar-derived problems.", "zh-CN": "研究者设计神经 clause-guidance 模型、证明轨迹训练数据、混合与两阶段搜索策略、E prover 集成以及基于 Mizar 衍生问题的评测方案。" } }, "systems": [ "e-prover", "deep-network-guided-proof-search" ], "organizations": [ "google-research", "university-of-innsbruck" ], "people": [ "sarah-loos", "geoffrey-irving", "christian-szegedy", "cezary-kaliszyk" ], "problems": [ "automated-theorem-proving", "mizar-theorem-proving" ], "methods": [ "deep-learning", "clause-selection", "proof-search", "saturation-based-theorem-proving", "supervised-learning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2017-01-24", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and LPAR research records establish the neural proof-search guidance method and the reported Mizar-derived theorem-proving results. The Chronicle does not record a directly inspectable proof artifact or independent replay for this event, so formal assurance remains `none`.", "zh-CN": "arXiv 与 LPAR 研究记录确认了神经证明搜索引导方法及论文报告的 Mizar 衍生定理证明结果。Chronicle 当前未记录可直接检查的证明 artifact 或独立 replay，因此 formal assurance 保持为 `none`。" } } ] }, "sources": [ { "id": "arxiv-deep-network-proof-search-1701.06972", "tier": "S1", "type": "paper", "title": "Deep Network Guided Proof Search", "url": "https://arxiv.org/abs/1701.06972", "primary": true, "published_date": "2017-01-24", "accessed_at": "2026-09-15" }, { "id": "easychair-deep-network-proof-search-lpar2017", "tier": "S1", "type": "paper", "title": "Deep Network Guided Proof Search — LPAR-21", "url": "https://easychair.org/publications/paper/ND13", "primary": true, "published_date": "2017-05-04", "accessed_at": "2026-09-15" }, { "id": "google-research-deep-network-proof-search", "tier": "S2", "type": "official_announcement", "title": "Deep Network Guided Proof Search — Google Research publication record", "url": "https://research.google/pubs/deep-network-guided-proof-search-2/", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-2016-deepmath" ], "successors": [ "evt-2018-rl-theorem-proving" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "theorem-proving", "deep-learning", "e-prover", "mizar", "clause-selection", "proof-search", "automated-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2016-semantic-parsing-math", "slug": "semantic-parsing-mathematics", "title": { "en": "Statistical and semantic parsing advances early mathematical autoformalization", "zh-CN": "统计与语义解析推进早期数学自动形式化" }, "dates": { "event": "2016-11-29", "first_public_claim": "2016-11-29", "paper_release": "2016-11-29", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "This work was an important early autoformalization milestone because it treated the mapping from ambiguous, informalized mathematical expressions to formal syntax as a learnable parsing problem and combined statistical structure prediction with formal semantic checks. It established a concrete pre-neural-machine-translation route from informal mathematical text toward machine-checkable representations and directly preceded later Mizar autoformalization systems.", "zh-CN": "该工作是早期自动形式化的重要里程碑之一：它把从带歧义的 informalized 数学表达映射到形式语法的问题明确建模为可学习的解析任务，并将统计结构预测与形式语义检查结合。它在神经机器翻译路线之前就建立了从非形式数学文本走向机器可检查表示的具体方案，并直接早于后来的 Mizar 自动形式化系统。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "informal", "formal", "hybrid" ], "claim": { "en": "Cezary Kaliszyk, Josef Urban and Jiří Vyskočil proposed a context-based parser for mathematical expressions that learned deep parse trees from aligned informal/formal corpora and pruned candidate parses using type checking and large-theory automated theorem proving. The paper reported substantial improvements over earlier parsing results on the Flyspeck-derived evaluation.", "zh-CN": "Cezary Kaliszyk、Josef Urban 与 Jiří Vyskočil 提出一种面向数学表达的上下文解析方法：从对齐的 informal / formal 语料中学习深层解析树，并利用类型检查与大型理论自动定理证明对候选解析进行语义剪枝。论文报告该方法在基于 Flyspeck 的评测上显著改善了此前的解析结果。" }, "summary": { "en": "The system learns how ambiguous mathematical notation is parsed from aligned corpora and then uses formal semantic constraints to reject syntactically plausible but mathematically ill-typed or unsupported interpretations. This creates a hybrid statistical-symbolic pipeline in which learning proposes formal structures and theorem-proving machinery helps validate them.", "zh-CN": "该系统从对齐语料中学习如何解析有歧义的数学记号，再使用形式语义约束排除语法上合理但类型不成立或缺乏支持的解释。由此形成统计学习与符号推理结合的混合流程：学习模型提出形式结构，类型检查和定理证明机制帮助筛选与验证候选。" }, "why_it_matters": { "en": "Autoformalization depends on bridging human mathematical notation and formal proof languages. This work showed before modern neural translation and LLMs that aligned mathematical corpora plus formal semantic feedback could make that interface empirically tractable, establishing a lineage that later moved toward neural translation and large-language-model formalization.", "zh-CN": "自动形式化的核心难点之一，是连接人类数学记号与形式证明语言。该工作在现代神经翻译和 LLM 之前就展示了：对齐数学语料与形式语义反馈可以把这一接口问题转化为可实验研究任务，并形成后来走向神经翻译与大语言模型形式化的历史谱系。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Statistical learning produced candidate formal parse trees from informalized mathematical expressions, while type checking and automated theorem proving supplied machine-executable semantic filtering of those candidates.", "zh-CN": "统计学习模型从 informalized 数学表达生成候选形式解析树，类型检查与自动定理证明则为这些候选提供机器可执行的语义筛选。" } }, "human_contribution": { "description": { "en": "Researchers constructed aligned corpora, designed the context-based parser and semantic-pruning pipeline, selected formal checking components and evaluated the resulting system on Flyspeck-derived material.", "zh-CN": "研究者构建对齐语料、设计上下文解析器与语义剪枝流程、选择形式检查组件，并在 Flyspeck 衍生数据上评测系统。" } }, "systems": [ "semantic-parsing-math", "hol-light" ], "organizations": [ "university-of-innsbruck", "czech-technical-university" ], "people": [ "cezary-kaliszyk", "josef-urban", "jiri-vyskocil" ], "problems": [ "mathematical-autoformalization", "mathematical-semantic-parsing" ], "methods": [ "statistical-parsing", "context-based-learning", "aligned-corpus-learning", "type-checking", "automated-theorem-proving", "semantic-pruning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2016-11-29", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record establishes the context-based mathematical parsing method and the reported Flyspeck-derived evaluation. E2 records a public research result and does not imply independent reproduction or validation of every generated parse.", "zh-CN": "arXiv 研究记录确认了上下文数学解析方法以及论文报告的 Flyspeck 衍生评测。E2 表示已有公开研究结果，并不表示所有生成解析都获得独立复现或验证。" } } ] }, "sources": [ { "id": "arxiv-semantic-parsing-math-1611.09703", "tier": "S1", "type": "paper", "title": "Semantic Parsing of Mathematics by Context-based Learning from Aligned Corpora and Theorem Proving", "url": "https://arxiv.org/abs/1611.09703", "primary": true, "published_date": "2016-11-29", "accessed_at": "2026-09-15" }, { "id": "ai4reason-semantic-parsing-2016", "tier": "S2", "type": "official_announcement", "title": "AI4REASON 2016 publication record — Semantic Parsing of Mathematics", "url": "https://ai4reason.org/activities.html", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2018-neural-mizar-autoformalization" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "autoformalization", "semantic-parsing", "informal-mathematics", "formal-mathematics", "flyspeck", "statistical-learning", "theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2016-holophrasm", "slug": "holophrasm-neural-theorem-prover", "title": { "en": "Holophrasm builds a neural end-to-end theorem prover for Metamath", "zh-CN": "Holophrasm 构建面向 Metamath 的神经端到端定理证明器" }, "dates": { "event": "2016-08-08", "first_public_claim": "2016-08-08", "paper_release": "2016-08-08", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Holophrasm was an important early neural theorem prover that moved beyond premise scoring to search over complete formal proof trees in Metamath. It combined learned proof-step generation, neural evaluation and bandit-style search in one system, creating a direct historical precursor to later Metamath neural provers and synthetic-data systems such as MetaGen.", "zh-CN": "Holophrasm 是较早具有代表性的神经定理证明器之一，从前提评分进一步走向在 Metamath 中搜索完整形式证明树。它把学习式证明步骤生成、神经评估与 bandit 风格搜索整合到统一系统中，成为后来 Metamath 神经证明器以及 MetaGen 等合成数据系统的直接历史前序。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Daniel Whalen introduced Holophrasm, a neural automated theorem prover for Metamath that explored partial proof trees with a neural-network-augmented bandit algorithm and used a sequence-to-sequence model to enumerate proof actions. The paper reported proving about 14% of its held-out test theorems from Metamath's `set.mm` corpus.", "zh-CN": "Daniel Whalen 提出 Holophrasm：一个面向 Metamath 的神经自动定理证明器，使用神经网络增强的 bandit 算法探索部分证明树，并利用序列到序列模型枚举证明动作。论文报告其在 Metamath `set.mm` 留出测试定理上证明了约 14%。" }, "summary": { "en": "Holophrasm parses Metamath statements into tree structures, learns neural models for proof-step generation and proof-state evaluation, and combines them with search over candidate proof trees. The public release includes model-training and proof-search code, saved proof outputs, and instructions for replaying generated proofs through Metamath's verifier.", "zh-CN": "Holophrasm 将 Metamath 陈述解析为树结构，训练用于证明步骤生成与证明状态评估的神经模型，并与候选证明树搜索结合。公开版本包含模型训练与证明搜索代码、保存的证明结果，以及通过 Metamath verifier 重放和检查生成证明的说明。" }, "why_it_matters": { "en": "The project demonstrated a pre-Transformer route to neural proof generation in which learned models actively construct formal proof steps rather than only rank premises. Its Metamath data-processing and prover structure were reused by later work, including MetaGen, making it a durable part of the lineage of neural formal theorem proving.", "zh-CN": "该项目在 Transformer 时代之前就展示了一条神经证明生成路线：学习模型主动构造形式证明步骤，而不仅仅为前提排序。其 Metamath 数据处理与证明器结构后来被包括 MetaGen 在内的工作继续使用，因此成为神经形式定理证明演化中的重要前序。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Learned neural models proposed proof actions and evaluated proof states while the search procedure assembled complete formal proofs; successful outputs could then be checked by Metamath without human step-by-step proof construction.", "zh-CN": "学习式神经模型负责提出证明动作并评估证明状态，搜索过程组装完整形式证明；成功输出随后可由 Metamath 检查，无需人类逐步构造证明。" } }, "human_contribution": { "description": { "en": "The researcher designed the Metamath parser, neural models, search algorithm, training pipeline and evaluation protocol, and packaged the generated proofs for replay and verification.", "zh-CN": "研究者设计 Metamath 解析器、神经模型、搜索算法、训练流程和评测协议，并将生成证明整理为可重放和验证的形式。" } }, "systems": [ "holophrasm", "metamath" ], "organizations": [], "people": [ "daniel-whalen" ], "problems": [ "metamath-theorem-proving", "automated-theorem-proving" ], "methods": [ "neural-theorem-proving", "sequence-to-sequence-generation", "bandit-search", "proof-tree-search", "proof-step-generation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2016-08-08", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record establishes Holophrasm, its neural proof-search architecture and the reported Metamath evaluation. Machine checking refers to formal proofs that can be replayed through Metamath and does not imply independent reproduction of the paper's aggregate success rate.", "zh-CN": "arXiv 研究记录确认了 Holophrasm、其神经证明搜索架构以及论文报告的 Metamath 评测。machine_checked 仅指形式证明可通过 Metamath 重放检查，并不表示论文报告的整体成功率已得到独立复现。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public Holophrasm repository exposes training and search code, saved proof outputs and explicit Metamath verification instructions. E3 denotes inspectable artifacts rather than an independent rerun of the complete experiment.", "zh-CN": "公开 Holophrasm 仓库提供训练与搜索代码、保存的证明输出以及明确的 Metamath 验证说明。E3 表示存在可直接检查的研究产物，而不是 Chronicle 已独立重跑完整实验。" } } ] }, "sources": [ { "id": "arxiv-holophrasm-1608.02644", "tier": "S1", "type": "paper", "title": "Holophrasm: a neural Automated Theorem Prover for higher-order logic", "url": "https://arxiv.org/abs/1608.02644", "primary": true, "published_date": "2016-08-08", "accessed_at": "2026-09-15" }, { "id": "github-dwhalen-holophrasm", "tier": "S1", "type": "repository", "title": "Holophrasm neural Metamath prover implementation", "url": "https://github.com/dwhalen/holophrasm", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "holophrasm-repository", "kind": "code", "title": "Holophrasm code, proof search and verification workflow", "url": "https://github.com/dwhalen/holophrasm" } ], "relationships": { "predecessors": [], "successors": [ "evt-2020-metagen" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "holophrasm", "metamath", "theorem-proving", "neural-theorem-proving", "proof-generation", "proof-search", "deep-learning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2016-deepmath", "slug": "deepmath-premise-selection", "title": { "en": "DeepMath brings deep sequence models to large-scale premise selection", "zh-CN": "DeepMath 将深度序列模型引入大规模前提选择" }, "dates": { "event": "2016-06-14", "first_public_claim": "2016-06-14", "paper_release": "2016-06-14", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "DeepMath was an important early large-scale application of deep neural sequence models to premise selection over formal mathematics. By learning directly from Mizar theorem and proof corpora without relying on the hand-engineered feature pipelines that dominated earlier systems, it helped establish deep learning as a practical representation-and-ranking approach for large-theory theorem proving and directly preceded neural guidance inside prover search.", "zh-CN": "DeepMath 是较早把深度神经序列模型大规模应用于形式数学前提选择的重要工作。它直接从 Mizar 定理与证明语料中学习，而不再主要依赖此前系统中的人工特征工程，为大型理论定理证明建立了深度学习表示与排序的具体路线，并直接早于后来把神经引导接入证明器内部搜索的工作。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Alexander A. Alemi, François Chollet, Niklas Eén, Geoffrey Irving, Christian Szegedy and Josef Urban trained neural sequence models to rank candidate premises for Mizar conjectures. The paper reported competitive large-scale premise-selection results using a two-stage architecture that avoided the hand-engineered features used by earlier state-of-the-art systems.", "zh-CN": "Alexander A. Alemi、François Chollet、Niklas Eén、Geoffrey Irving、Christian Szegedy 与 Josef Urban 训练神经序列模型，为 Mizar 猜想排序候选前提。论文报告其两阶段架构在大规模前提选择上取得有竞争力的结果，同时避免了此前先进系统所依赖的人工设计特征。" }, "summary": { "en": "DeepMath encodes conjectures and candidate premises with recurrent and convolutional neural architectures and learns whether a premise is useful for a target theorem. The release turned large formal proof corpora into training data for neural relevance models, making representation learning a central component of automated theorem-proving pipelines.", "zh-CN": "DeepMath 使用循环与卷积神经架构编码猜想和候选前提，并学习判断某个前提是否有助于目标定理。该工作把大型形式证明语料转化为神经相关性模型的训练数据，使表示学习成为自动定理证明流程中的核心组件之一。" }, "why_it_matters": { "en": "Premise selection is a major bottleneck when automated provers operate over large mathematical libraries. DeepMath showed that neural models could learn useful relevance signals at this scale, supplying a methodological bridge from earlier feature-based learning to later neural proof-search guidance, graph representations and learned retrieval systems for formal mathematics.", "zh-CN": "当自动证明器面对大型数学库时，前提选择是关键瓶颈之一。DeepMath 展示了神经模型能够在这一规模上学习有效的相关性信号，为从早期特征工程式学习走向后来的神经证明搜索引导、图表示与形式数学学习式检索系统提供了方法桥梁。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Neural models ranked candidate formal premises for target conjectures, supplying learned guidance to downstream automated theorem proving rather than constructing complete proofs by themselves.", "zh-CN": "神经模型为目标猜想排序候选形式前提，为后续自动定理证明提供学习式引导，而不是独立构造完整证明。" } }, "human_contribution": { "description": { "en": "Researchers designed the premise-selection task formulation, neural sequence architectures, training corpus construction, evaluation protocol and integration with large-theory theorem-proving workflows.", "zh-CN": "研究者设计前提选择任务、神经序列架构、训练语料构建、评测协议以及与大型理论自动定理证明流程的集成方式。" } }, "systems": [ "deepmath", "mizar" ], "organizations": [ "google-research", "czech-technical-university" ], "people": [ "alexander-a-alemi", "francois-chollet", "niklas-een", "geoffrey-irving", "christian-szegedy", "josef-urban" ], "problems": [ "premise-selection", "automated-theorem-proving", "mizar-theorem-proving" ], "methods": [ "neural-premise-selection", "sequence-modeling", "convolutional-neural-network", "recurrent-neural-network", "representation-learning" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2016-06-14", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv and NeurIPS research records establish the DeepMath premise-selection approach and the reported Mizar evaluation. This records the public research claim and does not imply independent reproduction of the reported metrics.", "zh-CN": "arXiv 与 NeurIPS 研究记录确认了 DeepMath 的前提选择方法及论文报告的 Mizar 评测。这一记录确认公开研究主张，并不表示论文报告的指标已获得独立复现。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The public TensorFlow Deepmath repository retains the `deepmath/premises` implementation with neural premise-selection models. E3 denotes inspectable research code rather than independent reproduction of the published benchmark results.", "zh-CN": "TensorFlow 公开 Deepmath 仓库保留 `deepmath/premises` 前提选择实现及相关神经模型。E3 表示存在可直接检查的研究代码，而非论文 benchmark 结果已获独立复现。" } } ] }, "sources": [ { "id": "arxiv-deepmath-1606.04442", "tier": "S1", "type": "paper", "title": "DeepMath - Deep Sequence Models for Premise Selection", "url": "https://arxiv.org/abs/1606.04442", "primary": true, "published_date": "2016-06-14", "accessed_at": "2026-09-15" }, { "id": "neurips-deepmath-2016", "tier": "S1", "type": "paper", "title": "DeepMath - Deep Sequence Models for Premise Selection — NIPS 2016", "url": "https://proceedings.neurips.cc/paper/2016/hash/f197002b9a0853eca5e046d9ca4663d5-Abstract.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "github-tensorflow-deepmath-premises", "tier": "S1", "type": "repository", "title": "TensorFlow Deepmath premise-selection implementation", "url": "https://github.com/tensorflow/deepmath/tree/master/deepmath/premises", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "deepmath-premise-selection-code", "kind": "code", "title": "Deepmath neural premise-selection implementation", "url": "https://github.com/tensorflow/deepmath/tree/master/deepmath/premises" } ], "relationships": { "predecessors": [], "successors": [ "evt-2017-deep-network-guided-proof-search" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "deepmath", "premise-selection", "mizar", "theorem-proving", "deep-learning", "formal-mathematics", "sequence-models" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2016-aitp", "slug": "aitp-conference-inaugural", "title": { "en": "The first AITP conference establishes a recurring AI-and-theorem-proving forum", "zh-CN": "首届 AITP 会议建立 AI 与定理证明的持续性学术论坛" }, "dates": { "event": "2016-04-03", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-14", "last_updated": "2026-09-14" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "AITP is a field-building milestone because its 2016 inaugural meeting created a dedicated scholarly forum at the intersection of artificial intelligence, automated and interactive theorem proving, machine learning, proof assistants and computer-understandable mathematics. The series then continued annually through 2026, with a 2027 edition announced, demonstrating durable institutional continuity rather than a one-off workshop.", "zh-CN": "AITP 构成领域建构里程碑，因为其 2016 年首届会议建立了一个专门连接人工智能、自动与交互式定理证明、机器学习、证明助手和机器可理解数学的学术论坛。该系列随后持续每年举办至 2026 年，并已公布 2027 年会议，体现出持续性的学术制度化，而非一次性 workshop。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The first Conference on Artificial Intelligence and Theorem Proving (AITP) was held in Obergurgl, Austria, on 3–7 April 2016. Its program combined invited and contributed work on AI for automated and interactive theorem proving, machine learning for proof guidance, computer understanding of mathematics, and related topics; contributed abstracts were selected through a program committee. By 2026 the conference had continued as an annual series, with AITP 2027 already announced.", "zh-CN": "首届 Artificial Intelligence and Theorem Proving Conference（AITP）于 2016 年 4 月 3–7 日在奥地利 Obergurgl 举行。会议议程结合邀请报告与投稿报告，主题覆盖面向自动与交互式定理证明的 AI、机器学习证明引导、机器理解数学等方向，投稿摘要由 program committee 进行筛选。到 2026 年，该会议已连续发展为年度系列，并已公布 AITP 2027。" }, "summary": { "en": "AITP 2016 explicitly positioned itself as a forum for combining AI and reasoning methods over large mathematical and scientific corpora. The inaugural program included focused sessions on AI for ATP/ITP and mathematics, informal and semi-formal mathematical understanding, modern AI methods, and contributed talks. Its official series record documents yearly meetings from 2016 through 2026.", "zh-CN": "AITP 2016 明确将自身定位为讨论如何把 AI 与推理方法用于大规模数学和科学语料的论坛。首届议程设置了面向 ATP / ITP 与数学的 AI、非形式与半形式数学理解、现代 AI 方法等专题，并包含投稿报告。官方系列记录显示会议从 2016 年起持续每年举办至 2026 年。" }, "why_it_matters": { "en": "Before the recent LLM-centered wave of AI4Math, AITP provided a durable meeting point for researchers working across machine learning, automated reasoning, proof assistants and mathematical knowledge. Its continuity makes the inaugural conference useful historical evidence of the institutional formation of an AI-for-theorem-proving community.", "zh-CN": "在近年来以 LLM 为中心的 AI4Math 浪潮之前，AITP 已为机器学习、自动推理、证明助手与数学知识处理研究者提供了持续性的共同交流场所。其多年连续举办，使首届会议成为 AI 定理证明共同体制度化形成的重要历史证据。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records the establishment of a scholarly community venue rather than an AI system performing mathematical work, so an operative AI role is not applicable.", "zh-CN": "本事件记录的是学术共同体 venue 的建立，而不是某个 AI 系统执行数学工作，因此不存在适用的具体 AI role。" } }, "human_contribution": { "description": { "en": "Human organizers established the conference, assembled the program committee and invited program, selected contributed abstracts, hosted the inaugural meeting, and sustained the recurring series.", "zh-CN": "人类组织者建立会议、组建 program committee 与邀请报告体系、筛选投稿摘要、举办首届会议，并持续维护后续年度系列。" } }, "systems": [], "organizations": [ "university-of-innsbruck" ], "people": [ "thomas-c-hales", "cezary-kaliszyk", "stephan-schulz", "josef-urban" ], "problems": [], "methods": [ "scholarly-venue", "theorem-proving-community" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2016-04-03", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official AITP 2016 page and conference proceedings establish the inaugural meeting, its dates, program committee, review process and AI/theorem-proving scope.", "zh-CN": "AITP 2016 官方页面与会议 proceedings 记录了首届会议、日期、program committee、投稿筛选流程以及 AI / 定理证明主题范围。" } }, { "date": "2026-09-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official AITP series page documents annual editions from 2016 through 2026 and an announced 2027 edition, supporting the Chronicle's durability assessment without implying endorsement of venue prestige.", "zh-CN": "AITP 官方系列页面记录了 2016–2026 年逐年举办的会议以及已公布的 2027 年会议，从而支持 Chronicle 对其持续性的判断，但不代表对 venue 声望作出背书。" } } ] }, "sources": [ { "id": "aitp-2016-official", "tier": "S2", "type": "official_announcement", "title": "AITP 2016: 1st Conference on Artificial Intelligence and Theorem Proving", "url": "https://aitp-conference.org/2016/", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "aitp-2016-proceedings", "tier": "S1", "type": "other", "title": "AITP 2016: The First Conference on Artificial Intelligence and Theorem Proving — Abstracts of the talks", "url": "https://aitp-conference.org/2016/aitp_proceedings.pdf", "primary": true, "published_date": null, "accessed_at": "2026-09-14" }, { "id": "aitp-series-official", "tier": "S2", "type": "official_announcement", "title": "Conference on Artificial Intelligence and Theorem Proving — AITP series", "url": "https://aitp-conference.org/", "primary": false, "published_date": null, "accessed_at": "2026-09-14" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2021-math-ai-workshop" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "aitp", "field-building", "conference", "theorem-proving", "automated-reasoning", "proof-assistants", "machine-learning" ], "editorial": { "created_at": "2026-09-14", "last_reviewed": "2026-09-14", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2015-ai4reason", "slug": "ai4reason-project-launch", "title": { "en": "AI4REASON launches a research program coupling machine learning with large-scale automated reasoning", "zh-CN": "AI4REASON 启动机器学习与大规模自动推理融合研究计划" }, "dates": { "event": "2015-09-01", "first_public_claim": "2015-09-01", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The ERC-funded AI4REASON project institutionalized a multi-year research agenda explicitly combining machine learning, automated reasoning and self-improving deduction–learning loops over large formal, semi-formal and informal corpora.", "zh-CN": "ERC 资助的 AI4REASON 将机器学习、自动推理及面向大型形式/半形式/非形式语料的自我改进“演绎—学习”循环制度化为多年研究议程。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The European Commission records AI4REASON as starting on 1 September 2015 with the goal of developing AI methods that combine automated reasoning and machine learning into independent self-improving systems.", "zh-CN": "欧盟委员会记录 AI4REASON 于 2015 年 9 月 1 日启动，其目标是开发把自动推理与机器学习结合成独立自我改进系统的 AI 方法。" }, "summary": { "en": "The project focused on large and complex theories, learning from reasoning traces, feedback loops between deduction and learning, and knowledge accumulation across multiple mathematical representation styles.", "zh-CN": "项目聚焦大型复杂理论、从推理轨迹学习、演绎与学习之间的反馈循环，以及跨多种数学表示风格积累推理知识。" }, "why_it_matters": { "en": "AI4REASON helped consolidate learning-guided automated reasoning into a sustained, explicitly named AI research program immediately before the deep-learning theorem-proving wave represented by DeepMath and related systems.", "zh-CN": "AI4REASON 在 DeepMath 等深度学习定理证明浪潮之前，把学习引导自动推理整合为持续且明确命名的 AI 研究计划。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This Event records the launch of a research program rather than a single AI system executing a mathematical task.", "zh-CN": "该事件记录研究计划启动，而非某个单一 AI 系统执行数学任务。" } }, "human_contribution": { "description": { "en": "Josef Urban and project collaborators formulated and executed the research agenda with ERC support.", "zh-CN": "Josef Urban 与项目合作者在 ERC 支持下制定并推进研究议程。" } }, "systems": [], "organizations": [ "czech-technical-university", "european-research-council" ], "people": [ "josef-urban" ], "problems": [], "methods": [], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2015-09-01", "status": "claimed", "evidence_level": "E2", "note": { "en": "The European Commission CORDIS project record supplies the exact start date, funding context and technical research objectives.", "zh-CN": "欧盟委员会 CORDIS 项目记录提供精确启动日期、资助背景与技术研究目标。" } } ] }, "sources": [ { "id": "cordis-ai4reason", "tier": "S2", "type": "official_announcement", "title": "Artificial Intelligence for Large-Scale Computer-Assisted Reasoning", "url": "https://cordis.europa.eu/project/id/649043", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "ai4reason", "field-building", "machine-learning", "automated-reasoning", "large-theory-reasoning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2015-lean", "slug": "lean-theorem-prover-cade-2015", "title": { "en": "Lean is presented at CADE-25 as an open theorem prover for formal mathematics", "zh-CN": "Lean 在 CADE-25 作为面向形式数学的开放证明器公开展示" }, "dates": { "event": "2015-08-07", "first_public_claim": null, "paper_release": "2015-07-30", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure", "formalization" ], "significance": { "tier": "H2", "rationale": { "en": "Lean established a new dependent-type proof-assistant platform explicitly designed to combine interactive theorem proving with automation, laying the technical foundation for the later Lean/mathlib ecosystem and a major share of modern AI-assisted formal mathematics.", "zh-CN": "Lean 建立了新的依赖类型证明助手平台，并从设计上明确结合交互式定理证明与自动化，为后来的 Lean/mathlib 生态以及现代 AI 辅助形式数学的重要路线奠定技术基础。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "At CADE-25 on 7 August 2015, Leonardo de Moura and collaborators presented Lean as a new open-source theorem prover with a small trusted kernel based on dependent type theory and an explicit goal of bridging interactive and automated theorem proving. The Springer CADE-25 proceedings containing the system description were published on 30 July 2015. The official Lean history records the first repository commit in July 2013 and the official Lean 0.1 release in June 2014; because those earlier records are month-precision only, this Event uses the exact CADE presentation date as its canonical public anchor.", "zh-CN": "2015 年 8 月 7 日 CADE-25 上，Leonardo de Moura 与合作者将 Lean 公开描述为一种新的开源定理证明器：它采用基于依赖类型理论的小型可信内核，并明确以连接交互式与自动定理证明为目标。收录该系统论文的 Springer CADE-25 proceedings 于 2015 年 7 月 30 日出版。Lean 官方历史记录其仓库首次 commit 于 2013 年 7 月、Lean 0.1 正式发布于 2014 年 6 月；由于这些更早记录仅精确到月份，本条采用具有精确日期的 CADE 展示作为 canonical 公开锚点。" }, "summary": { "en": "Lean combined a small proof-checking kernel, an expressive dependent type theory, interactive proof development and extensible automation in one open platform intended for formalized mathematics as well as verification.", "zh-CN": "Lean 在一个开放平台中结合小型证明检查内核、富表达力的依赖类型理论、交互式证明开发与可扩展自动化，并同时面向形式化数学与验证任务。" }, "why_it_matters": { "en": "The system became a durable substrate for large formal mathematical libraries and later learning-based theorem provers, making its pre-2016 introduction essential historical context for the Chronicle's later Lean-centered AI4Math milestones.", "zh-CN": "该系统后来成为大型形式数学库与学习式定理证明器的长期基础，因此其 2016 年以前的形成是理解 Chronicle 后续大量 Lean 相关 AI4Math 里程碑所必需的历史背景。" }, "ai_role": { "level": "computation_only", "description": { "en": "Lean's trusted kernel mechanically checks formal proof terms, while its proof language and automation support construction of proofs; humans supplied the mathematical statements, formalizations and system design.", "zh-CN": "Lean 的可信内核机械检查形式证明项，其证明语言与自动化支持证明构造；数学陈述、形式化内容与系统设计主要由人类提供。" } }, "human_contribution": { "description": { "en": "Leonardo de Moura, Soonho Kong, Jeremy Avigad, Floris van Doorn, Jakob von Raumer and collaborators designed and implemented the early Lean system, its kernel, elaborator, automation interfaces and mathematical applications.", "zh-CN": "Leonardo de Moura、Soonho Kong、Jeremy Avigad、Floris van Doorn、Jakob von Raumer 与合作者设计并实现早期 Lean 系统，包括内核、elaborator、自动化接口及数学应用。" } }, "systems": [ "lean" ], "organizations": [ "microsoft-research", "carnegie-mellon-university" ], "people": [ "leonardo-de-moura", "soonho-kong", "jeremy-avigad", "floris-van-doorn", "jakob-von-raumer" ], "problems": [ "formal-mathematical-knowledge", "interactive-theorem-proving" ], "methods": [ "dependent-type-theory", "proof-checking", "interactive-theorem-proving", "automated-theorem-proving" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "2015-07-30", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Springer published the CADE-25 proceedings containing the Lean system description, documenting the architecture, goals and use of the prover in formal mathematics.", "zh-CN": "Springer 出版收录 Lean 系统论文的 CADE-25 proceedings，记录其架构、目标及在形式数学中的使用。" } }, { "date": "2015-08-07", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The official CADE presentation, official project history and preserved open-source Lean 3 repository make the early system lineage and implementation directly inspectable. The exact June 2014 Lean 0.1 release day is not inferred from month-only historical metadata.", "zh-CN": "CADE 官方展示、项目官方历史与保留的开源 Lean 3 仓库使早期系统谱系与实现可直接检查；本记录不根据只有月份精度的历史元数据推断 2014 年 6 月 Lean 0.1 的具体发布日期。" } } ] }, "sources": [ { "id": "cade-lean-system-2015", "tier": "S1", "type": "paper", "title": "The Lean Theorem Prover (System Description)", "url": "https://doi.org/10.1007/978-3-319-21401-6_26", "primary": true, "published_date": "2015-07-30", "accessed_at": "2026-09-15" }, { "id": "lean-cade-presentation-2015", "tier": "S2", "type": "official_announcement", "title": "The Lean Theorem Prover — CADE 2015 presentation", "url": "https://lean-lang.org/presentations/20150807_CADE", "primary": true, "published_date": "2015-08-07", "accessed_at": "2026-09-15" }, { "id": "lean-official-history", "tier": "S2", "type": "official_announcement", "title": "A Brief History of Lean", "url": "https://lean-lang.org/fro/about/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "lean3-repository", "tier": "S1", "type": "repository", "title": "Lean 3 theorem prover repository", "url": "https://github.com/leanprover/lean3", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "lean3-source", "kind": "code", "title": "Lean 3 theorem prover source repository", "url": "https://github.com/leanprover/lean3" } ], "relationships": { "predecessors": [], "successors": [ "evt-2017-mathlib3" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "lean", "proof-assistant", "dependent-types", "automated-theorem-proving", "formalization" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2014-flyspeck-completion", "slug": "flyspeck-kepler-completion", "title": { "en": "Flyspeck completes a formal proof of the Kepler conjecture", "zh-CN": "Flyspeck 完成克卜勒猜想形式证明" }, "dates": { "event": "2014-08-10", "first_public_claim": "2014-08-10", "paper_release": "2015-01-09", "artifact_release": "2014-08-10", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "Completion of Flyspeck demonstrated that an exceptionally large research proof combining hundreds of pages of mathematics and extensive computation could be reconstructed as a proof-assistant-checked formal development.", "zh-CN": "Flyspeck 的完成展示了：一个结合数百页数学文本与大量计算的超大型研究证明，可以被重构为由证明助手完整检查的形式工程。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The Flyspeck project records 10 August 2014 as its completion date after constructing a formal proof of the Kepler conjecture using HOL Light and Isabelle; the official paper was released on 9 January 2015.", "zh-CN": "Flyspeck 项目将 2014 年 8 月 10 日记录为完成日期；项目使用 HOL Light 与 Isabelle 构建克卜勒猜想形式证明，官方论文于 2015 年 1 月 9 日发布。" }, "summary": { "en": "The completed development formalized both the mathematical text and the large computational components needed for the Kepler-conjecture proof.", "zh-CN": "完成后的工程同时形式化克卜勒猜想证明的数学文本与大型计算部分。" }, "why_it_matters": { "en": "Flyspeck became a benchmark for the scale, collaboration and engineering required to make complex research mathematics fully machine-checkable.", "zh-CN": "Flyspeck 成为衡量复杂研究数学实现全面机器可检查所需规模、协作与工程能力的重要参照。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Human formalizers constructed the development while HOL Light and Isabelle executed trusted proof checking and verified computations.", "zh-CN": "人类形式化者构建工程，HOL Light 与 Isabelle 执行可信证明检查与验证计算。" } }, "human_contribution": { "description": { "en": "Thomas Hales and a large international team formalized the proof, mathematical libraries and computational verification components over more than a decade.", "zh-CN": "Thomas Hales 与大型国际团队历时十余年形式化证明、数学库及计算验证组件。" } }, "systems": [ "flyspeck", "hol-light", "isabelle" ], "organizations": [], "people": [ "thomas-hales" ], "problems": [ "kepler-conjecture" ], "methods": [ "formalization", "proof-checking", "verified-computation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2014-08-10", "status": "claimed", "evidence_level": "E3", "note": { "en": "The public Flyspeck repository records the project completion date and exposes the formal development.", "zh-CN": "Flyspeck 公开仓库记录项目完成日期并提供形式化工程。" } }, { "date": "2015-01-09", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The official research paper documents the completed formal proof. E3 reflects inspectable artifacts and does not mean Chronicle independently replayed the entire development.", "zh-CN": "官方研究论文记录完成后的形式证明。E3 表示存在可检查 artifacts，并不意味着 Chronicle 独立重放整个工程。" } } ] }, "sources": [ { "id": "github-flyspeck-completion", "tier": "S1", "type": "repository", "title": "The Flyspeck Project repository", "url": "https://github.com/flyspeck/flyspeck", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "arxiv-flyspeck-1501.02155", "tier": "S1", "type": "paper", "title": "A formal proof of the Kepler conjecture", "url": "https://arxiv.org/abs/1501.02155", "primary": true, "published_date": "2015-01-09", "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "flyspeck-formal-development", "kind": "proof", "title": "Flyspeck formal proof repository", "url": "https://github.com/flyspeck/flyspeck" } ], "relationships": { "predecessors": [ "evt-2003-flyspeck-launch" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "flyspeck", "kepler-conjecture", "formalization", "machine-checked-proof" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2013-mizar40", "slug": "mizar40-ai-atp", "title": { "en": "MizAR 40 scales AI/ATP methods across the full Mizar Mathematical Library", "zh-CN": "MizAR 40 将 AI/ATP 方法扩展到完整 Mizar Mathematical Library" }, "dates": { "event": "2013-10-10", "first_public_claim": "2013-10-10", "paper_release": "2013-10-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "benchmark" ], "significance": { "tier": "H2", "rationale": { "en": "MizAR 40 demonstrated that a suite of learned premise-selection and ATP methods could operate at the scale of the entire Mizar Mathematical Library, turning large formal mathematics into an online AI-assisted reasoning service and corpus-wide evaluation surface.", "zh-CN": "MizAR 40 展示多种学习式前提选择与 ATP 方法能够在完整 Mizar Mathematical Library 规模上运行，把大型形式数学转化为在线 AI 辅助推理服务与全库评测面。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The 10 October 2013 paper reported an AI/ATP system that automatically proved 40% of the theorems in the then-current Mizar Mathematical Library within 30 seconds on a 14-CPU machine.", "zh-CN": "2013 年 10 月 10 日论文报告一个 AI/ATP 系统，在 14 CPU 机器上以 30 秒限制自动证明当时 Mizar Mathematical Library 中 40% 的定理。" }, "summary": { "en": "The system scaled fast learned relevance methods over roughly 150,000 MML formulas and deployed them within the MizAR online reasoning service.", "zh-CN": "系统把快速学习式相关性方法扩展到约 15 万条 MML 公式，并部署到 MizAR 在线推理服务。" }, "why_it_matters": { "en": "The work made corpus-scale formal mathematics a practical target for integrated machine learning and automated reasoning rather than a small benchmark exercise.", "zh-CN": "该工作使全库规模的形式数学成为机器学习与自动推理集成的实际目标，而不再只是小型 benchmark 实验。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Learned relevance methods selected useful formulas and ATP systems attempted proofs across the library at scale.", "zh-CN": "学习式相关性方法选择有用公式，ATP 系统在全库规模上自动尝试证明。" } }, "human_contribution": { "description": { "en": "Researchers engineered and optimized the learning methods, ATP portfolio, Mizar translations and online service.", "zh-CN": "研究者设计并优化学习方法、ATP 组合、Mizar 翻译与在线服务。" } }, "systems": [ "mizar", "mizar40", "mizar-online-reasoning" ], "organizations": [ "university-of-innsbruck" ], "people": [ "cezary-kaliszyk", "josef-urban" ], "problems": [ "large-theory-theorem-proving" ], "methods": [ "machine-learning", "premise-selection", "automated-theorem-proving", "large-theory-reasoning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2013-10-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv paper establishes the system and reports the corpus-scale evaluation; Chronicle does not treat the percentage as independently reproduced.", "zh-CN": "arXiv 论文确认系统并报告全库评测；Chronicle 不把该百分比视为独立复现结果。" } } ] }, "sources": [ { "id": "arxiv-mizar40-1310.2805", "tier": "S1", "type": "paper", "title": "MizAR 40 for Mizar 40", "url": "https://arxiv.org/abs/1310.2805", "primary": true, "published_date": "2013-10-10", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mizar", "mizar40", "machine-learning", "automated-theorem-proving", "large-theory-reasoning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2013-holyhammer", "slug": "holyhammer-hol-light-ai-atp", "title": { "en": "HOL(y)Hammer combines learned premise selection with ATPs for HOL Light", "zh-CN": "HOL(y)Hammer 将学习式前提选择与 ATP 接入 HOL Light" }, "dates": { "event": "2013-09-19", "first_public_claim": "2013-09-19", "paper_release": "2013-09-19", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "HOL(y)Hammer deployed machine-learned premise selection and multiple automated reasoning systems as an online service for large HOL Light developments, bringing large-theory AI/ATP methods into routine formal mathematics workflows.", "zh-CN": "HOL(y)Hammer 将机器学习前提选择与多个自动推理系统部署为面向大型 HOL Light 工程的在线服务，使 large-theory AI/ATP 方法进入日常形式数学流程。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Kaliszyk and Urban released HOL(y)Hammer as an online AI/ATP service on 19 September 2013, combining several premise-selection methods trained on project proofs with multiple automated theorem provers.", "zh-CN": "Kaliszyk 与 Urban 于 2013 年 9 月 19 日发布 HOL(y)Hammer，将基于项目证明训练的多种前提选择方法与多个自动定理证明器结合为在线 AI/ATP 服务。" }, "summary": { "en": "Users could upload HOL Light developments and ask the service to attack new conjectures using learned relevance models, parallel ATP combinations and decision procedures.", "zh-CN": "用户可以上传 HOL Light 工程，并让服务使用学习式相关性模型、并行 ATP 组合与决策过程处理新猜想。" }, "why_it_matters": { "en": "It provided an early mature example of machine learning embedded in a proof-assistant service over substantial formal mathematical libraries.", "zh-CN": "它较早展示了机器学习如何作为成熟服务嵌入证明助手，并在大规模形式数学库上工作。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Learned models selected premises and automated provers searched for proofs, while users supplied target conjectures inside HOL Light projects.", "zh-CN": "学习模型选择前提，自动证明器搜索证明，用户在 HOL Light 工程中提供目标猜想。" } }, "human_contribution": { "description": { "en": "Researchers engineered the service, learning methods, ATP portfolio, project processing and interfaces.", "zh-CN": "研究者工程化实现服务、学习方法、ATP 组合、项目处理与交互接口。" } }, "systems": [ "holyhammer", "hol-light" ], "organizations": [ "university-of-innsbruck" ], "people": [ "cezary-kaliszyk", "josef-urban" ], "problems": [ "higher-order-logic-theorem-proving" ], "methods": [ "machine-learning", "premise-selection", "automated-theorem-proving", "portfolio-reasoning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2013-09-19", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The arXiv research record establishes the service architecture and reported HOL Light deployment.", "zh-CN": "arXiv 研究记录确认服务架构及论文报告的 HOL Light 部署。" } } ] }, "sources": [ { "id": "arxiv-holyhammer-1309.4962", "tier": "S1", "type": "paper", "title": "HOL(y)Hammer: Online ATP Service for HOL Light", "url": "https://arxiv.org/abs/1309.4962", "primary": true, "published_date": "2013-09-19", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "holyhammer", "hol-light", "premise-selection", "machine-learning", "automated-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2013-odd-order-coq", "slug": "odd-order-theorem-coq", "title": { "en": "Coq completes a machine-checked formal proof of the Odd Order Theorem", "zh-CN": "Coq 完成奇数阶定理的机器检查形式证明" }, "dates": { "event": "2013-07-22", "first_public_claim": "2013-07-22", "paper_release": "2013-07-22", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "The six-year Coq formalization of the Feit–Thompson Odd Order Theorem demonstrated that proof assistants could sustain a deep research-level argument while simultaneously building reusable libraries across finite group theory, algebra and number systems.", "zh-CN": "历时六年的 Feit–Thompson 奇数阶定理 Coq 形式化展示了证明助手能够承载深层研究级数学论证，并同时建设有限群论、代数和数系等可复用形式库。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The ITP 2013 paper reports a complete constructive formalization of the Feit–Thompson Odd Order Theorem in Coq, relying only on the axioms and rules of Coq's foundational framework.", "zh-CN": "ITP 2013 论文报告在 Coq 中完成 Feit–Thompson 奇数阶定理的完整构造性形式化，其证明只依赖 Coq 基础框架中的公理与规则。" }, "summary": { "en": "The project formalized the theorem together with a substantial mathematical library spanning group theory, linear algebra, Galois theory and real/complex algebraic numbers.", "zh-CN": "项目在形式化定理本身的同时，建立了覆盖群论、线性代数、Galois 理论及实/复代数数的大规模数学库。" }, "why_it_matters": { "en": "It raised the demonstrated scale and depth of machine-checked research mathematics and strengthened the library infrastructure later available to automation and AI systems.", "zh-CN": "它显著提高机器检查研究数学所展示的规模与深度，并强化了后来可供自动化与 AI 系统使用的形式库基础设施。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Human authors constructed the formal proof while Coq checked every formal inference under its foundational rules.", "zh-CN": "人类作者构造形式证明，Coq 按其基础规则检查每一步形式推理。" } }, "human_contribution": { "description": { "en": "The collaboration formalized the mathematics, engineered reusable libraries and developed proof methodology and tooling needed for the large project.", "zh-CN": "协作团队形式化数学内容、建设可复用形式库，并开发大型工程所需的证明方法与工具。" } }, "systems": [ "coq" ], "organizations": [ "microsoft-research", "inria" ], "people": [ "georges-gonthier", "jeremy-avigad" ], "problems": [ "odd-order-theorem" ], "methods": [ "formalization", "proof-checking", "mathematical-library" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2013-07-22", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The peer-reviewed ITP paper documents the complete Coq formalization; machine checking reflects Coq verification and does not mean Chronicle independently replayed the full development.", "zh-CN": "ITP 同行评议论文记录了完整 Coq 形式化；machine_checked 表示由 Coq 完成验证，并不表示 Chronicle 独立重放全部工程。" } } ] }, "sources": [ { "id": "itp-odd-order-2013", "tier": "S1", "type": "paper", "title": "A Machine-Checked Proof of the Odd Order Theorem", "url": "https://doi.org/10.1007/978-3-642-39634-2_14", "primary": true, "published_date": "2013-07-22", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "odd-order-theorem", "coq", "formalization", "machine-checked-proof" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2010-sledgehammer", "slug": "sledgehammer-isabelle-atp", "title": { "en": "Sledgehammer makes external automated provers practical inside Isabelle", "zh-CN": "Sledgehammer 将外部自动证明器实用化地接入 Isabelle" }, "dates": { "event": "2010-07-14", "first_public_claim": null, "paper_release": "2010-07-14", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Sledgehammer established a practical architecture for combining an interactive proof assistant with powerful external ATP systems, automatically selecting relevant facts and turning external search into proof-assistant-native progress.", "zh-CN": "Sledgehammer 建立了交互式证明助手与强大外部 ATP 的实用结合架构，自动选择相关事实，并把外部搜索转化为证明助手内部可用的证明进展。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "At PAAR-2010 on 14 July 2010, Lawrence Paulson and Jasmin Blanchette presented three years of experience with Sledgehammer as a practical link between Isabelle and automatic theorem provers.", "zh-CN": "Lawrence Paulson 与 Jasmin Blanchette 在 2010 年 7 月 14 日 PAAR-2010 报告三年 Sledgehammer 使用经验，将其定位为 Isabelle 与自动定理证明器之间的实用桥梁。" }, "summary": { "en": "Sledgehammer selects relevant Isabelle facts, translates proof obligations to external ATPs and uses the returned information to help construct proof-assistant-checked proofs.", "zh-CN": "Sledgehammer 自动选择 Isabelle 相关事实，将证明义务翻译给外部 ATP，并利用返回结果帮助构造由证明助手检查的证明。" }, "why_it_matters": { "en": "The system made strong automation accessible in routine interactive proving and became an important precedent for later AI assistants that orchestrate external search while retaining trusted proof checking.", "zh-CN": "该系统让强自动化进入日常交互式证明流程，并成为后来“外部搜索 + 可信证明检查”AI 助手的重要前史。" }, "ai_role": { "level": "ai_substantive_support", "description": { "en": "Automated premise selection and external provers supplied substantial proof search, while Isabelle retained the trusted formal proof environment.", "zh-CN": "自动前提选择与外部证明器承担大量证明搜索，Isabelle 保留可信形式证明环境。" } }, "human_contribution": { "description": { "en": "Researchers designed the translation, relevance filtering, prover orchestration and proof reconstruction mechanisms; users supplied formal goals and integrated resulting proof steps.", "zh-CN": "研究者设计翻译、相关性筛选、证明器编排与证明重建机制；用户提供形式目标并整合所得证明步骤。" } }, "systems": [ "sledgehammer", "isabelle" ], "organizations": [ "university-of-cambridge" ], "people": [ "lawrence-paulson", "jasmin-blanchette" ], "problems": [ "interactive-theorem-proving" ], "methods": [ "premise-selection", "automated-theorem-proving", "proof-reconstruction" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2010-07-14", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The PAAR-2010 program and proceedings document Sledgehammer's practical Isabelle/ATP workflow; machine checking refers to proof-assistant validation of reconstructed formal proofs, not independent reproduction of reported usage results.", "zh-CN": "PAAR-2010 议程与 proceedings 记录了 Sledgehammer 的 Isabelle/ATP 工作流；machine_checked 指重建形式证明由证明助手验证，并不表示 Chronicle 独立复现使用结果。" } } ] }, "sources": [ { "id": "paar-sledgehammer-2010", "tier": "S1", "type": "paper", "title": "Three Years of Experience with Sledgehammer, a Practical Link between Automatic and Interactive Theorem Provers", "url": "https://www.eprover.org/EVENTS/PAAR-2010/paar-2010.html", "primary": true, "published_date": "2010-07-14", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "sledgehammer", "isabelle", "automated-theorem-proving", "interactive-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2007-mptp-challenge", "slug": "mptp-large-theory-challenge", "title": { "en": "The MPTP Challenge benchmarks AI-assisted automated reasoning in large mathematical theories", "zh-CN": "MPTP Challenge 对大型数学理论中的 AI 辅助自动推理进行统一评测" }, "dates": { "event": "2007-07-16", "first_public_claim": null, "paper_release": null, "artifact_release": "2007-07-16", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "competition", "benchmark", "dataset" ], "significance": { "tier": "H2", "rationale": { "en": "The MPTP Challenge created a large-theory competition setting where systems could exploit complementary AI methods, including learning from previous solutions, over a shared corpus derived from formal mathematics.", "zh-CN": "MPTP Challenge 建立大型理论竞赛环境，允许系统在共享形式数学语料上使用包括“从此前解答学习”在内的互补 AI 方法。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The official MPTP Challenge page records accumulated results on 16 July 2007 for 252 large-theory problems, under rules that explicitly allowed systems to retune and learn during execution.", "zh-CN": "MPTP Challenge 官方页面记录了 2007 年 7 月 16 日对 252 个大型理论问题的累计结果，其规则明确允许系统在执行过程中重新调节并学习。" }, "summary": { "en": "The challenge supplied common Mizar-derived problems, public rules and a total resource budget intended to make learning, premise selection and other large-theory reasoning strategies directly comparable.", "zh-CN": "竞赛提供统一的 Mizar 衍生问题、公开规则与总资源预算，使学习、前提选择和其他大型理论推理策略能够直接比较。" }, "why_it_matters": { "en": "It helped establish large-theory theorem proving as a benchmarked AI problem rather than only a collection of isolated prover demonstrations.", "zh-CN": "它推动大型理论定理证明从零散证明器展示转向可统一 benchmark 的 AI 研究问题。" }, "ai_role": { "level": "computation_only", "description": { "en": "Automated reasoning systems solved formal problems and could use machine learning from prior solutions; the Event's historical contribution is the evaluation setting.", "zh-CN": "自动推理系统求解形式问题，并可从此前解答进行机器学习；该事件的历史贡献主要在统一评测环境。" } }, "human_contribution": { "description": { "en": "Josef Urban and Geoff Sutcliffe organized the challenge, problem corpus, rules and result collection.", "zh-CN": "Josef Urban 与 Geoff Sutcliffe 组织竞赛、问题语料、规则与结果收集。" } }, "systems": [ "mptp" ], "organizations": [], "people": [ "josef-urban", "geoff-sutcliffe" ], "problems": [ "large-theory-theorem-proving" ], "methods": [ "benchmarking", "premise-selection", "machine-learning", "automated-theorem-proving" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "2007-07-16", "status": "claimed", "evidence_level": "E3", "note": { "en": "The official challenge page preserves the rules, problem setup and accumulated results, making the benchmark artifact directly inspectable.", "zh-CN": "官方 Challenge 页面保留规则、问题设置与累计结果，使 benchmark artifact 可直接检查。" } } ] }, "sources": [ { "id": "mptp-challenge-official", "tier": "S1", "type": "benchmark", "title": "The MPTP Challenges", "url": "https://tptp.org/Challenges/MPTPChallenge/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "mptp-challenge-benchmark", "kind": "benchmark", "title": "MPTP Challenge problems and results", "url": "https://tptp.org/Challenges/MPTPChallenge/" } ], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2007-malarea" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mptp", "competition", "benchmark", "large-theory-reasoning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2007-malarea", "slug": "malarea-learning-reasoning-loop", "title": { "en": "MaLARea closes a machine-learning and theorem-proving feedback loop over large theories", "zh-CN": "MaLARea 在大型理论上建立机器学习与定理证明反馈循环" }, "dates": { "event": "2007-06-27", "first_public_claim": "2007-06-27", "paper_release": "2007-06-27", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "MaLARea made large-theory reasoning explicitly iterative: machine learning selects useful knowledge, ATP systems attempt proofs, and successful results are fed back into the learner for subsequent problems.", "zh-CN": "MaLARea 将大型理论推理明确组织为迭代循环：机器学习选择有用知识，ATP 尝试证明，成功结果再反馈给学习器用于后续问题。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Josef Urban's MaLARea paper was published with the ESARLT 2007 workshop proceedings on 27 June 2007 and described a metasystem combining machine learning, automated theorem proving and model finding for large theories.", "zh-CN": "Josef Urban 的 MaLARea 论文于 2007 年 6 月 27 日随 ESARLT 2007 proceedings 发布，描述一个结合机器学习、自动定理证明与模型查找的大型理论元系统。" }, "summary": { "en": "The system repeatedly trains relevance models from existing proofs, invokes automated provers on selected premises and incorporates newly found proofs into subsequent learning rounds.", "zh-CN": "系统反复从已有证明训练相关性模型，在筛选前提上调用自动证明器，并把新找到的证明纳入后续学习轮次。" }, "why_it_matters": { "en": "The deduction–learning feedback loop became a core pattern for later self-improving theorem-proving systems and anticipated modern search-and-learning agents for formal mathematics.", "zh-CN": "“演绎—学习”反馈循环后来成为自我改进式定理证明系统的核心范式，并预示现代形式数学中的 search-and-learning agents。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "Learned premise-selection models and automated provers interacted in an autonomous loop that improved from previous proof results.", "zh-CN": "学习式前提选择模型与自动证明器在自主循环中协作，并从此前证明结果持续改进。" } }, "human_contribution": { "description": { "en": "Josef Urban designed the metasystem, learning/reasoning loop, data interfaces and experiments.", "zh-CN": "Josef Urban 设计元系统、学习/推理循环、数据接口与实验。" } }, "systems": [ "malarea" ], "organizations": [ "charles-university" ], "people": [ "josef-urban" ], "problems": [ "large-theory-theorem-proving" ], "methods": [ "machine-learning", "premise-selection", "automated-theorem-proving", "model-finding", "feedback-loop" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2007-06-27", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The CEUR proceedings establish the MaLARea system and its learning/reasoning architecture.", "zh-CN": "CEUR proceedings 确认 MaLARea 系统及其学习/推理架构。" } } ] }, "sources": [ { "id": "ceur-malarea-2007", "tier": "S1", "type": "paper", "title": "MaLARea: a Metasystem for Automated Reasoning in Large Theories", "url": "https://ceur-ws.org/Vol-257/05_Urban.pdf", "primary": true, "published_date": "2007-06-27", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-2007-mptp-challenge" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "malarea", "machine-learning", "theorem-proving", "large-theory-reasoning" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2005-four-colour-coq", "slug": "four-colour-theorem-coq", "title": { "en": "Coq fully checks a formal proof of the Four Colour Theorem", "zh-CN": "Coq 完整检查四色定理形式证明" }, "dates": { "event": "2005-04-21", "first_public_claim": "2005-04-21", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "proof" ], "significance": { "tier": "H2", "rationale": { "en": "Gonthier's Coq development showed that a celebrated theorem whose earlier proof depended on extensive custom computation could be recast as a fully machine-checked formal proof covering both mathematical and computational reasoning.", "zh-CN": "Gonthier 的 Coq 工程展示了：一个此前高度依赖定制计算的著名定理，可以被重构为同时覆盖数学论证与计算部分的完整机器检查形式证明。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "By 21 April 2005, Georges Gonthier's report “A computer-checked proof of the Four Colour Theorem” was publicly circulating and described a successful formalization fully checked by Coq v7.3.1.", "zh-CN": "至 2005 年 4 月 21 日，Georges Gonthier 的“A computer-checked proof of the Four Colour Theorem”报告已公开传播，其中描述了由 Coq v7.3.1 完整检查的成功形式化证明。" }, "summary": { "en": "The formal development encoded the combinatorial argument and computational case checking inside Coq so that correctness reduced to the proof assistant's general verification mechanisms rather than theorem-specific external programs.", "zh-CN": "该形式化把组合论证与计算机分类检查都纳入 Coq，使正确性依赖通用证明助手验证机制，而非四色定理专用外部程序。" }, "why_it_matters": { "en": "It became a landmark demonstration that large computer-assisted proofs could be transformed into auditable machine-checked mathematics.", "zh-CN": "它成为大型计算机辅助证明可以转化为可审计机器检查数学的标志性示范。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Humans engineered the formal proof while Coq executed and checked all formal logical and computational steps.", "zh-CN": "人类设计形式证明工程，Coq 执行并检查全部形式逻辑与计算步骤。" } }, "human_contribution": { "description": { "en": "Georges Gonthier designed and implemented the formalization, proof scripts, tactics and mathematical encodings.", "zh-CN": "Georges Gonthier 设计并实现形式化、证明脚本、tactics 与数学编码。" } }, "systems": [ "coq" ], "organizations": [ "microsoft-research" ], "people": [ "georges-gonthier" ], "problems": [ "four-colour-theorem" ], "methods": [ "formalization", "proof-checking", "verified-computation" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "2005-04-21", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The primary report states that the proof was fully checked by Coq; the dated independent announcement establishes that the report was publicly available by 21 April 2005.", "zh-CN": "原始报告明确说明证明由 Coq 完整检查；带日期的独立公开记录确认该报告至迟于 2005 年 4 月 21 日已经公开。" } } ] }, "sources": [ { "id": "gonthier-four-colour-report", "tier": "S1", "type": "paper", "title": "A computer-checked proof of the Four Colour Theorem", "url": "https://www.cl.cam.ac.uk/~lp15/Pages/4colproof.pdf", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "zach-four-colour-coq-2005", "tier": "S3", "type": "community", "title": "Four Color Theorem Verified in Coq", "url": "https://richardzach.org/2005/04/four-color-theorem-verified-in-coq/", "primary": false, "published_date": "2005-04-21", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "four-colour-theorem", "coq", "formalization", "machine-checked-proof" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-2003-flyspeck-launch", "slug": "flyspeck-project-launch", "title": { "en": "Flyspeck launches a long-term formal proof of the Kepler conjecture", "zh-CN": "Flyspeck 启动克卜勒猜想长期形式化证明工程" }, "dates": { "event": "2003-01-15", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Flyspeck turned the verification of a major, computer-intensive mathematical proof into a long-running collaborative formalization project spanning proof text, computation and reusable proof-assistant infrastructure.", "zh-CN": "Flyspeck 将一个重要且高度依赖计算的数学证明验证问题转化为长期协作形式化工程，同时覆盖数学文本、计算过程与可复用证明助手基础设施。" } }, "mathematical_novelty": { "type": "formalization_of_known_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Thomas Hales announced the Flyspeck project at the January 15–18, 2003 Joint Mathematics Meetings in Baltimore with the goal of producing a fully formal proof of the Kepler conjecture; because the exact announcement day is not preserved in the cited record, the canonical date uses the meeting opening day.", "zh-CN": "Thomas Hales 在 2003 年 1 月 15–18 日巴尔的摩 Joint Mathematics Meetings 上宣布 Flyspeck，目标是给出克卜勒猜想的完整形式证明；由于所引史料未保留具体宣布日，本条以会议开幕日作为 canonical 日期锚点。" }, "summary": { "en": "The project aimed to formalize both the written mathematical argument and the computer calculations underlying Hales's proof, eventually using HOL Light and Isabelle.", "zh-CN": "项目计划同时形式化 Hales 证明中的书面数学论证与计算机计算部分，最终主要使用 HOL Light 与 Isabelle 完成。" }, "why_it_matters": { "en": "Flyspeck became a defining large-scale demonstration that proof assistants could audit extremely complex research mathematics end to end.", "zh-CN": "Flyspeck 后来成为大型证明助手工程的代表案例，展示形式系统能够端到端审计极其复杂的研究数学。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Humans led the formalization while proof assistants executed trusted inference, proof checking and large verified computations.", "zh-CN": "人类主导形式化，证明助手执行可信推理、证明检查与大规模验证计算。" } }, "human_contribution": { "description": { "en": "Hales and an international collaboration organized the formalization, decomposed the original proof and implemented the formal libraries and verification pipeline.", "zh-CN": "Hales 与国际协作团队组织形式化、拆解原始证明，并实现形式库与验证流程。" } }, "systems": [ "flyspeck", "hol-light", "isabelle" ], "organizations": [], "people": [ "thomas-hales" ], "problems": [ "kepler-conjecture" ], "methods": [ "formalization", "proof-checking", "verified-computation" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "2003-01-15", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official published Flyspeck account states that Hales announced the project at the January 2003 Joint Mathematics Meetings; the AMS archive fixes the meeting to January 15–18.", "zh-CN": "Flyspeck 官方发表记录说明 Hales 在 2003 年 1 月 Joint Mathematics Meetings 宣布该项目；AMS 档案确认会议日期为 1 月 15–18 日。" } } ] }, "sources": [ { "id": "flyspeck-official-account-2017", "tier": "S1", "type": "paper", "title": "A formal proof of the Kepler conjecture", "url": "https://arxiv.org/abs/1501.02155", "primary": true, "published_date": "2015-01-09", "accessed_at": "2026-09-15" }, { "id": "ams-jmm-baltimore-2003", "tier": "S2", "type": "official_announcement", "title": "Joint Mathematics Meetings Baltimore 2003 program", "url": "https://jointmathematicsmeetings.org/meetings/national/jmm-archive/2074_program_saturday.html", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-2014-flyspeck-completion" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "flyspeck", "kepler-conjecture", "formalization", "proof-assistant" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1998-hr", "slug": "hr-automated-theory-formation", "title": { "en": "HR automates mathematical concept formation and theory exploration", "zh-CN": "HR 自动化数学概念形成与理论探索" }, "dates": { "event": "1998-07-26", "first_public_claim": "1998-07-26", "paper_release": "1998-07-26", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H2", "rationale": { "en": "HR extended automated mathematical discovery from heuristic conjecturing toward a broader theory-formation loop that invents concepts, calculates examples, formulates conjectures and later integrates theorem proving and model finding.", "zh-CN": "HR 将自动数学发现从启发式猜想生成进一步推进为更完整的 theory-formation 循环，包括创造概念、计算例子、形成猜想，并在后续系统中结合定理证明与模型查找。" } }, "mathematical_novelty": { "type": "new_conjecture" }, "interfaces": [ "symbolic" ], "claim": { "en": "Simon Colton presented HR at AAAI/IAAI 1998 as a system for automatically producing, assessing and displaying concepts in finite algebras; subsequent HR work expanded the same system into conjecturing and theorem-settling workflows.", "zh-CN": "Simon Colton 在 AAAI/IAAI 1998 展示 HR：系统能够在有限代数中自动产生、评估与展示概念；后续 HR 工作又把同一系统扩展到猜想形成与定理判定流程。" }, "summary": { "en": "HR searches a space of mathematical concepts, evaluates their interest and uses generated concepts to drive further examples, classifications and conjectures.", "zh-CN": "HR 搜索数学概念空间、评估概念的有趣程度，并利用生成概念继续驱动例子、分类与猜想探索。" }, "why_it_matters": { "en": "HR is a direct historical precursor to contemporary AI systems aimed at open-ended mathematical discovery rather than only proving supplied statements.", "zh-CN": "HR 是当代开放式 AI 数学发现系统的直接历史前序之一，其目标并非只证明给定命题，而是参与形成数学理论本身。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The system autonomously generated and assessed mathematical concepts and used them to structure subsequent theory exploration.", "zh-CN": "系统自主生成并评估数学概念，并利用这些概念组织后续理论探索。" } }, "human_contribution": { "description": { "en": "Simon Colton and collaborators designed the production rules, interestingness measures, domain representations and later theorem-proving integrations.", "zh-CN": "Simon Colton 与合作者设计概念生成规则、有趣度指标、领域表示及后续定理证明集成。" } }, "systems": [ "hr" ], "organizations": [ "university-of-edinburgh" ], "people": [ "simon-colton" ], "problems": [ "automated-mathematical-discovery" ], "methods": [ "concept-formation", "automated-theory-formation", "conjecture-generation" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1998-07-26", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The AAAI/IAAI 1998 proceedings establish the early HR concept-formation system; later publications document its broader automated theory-formation capabilities.", "zh-CN": "AAAI/IAAI 1998 proceedings 确认早期 HR 概念形成系统；后续论文记录其更完整的自动理论形成能力。" } } ] }, "sources": [ { "id": "aaai-hr-1998", "tier": "S1", "type": "paper", "title": "HR - Automatic Concept Formation in Finite Algebras", "url": "https://auld.aaai.org/Library/AAAI/aaai98contents.php", "primary": true, "published_date": "1998-07-26", "accessed_at": "2026-09-15" }, { "id": "liep-hr-theory-formation-2000", "tier": "S1", "type": "paper", "title": "Automated Theory Formation Applied to Four Learning Tasks", "url": "https://www.ida.liu.se/ext/epa/cis/2000/038/cover.bak", "primary": true, "published_date": "2000-12-30", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "hr", "mathematical-discovery", "concept-formation", "automated-theory-formation" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1996-robbins-eqp", "slug": "robbins-conjecture-eqp", "title": { "en": "EQP finds a proof resolving the Robbins conjecture", "zh-CN": "EQP 找到解决 Robbins 猜想的证明" }, "dates": { "event": "1996-10-10", "first_public_claim": "1996-10-10", "paper_release": null, "artifact_release": "1996-10-10", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "discovery", "system" ], "significance": { "tier": "H2", "rationale": { "en": "EQP's Robbins-algebra proof is a landmark case in which an automated theorem prover produced the key proof of a long-standing open algebraic question, demonstrating ATP as a tool for new mathematical results rather than only benchmark reproving.", "zh-CN": "EQP 对 Robbins algebra 的证明是自动定理证明器解决长期开放代数问题的标志性案例，展示 ATP 不仅可以重新证明已知命题，也能参与获得新的数学结果。" } }, "mathematical_novelty": { "type": "new_proof" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "On 10 October 1996, William McCune's EQP found a proof showing that Robbins algebras are Boolean; the proof was subsequently checked with the Otter theorem prover and studied by mathematicians.", "zh-CN": "1996 年 10 月 10 日，William McCune 的 EQP 找到证明 Robbins algebra 为 Boolean algebra 的证明；随后该证明由 Otter 定理证明器检查并由数学家研究。" }, "summary": { "en": "The automated search produced a compact equational derivation in a problem that had resisted prior human and machine efforts for decades.", "zh-CN": "自动搜索在一个数十年未解决、长期接受人类与机器尝试的问题上产生了紧凑的等式推导。" }, "why_it_matters": { "en": "The event supplied early evidence that automated theorem proving could contribute directly to unresolved mathematics, a central ambition of modern AI4Math.", "zh-CN": "该事件较早证明自动定理证明能够直接参与未解决数学问题，这也是现代 AI4Math 的核心目标之一。" }, "ai_role": { "level": "ai_primary_human_verified", "description": { "en": "EQP autonomously searched for and found the formal proof; separate automated checking and human mathematical inspection followed.", "zh-CN": "EQP 自主搜索并找到形式证明；之后进行了独立的自动检查与人类数学审阅。" } }, "human_contribution": { "description": { "en": "William McCune developed the prover and search setup; mathematicians contextualized, simplified and communicated the machine-found proof.", "zh-CN": "William McCune 开发证明器与搜索设置；数学家对机器找到的证明进行解释、化简与传播。" } }, "systems": [ "eqp", "otter" ], "organizations": [ "argonne-national-laboratory" ], "people": [ "william-mccune" ], "problems": [ "robbins-conjecture" ], "methods": [ "equational-theorem-proving", "automated-proof-search" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "machine_checked", "history": [ { "date": "1996-10-10", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The Argonne technical report records the EQP proof and subsequent Otter verification; machine checking does not convert Chronicle into an independent mathematical-priority arbiter.", "zh-CN": "Argonne 技术报告记录了 EQP 证明及后续 Otter 检查；machine checking 不意味着 Chronicle 自行裁决历史优先权。" } } ] }, "sources": [ { "id": "argonne-robbins-eqp-report", "tier": "S1", "type": "paper", "title": "Solution of the Robbins Problem", "url": "https://ftp.mcs.anl.gov/pub/tech_reports/reports/P642.pdf", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "robbins-eqp-proof-record", "kind": "proof", "title": "EQP Robbins proof record in the Argonne report", "url": "https://ftp.mcs.anl.gov/pub/tech_reports/reports/P642.pdf" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "robbins-conjecture", "eqp", "automated-theorem-proving", "machine-found-proof" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1996-casc", "slug": "cade-atp-system-competition", "title": { "en": "The CADE ATP System Competition institutionalizes head-to-head theorem-prover evaluation", "zh-CN": "CADE ATP System Competition 将定理证明器统一竞赛评测制度化" }, "dates": { "event": "1996-08-01", "first_public_claim": "1996-08-01", "paper_release": null, "artifact_release": "1996-08-01", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "competition", "benchmark", "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The first CADE ATP System Competition created a recurring common evaluation setting for fully automatic theorem provers, reinforcing TPTP-based benchmarking as field infrastructure.", "zh-CN": "首届 CADE ATP System Competition 为全自动定理证明器建立持续性的统一评测环境，并强化以 TPTP 为基础的 benchmark 制度。" } }, "mathematical_novelty": { "type": "benchmark_result" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The CADE competition held on 1 August 1996 compared automated theorem-proving systems under common resource limits and problem sets, inaugurating the competition series later known as CASC.", "zh-CN": "1996 年 8 月 1 日举行的 CADE 竞赛在统一资源限制与问题集下比较自动定理证明系统，并开启后来称为 CASC 的持续竞赛系列。" }, "summary": { "en": "Systems were evaluated in a shared computational environment on standardized theorem-proving problems, making performance comparisons more reproducible and visible.", "zh-CN": "各系统在共享计算环境与标准化定理证明问题上评测，使性能比较更可复现、更透明。" }, "why_it_matters": { "en": "Recurring competitions helped turn automated theorem proving into a benchmark-driven research community with shared evaluation practices.", "zh-CN": "持续竞赛推动自动定理证明形成拥有共同评测实践的 benchmark 驱动研究共同体。" }, "ai_role": { "level": "computation_only", "description": { "en": "Automated theorem provers solved benchmark problems; the Event's primary significance is comparative evaluation and field infrastructure.", "zh-CN": "自动定理证明器求解 benchmark 问题；该事件的主要意义在统一比较评测与领域基础设施。" } }, "human_contribution": { "description": { "en": "Organizers selected problems, defined divisions and resource limits, and ran systems in the common competition environment.", "zh-CN": "组织者选择问题、定义组别与资源限制，并在统一竞赛环境中运行各系统。" } }, "systems": [ "casc" ], "organizations": [ "cade" ], "people": [], "problems": [ "automated-theorem-proving" ], "methods": [ "benchmarking", "system-competition" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "1996-08-01", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official FLoC/CADE competition page records the date, entrants and evaluation setup.", "zh-CN": "FLoC/CADE 官方竞赛页面记录了日期、参赛系统与评测设置。" } } ] }, "sources": [ { "id": "cade-competition-1996", "tier": "S2", "type": "official_announcement", "title": "CADE ATP System Competition", "url": "https://lics.siglog.org/floc96/cade-comp.html", "primary": true, "published_date": "1996-08-01", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "casc", "cade", "competition", "benchmark", "automated-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1994-qed-manifesto", "slug": "qed-manifesto", "title": { "en": "The QED Manifesto articulates a shared vision for a machine-checked mathematical knowledge base", "zh-CN": "QED Manifesto 提出共享机器检查数学知识库愿景" }, "dates": { "event": "1994-05-15", "first_public_claim": "1994-05-15", "paper_release": "1994-05-15", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "The QED Manifesto articulated a collective vision of representing important mathematical knowledge formally and mechanically checking all proofs, making formalized mathematics a community-scale infrastructure goal.", "zh-CN": "QED Manifesto 提出把重要数学知识形式表示并机械检查全部证明的共同愿景，使形式化数学成为共同体规模的基础设施目标。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The manifesto dated 15 May 1994 proposed the QED project: a computer system representing important mathematical knowledge and techniques with strict formal internal representation and mechanical proof checking.", "zh-CN": "1994 年 5 月 15 日的宣言提出 QED Project：建立表示重要数学知识与技术的计算机系统，内部采用严格形式表示并机械检查证明。" }, "summary": { "en": "QED was a field-building vision rather than a single software release, calling for broad cooperation around shared formal mathematical knowledge.", "zh-CN": "QED 是领域建构愿景而非单一软件发布，主张围绕共享形式数学知识开展广泛协作。" }, "why_it_matters": { "en": "The manifesto anticipated later large formal libraries, interoperability ambitions and AI systems trained or evaluated over machine-readable mathematics.", "zh-CN": "该宣言预示了后来的大型形式数学库、互操作愿景以及在机器可读数学上训练和评测的 AI 系统。" }, "ai_role": { "level": "not_applicable", "description": { "en": "The milestone is a community vision and governance document, not an AI system performing mathematics.", "zh-CN": "该节点属于共同体愿景与治理文献，不是 AI 系统执行数学任务。" } }, "human_contribution": { "description": { "en": "The QED community formulated the shared vision for formal mathematical knowledge infrastructure.", "zh-CN": "QED 社群提出共享形式数学知识基础设施的愿景。" } }, "systems": [], "organizations": [], "people": [], "problems": [], "methods": [], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1994-05-15", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The dated manifesto directly records the proposed QED project and its goals.", "zh-CN": "带日期的宣言直接记录了 QED 项目及其目标。" } } ] }, "sources": [ { "id": "qed-manifesto-1994", "tier": "S1", "type": "community", "title": "The QED Manifesto", "url": "https://www.cs.ru.nl/~freek/qed/qed.pdf", "primary": true, "published_date": "1994-05-15", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "qed-manifesto", "field-building", "formal-mathematics", "mathematical-knowledge" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1993-tptp", "slug": "tptp-problem-library", "title": { "en": "TPTP establishes a shared benchmark library for automated theorem proving", "zh-CN": "TPTP 建立自动定理证明共享基准问题库" }, "dates": { "event": "1993-11-12", "first_public_claim": "1993-11-12", "paper_release": null, "artifact_release": "1993-11-12", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "benchmark", "dataset", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "TPTP standardized a large public problem library for automated theorem proving, enabling repeatable evaluation and meaningful cross-system comparisons over a shared corpus.", "zh-CN": "TPTP 将大型自动定理证明问题库标准化并公开，使可重复评测和跨系统比较建立在共同语料基础上。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The official TPTP history records the first public TPTP v1.0.0 release on Friday 12 November 1993, containing 2,295 problems across 23 domains.", "zh-CN": "TPTP 官方历史记录显示，首个公开版本 v1.0.0 于 1993 年 11 月 12 日星期五发布，包含 23 个领域、2,295 个问题。" }, "summary": { "en": "TPTP collected ATP test problems into standardized formats with domain classification and release/version discipline so theorem provers could be tested on comparable inputs.", "zh-CN": "TPTP 以统一格式整理 ATP 测试问题，并建立领域分类与版本发布规范，使定理证明器能够在可比较输入上进行测试。" }, "why_it_matters": { "en": "The library became core infrastructure for automated deduction and later supported system competitions, benchmarking and learning-guided theorem proving.", "zh-CN": "该问题库成为自动演绎核心基础设施，并进一步支撑系统竞赛、benchmark 与学习式定理证明。" }, "ai_role": { "level": "computation_only", "description": { "en": "AI and ATP systems are evaluated on the library; the milestone itself is benchmark infrastructure rather than an AI-generated mathematical result.", "zh-CN": "AI 与 ATP 系统在该问题库上接受评测；事件本身是 benchmark 基础设施而非 AI 生成数学结果。" } }, "human_contribution": { "description": { "en": "Geoff Sutcliffe, Christian Suttner and contributors curated, normalized and maintained the public problem library.", "zh-CN": "Geoff Sutcliffe、Christian Suttner 与贡献者整理、标准化并维护公共问题库。" } }, "systems": [ "tptp" ], "organizations": [], "people": [ "geoff-sutcliffe", "christian-suttner" ], "problems": [ "automated-theorem-proving" ], "methods": [ "benchmarking", "standardized-problem-formats" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "1993-11-12", "status": "claimed", "evidence_level": "E3", "note": { "en": "The official TPTP history and current library make the release chronology and benchmark artifacts directly inspectable.", "zh-CN": "TPTP 官方历史与当前问题库使发布 chronology 与 benchmark artifacts 可直接检查。" } } ] }, "sources": [ { "id": "tptp-official-history", "tier": "S1", "type": "benchmark", "title": "TPTP History", "url": "https://www.cs.miami.edu/home/geoff/Courses/TPTPSYS/TPTPWorld/TPTPHistory.shtml", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "tptp-problem-library", "kind": "benchmark", "title": "TPTP Problem Library", "url": "https://www.tptp.org/" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "tptp", "benchmark", "dataset", "automated-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1992-metamath", "slug": "metamath-formal-language", "title": { "en": "Metamath establishes a minimal formal language and independently checkable proof corpus", "zh-CN": "Metamath 建立极简形式语言与可独立检查证明语料" }, "dates": { "event": "1992-09-30", "first_public_claim": "1992-09-30", "paper_release": null, "artifact_release": "1992-09-30", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Metamath created a deliberately small formal proof language and verifier whose transparent proof objects later became a valuable substrate for neural theorem-proving systems such as Holophrasm and MetaGen.", "zh-CN": "Metamath 建立刻意极简的形式证明语言与验证器，其透明证明对象后来成为 Holophrasm、MetaGen 等神经定理证明系统的重要基础。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Metamath was developed in 1992; current official proof records retain exact contribution dates including 30 September 1992 for early corpus material, which provides the canonical historical anchor used here.", "zh-CN": "Metamath 于 1992 年开发；当前官方证明记录保留包括 1992 年 9 月 30 日在内的早期语料精确贡献日期，因此本条以该日期作为 canonical 历史锚点。" }, "summary": { "en": "Metamath separates a very small verifier from explicit proof objects, allowing a large body of formal mathematics to be checked with a minimal trusted mechanism.", "zh-CN": "Metamath 将极小验证器与显式证明对象分离，使大型形式数学语料可以由最小可信机制进行检查。" }, "why_it_matters": { "en": "Its transparent proof format and `set.mm` library later made Metamath attractive for machine learning, proof generation and synthetic theorem-data research.", "zh-CN": "其透明证明格式与 `set.mm` 数学库后来非常适合机器学习、证明生成与合成定理数据研究。" }, "ai_role": { "level": "computation_only", "description": { "en": "The verifier mechanically checks formal proof steps; the original formal content is human-authored.", "zh-CN": "验证器机械检查形式证明步骤；原始形式内容主要由人类编写。" } }, "human_contribution": { "description": { "en": "Norman Megill and contributors designed the language, verifier and formal library.", "zh-CN": "Norman Megill 与贡献者设计语言、验证器与形式数学库。" } }, "systems": [ "metamath" ], "organizations": [], "people": [ "norman-megill" ], "problems": [ "formal-mathematical-knowledge" ], "methods": [ "proof-checking", "formal-proof-language", "mathematical-library" ], "verification": { "evidence_level": "E3", "status": "claimed", "formal_assurance": "artifact_available", "history": [ { "date": "1992-09-30", "status": "claimed", "evidence_level": "E3", "note": { "en": "The live Metamath proof corpus is directly inspectable and retains historical contribution metadata for early formal content.", "zh-CN": "当前 Metamath 证明语料可直接检查，并保留早期形式内容的历史贡献元数据。" } } ] }, "sources": [ { "id": "metamath-early-proof-record", "tier": "S1", "type": "formal_artifact", "title": "Metamath Proof Explorer — early proof record", "url": "https://us.metamath.org/mpeuni/id1.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "metamath-proof-explorer", "kind": "proof", "title": "Metamath Proof Explorer", "url": "https://us.metamath.org/mpeuni/mmtheorems.html" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "metamath", "proof-checking", "formal-mathematics", "mathematical-library" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1988-isabelle", "slug": "isabelle-generic-theorem-prover", "title": { "en": "Isabelle develops a generic theorem-proving framework across object logics", "zh-CN": "Isabelle 建立跨对象逻辑的通用定理证明框架" }, "dates": { "event": "1988-05-23", "first_public_claim": null, "paper_release": "1988-05-23", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Isabelle generalized the LCF tradition into a theorem-proving framework supporting multiple object logics and substantial tactic automation, later becoming a major platform for formal mathematics and AI-assisted proving.", "zh-CN": "Isabelle 将 LCF 传统发展为支持多种对象逻辑与丰富 tactic 自动化的通用定理证明框架，后来成为形式数学与 AI 辅助证明的重要平台。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Isabelle was first made publicly available in 1986; Paulson's CADE-9 system abstract on 23 May 1988 provides the precise public research anchor used for this canonical Event date.", "zh-CN": "Isabelle 于 1986 年首次公开；Paulson 在 1988 年 5 月 23 日 CADE-9 的系统摘要为本 canonical Event 提供精确公开研究时间锚点。" }, "summary": { "en": "Isabelle used higher-order unification and a generic meta-level architecture to encode and reason within several object logics, with tactics and tacticals providing automation.", "zh-CN": "Isabelle 利用高阶合一与通用元逻辑架构编码多种对象逻辑，并通过 tactics 与 tacticals 提供自动化。" }, "why_it_matters": { "en": "Isabelle later supported major formal verification projects and created the environment in which Sledgehammer and other ATP/ML integrations matured.", "zh-CN": "Isabelle 后来承载大型形式验证工程，并成为 Sledgehammer 等 ATP/ML 融合系统发展的关键环境。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Users supplied formal goals and guidance while the system executed logical inference, unification and tactic automation.", "zh-CN": "用户提供形式目标与指导，系统执行逻辑推理、合一与 tactic 自动化。" } }, "human_contribution": { "description": { "en": "Lawrence Paulson and collaborators designed the generic architecture, object-logic encodings and automation mechanisms.", "zh-CN": "Lawrence Paulson 与合作者设计通用架构、对象逻辑编码与自动化机制。" } }, "systems": [ "isabelle" ], "organizations": [ "university-of-cambridge" ], "people": [ "lawrence-paulson" ], "problems": [ "generic-theorem-proving" ], "methods": [ "higher-order-unification", "tactics", "interactive-theorem-proving" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1988-05-23", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The CADE-9 proceedings establish the public system description; official Isabelle archives corroborate an earlier Isabelle86 release.", "zh-CN": "CADE-9 proceedings 确认了公开系统描述；Isabelle 官方档案同时佐证更早的 Isabelle86 版本。" } } ] }, "sources": [ { "id": "cade9-isabelle-1988", "tier": "S1", "type": "paper", "title": "Isabelle — The Next Seven Hundred Theorem Provers", "url": "https://link.springer.com/book/10.1007/BFb0012819", "primary": true, "published_date": "1988-05-23", "accessed_at": "2026-09-15" }, { "id": "isabelle-official-release-archive", "tier": "S2", "type": "official_announcement", "title": "Older Isabelle Releases", "url": "https://isabelle.in.tum.de/download_past.html", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-1979-edinburgh-lcf" ], "successors": [], "related": [ "evt-1988-hol" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "isabelle", "proof-assistant", "generic-theorem-prover", "formalization" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1988-hol", "slug": "hol-proof-generating-system", "title": { "en": "HOL consolidates LCF-style mechanized proof for higher-order logic", "zh-CN": "HOL 将 LCF 式机械证明体系扩展并整合到高阶逻辑" }, "dates": { "event": "1988-01-01", "first_public_claim": null, "paper_release": "1988-01-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "HOL adapted the LCF architecture to classical higher-order logic and became a major proof-assistant family supporting mechanized mathematics, hardware verification and later AI theorem-proving research.", "zh-CN": "HOL 将 LCF 架构应用于经典高阶逻辑，发展为重要证明助手家族，承载机械化数学、硬件验证以及后来的 AI 定理证明研究。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Mike Gordon's public system descriptions documented HOL as an LCF-derived proof-generating system for higher-order logic; the 1988 archival chapter provides a precise publication anchor after the January 1987 Cambridge technical report.", "zh-CN": "Mike Gordon 的公开系统文献将 HOL 描述为源自 LCF 的高阶逻辑 proof-generating system；1988 年档案性章节为 1987 年 1 月 Cambridge technical report 之后的系统记录提供精确出版锚点。" }, "summary": { "en": "HOL combined a small trusted logical basis, ML programming and tactics/tacticals for goal-directed interactive proof in higher-order logic.", "zh-CN": "HOL 结合小型可信逻辑基础、ML 编程与 tactics/tacticals，在高阶逻辑中支持目标驱动的交互式证明。" }, "why_it_matters": { "en": "HOL and its descendants supplied formal corpora and interactive environments later used by systems such as TacticToe, HOL(y)Hammer and learning-based theorem provers.", "zh-CN": "HOL 及其后继系统提供的形式语料与交互环境后来被 TacticToe、HOL(y)Hammer 等学习式定理证明系统广泛使用。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Humans directed proofs through tactics while the system mechanically executed inference and checked resulting derivations.", "zh-CN": "人类通过 tactics 引导证明，系统机械执行推理并检查最终推导。" } }, "human_contribution": { "description": { "en": "Mike Gordon and the HOL/LCF community designed the logic, trusted implementation and tactic-based interaction model.", "zh-CN": "Mike Gordon 与 HOL/LCF 社群设计逻辑、可信实现及基于 tactic 的交互模式。" } }, "systems": [ "hol", "lcf" ], "organizations": [ "university-of-cambridge" ], "people": [ "mike-gordon" ], "problems": [ "higher-order-logic-theorem-proving" ], "methods": [ "interactive-theorem-proving", "tactics", "trusted-kernel" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1988-01-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The archival HOL chapter and Cambridge technical-report record establish the system architecture and higher-order logic implementation.", "zh-CN": "HOL 档案章节与 Cambridge technical-report 记录确认了系统架构与高阶逻辑实现。" } } ] }, "sources": [ { "id": "hol-proof-generating-system-1988", "tier": "S1", "type": "paper", "title": "HOL: A Proof Generating System for Higher-Order Logic", "url": "https://doi.org/10.1007/978-1-4613-2007-4_3", "primary": true, "published_date": "1988-01-01", "accessed_at": "2026-09-15" }, { "id": "cambridge-hol-tr103", "tier": "S1", "type": "paper", "title": "HOL: A proof generating system for higher-order logic — Technical Report 103", "url": "https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-103.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-1979-edinburgh-lcf" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "hol", "proof-assistant", "higher-order-logic", "formalization" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1986-nuprl", "slug": "nuprl-constructive-proof-development", "title": { "en": "Nuprl demonstrates constructive proof development on substantial number theory", "zh-CN": "Nuprl 展示面向实质性数论的构造性证明开发" }, "dates": { "event": "1986-07-01", "first_public_claim": null, "paper_release": "1986-07-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Nuprl established a constructive type-theoretic proof-development environment in which formal proofs could carry computational content and support program extraction. Its early use on substantial number theory showed that interactive proof development could serve formal mathematics, not only program verification.", "zh-CN": "Nuprl 建立了构造类型论证明开发环境，使形式证明能够携带计算内容并支持程序抽取；其早期在实质性数论上的应用表明，交互式证明开发不仅可用于程序验证，也能够承载形式数学。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The CADE-8 proceedings, published on 1 July 1986, included Douglas Howe's experiment using Nuprl together with simple proof-assisting programs to constructively prove a substantial theorem of number theory. Cornell's official Nuprl documentation states that the system had been in use since June 1984 and was already accumulating a library of formal algorithmic mathematics.", "zh-CN": "1986 年 7 月 1 日出版的 CADE-8 proceedings 收录 Douglas Howe 的实验：使用 Nuprl 与一组简单 proof-assisting programs，对一个实质性数论定理进行构造性形式证明。Cornell 官方 Nuprl 文档同时记载，该系统自 1984 年 6 月起已投入使用，并开始积累形式化算法数学库。" }, "summary": { "en": "Nuprl combined constructive type theory, refinement-style proof development, tactics and computational interpretation of proofs. Complete proofs could be used to obtain programs meeting formal specifications, linking theorem proving, formal mathematics and verified programming in a single environment.", "zh-CN": "Nuprl 将构造类型论、refinement 式证明开发、tactics 与证明的计算解释结合起来；完整证明可以用于提取满足形式规格的程序，从而在同一环境中连接定理证明、形式数学与 verified programming。" }, "why_it_matters": { "en": "Nuprl represents a distinct foundational branch of machine-checked mathematics: rather than only certifying propositions, its constructive type theory treats proofs as computational objects. This lineage influenced proof assistants and formal-mathematics systems built around dependent and constructive type theories.", "zh-CN": "Nuprl 代表机器检查数学的一条重要基础路线：它不只验证命题，还在构造类型论中把证明视为具有计算含义的对象。这一路线影响了后来基于依赖类型与构造类型论的证明助手和形式数学系统。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Human users guided formal developments while Nuprl and auxiliary proof-assisting programs applied refinement rules, tactics and mechanical checking to construct certified proofs and computational content.", "zh-CN": "人类用户主导形式化开发，Nuprl 与辅助证明程序则应用 refinement rules、tactics 与机械检查来构造经认证的证明及其计算内容。" } }, "human_contribution": { "description": { "en": "Robert Constable and the Cornell PRL group designed and implemented the Nuprl proof-development environment; Douglas Howe conducted the early number-theory experiment documented at CADE-8.", "zh-CN": "Robert Constable 与 Cornell PRL 团队设计并实现 Nuprl 证明开发环境；Douglas Howe 完成了 CADE-8 所记录的早期数论实验。" } }, "systems": [ "nuprl" ], "organizations": [ "cornell-university" ], "people": [ "robert-constable", "douglas-howe" ], "problems": [ "constructive-mathematics", "number-theory-formalization", "program-synthesis" ], "methods": [ "constructive-type-theory", "proof-refinement", "tactics", "program-extraction", "interactive-theorem-proving" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1986-07-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The CADE-8 proceedings provide an exact publication anchor for the Nuprl number-theory experiment; Cornell's project documentation independently records that Nuprl had been used since June 1984.", "zh-CN": "CADE-8 proceedings 为 Nuprl 数论实验提供精确出版锚点；Cornell 项目文档则独立记录 Nuprl 自 1984 年 6 月起已投入使用。" } } ] }, "sources": [ { "id": "cade8-howe-nuprl-1986", "tier": "S1", "type": "paper", "title": "Implementing Number Theory: An Experiment with Nuprl", "url": "https://doi.org/10.1007/3-540-16780-3_108", "primary": true, "published_date": "1986-07-01", "accessed_at": "2026-09-15" }, { "id": "springer-cade8-proceedings-1986", "tier": "S1", "type": "paper", "title": "8th International Conference on Automated Deduction — Proceedings", "url": "https://doi.org/10.1007/3-540-16780-3", "primary": false, "published_date": "1986-07-01", "accessed_at": "2026-09-15" }, { "id": "cornell-nuprl-overview", "tier": "S2", "type": "official_announcement", "title": "Nuprl book overview and system background", "url": "https://nuprl-web.cs.cornell.edu/book/Overview.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "cornell-prl-origins", "tier": "S2", "type": "official_announcement", "title": "The Nature of the PRL Project — Background", "url": "https://nuprl-web.cs.cornell.edu/Intro/subintro.html", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [ "evt-1984-coq" ] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "nuprl", "constructive-type-theory", "proof-assistant", "formalization", "program-extraction", "interactive-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1986-graffiti", "slug": "graffiti-automated-conjecturing", "title": { "en": "Graffiti turns graph-theory conjecture generation into a sustained computer program", "zh-CN": "Graffiti 将图论猜想生成发展为持续运行的计算机计划" }, "dates": { "event": "1986-06-01", "first_public_claim": "1986-06-01", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Graffiti made automated conjecture generation a sustained research activity in graph theory, producing machine-suggested inequalities and conjectures that mathematicians could investigate.", "zh-CN": "Graffiti 将自动猜想生成发展为持续的图论研究活动，机器提出不等式与猜想，再由数学家研究其真伪与意义。" } }, "mathematical_novelty": { "type": "new_conjecture" }, "interfaces": [ "symbolic" ], "claim": { "en": "Fajtlowicz's Graffiti program generated graph-theoretic conjectures from a library of graphs and numerical invariants; the First Japan Conference on Graph Theory and Applications began on 1 June 1986 and provides the public conference anchor for the early Graffiti record.", "zh-CN": "Fajtlowicz 的 Graffiti 程序从图数据库与数值不变量自动生成图论猜想；1986 年 6 月 1 日开幕的 First Japan Conference on Graph Theory and Applications 为其早期公开记录提供会议锚点。" }, "summary": { "en": "Graffiti evaluated candidate relations between graph invariants, retained statements without known counterexamples and used heuristics to suppress trivial or redundant conjectures.", "zh-CN": "Graffiti 评估图不变量之间的候选关系，保留在已知图中没有反例的陈述，并用启发式删除平凡或重复猜想。" }, "why_it_matters": { "en": "It demonstrated a durable human–machine discovery workflow in which a computer proposes mathematical conjectures and the research community proves, disproves and refines them.", "zh-CN": "它展示了长期的人机数学发现流程：计算机提出猜想，研究共同体负责证明、反驳与改进。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The program autonomously generated and filtered candidate graph-theory conjectures from its knowledge base.", "zh-CN": "程序从其知识库自动生成并筛选图论候选猜想。" } }, "human_contribution": { "description": { "en": "Siemion Fajtlowicz designed the invariant library and conjecturing heuristics, while mathematicians evaluated and developed the generated conjectures.", "zh-CN": "Siemion Fajtlowicz 设计不变量库与猜想启发式，数学家评估并发展机器生成的猜想。" } }, "systems": [ "graffiti" ], "organizations": [ "university-of-houston" ], "people": [ "siemion-fajtlowicz" ], "problems": [ "graph-theory-conjecturing" ], "methods": [ "automated-conjecturing", "heuristic-filtering", "graph-invariants" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1988-01-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The proceedings article “On Conjectures of Graffiti” documents the system presented in the 1986 Hakone conference series.", "zh-CN": "Proceedings 论文“On Conjectures of Graffiti”记录了在 1986 年箱根会议中展示的系统。" } } ] }, "sources": [ { "id": "graffiti-hakone-proceedings", "tier": "S1", "type": "paper", "title": "On Conjectures of Graffiti", "url": "https://doi.org/10.1016/S0167-5060(08)70776-3", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "graffiti", "graph-theory", "conjecture-generation", "mathematical-discovery" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1984-coq", "slug": "coq-early-proof-checker", "title": { "en": "The Calculus of Constructions proof checker begins the Coq lineage", "zh-CN": "Calculus of Constructions 证明检查器开启 Coq 谱系" }, "dates": { "event": "1984-12-22", "first_public_claim": "1984-12-22", "paper_release": null, "artifact_release": "1984-12-22", "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "The early Calculus of Constructions checker became the direct lineage of Coq, establishing dependent-type proof checking as a durable platform for formal mathematics and mechanized reasoning.", "zh-CN": "早期 Calculus of Constructions 检查器直接发展为 Coq，建立了依赖类型证明检查这一长期用于形式数学与机械推理的平台路线。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The official Coq/Rocq history records version 1.10 as frozen on 22 December 1984, during the initial implementation of a Calculus of Constructions proof checker by Thierry Coquand and Gérard Huet.", "zh-CN": "Coq/Rocq 官方历史记录显示，Thierry Coquand 与 Gérard Huet 初步实现 Calculus of Constructions 证明检查器期间，版本 1.10 于 1984 年 12 月 22 日冻结。" }, "summary": { "en": "The system provided machine checking for proofs in the Calculus of Constructions and evolved through successive implementations into Coq and later Rocq.", "zh-CN": "该系统为 Calculus of Constructions 中的证明提供机器检查，并经过持续演化成为 Coq，后更名为 Rocq。" }, "why_it_matters": { "en": "Coq later supported major formalized-mathematics achievements and became an important environment for machine-learning and AI-assisted theorem proving.", "zh-CN": "Coq 后来承载多项重要形式化数学成果，并成为机器学习与 AI 辅助定理证明的重要环境。" }, "ai_role": { "level": "computation_only", "description": { "en": "The system mechanically checked formal proof terms; humans supplied the formal statements and proof constructions.", "zh-CN": "系统机械检查形式证明项；形式陈述与证明构造主要由人类提供。" } }, "human_contribution": { "description": { "en": "Thierry Coquand, Gérard Huet and collaborators designed the type theory and implemented the early checker.", "zh-CN": "Thierry Coquand、Gérard Huet 及合作者设计类型理论并实现早期检查器。" } }, "systems": [ "coq", "calculus-of-constructions" ], "organizations": [ "inria" ], "people": [ "thierry-coquand", "gerard-huet" ], "problems": [ "formal-proof-checking" ], "methods": [ "dependent-type-theory", "proof-checking", "calculus-of-constructions" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "1984-12-22", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official project history supplies the dated version record and describes the initial Calculus of Constructions implementation.", "zh-CN": "官方项目历史提供了带日期的版本记录，并描述初始 Calculus of Constructions 实现。" } } ] }, "sources": [ { "id": "rocq-official-history-1984", "tier": "S2", "type": "official_announcement", "title": "Coq / Rocq historical notes", "url": "https://rocq-prover.org/doc/V8.20.1/refman/history.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "coq", "proof-assistant", "dependent-types", "formalization" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1979-edinburgh-lcf", "slug": "edinburgh-lcf-trusted-kernel-tactics", "title": { "en": "Edinburgh LCF consolidates the trusted-kernel, ML and tactics architecture for interactive theorem proving", "zh-CN": "Edinburgh LCF 确立可信内核、ML 与 tactics 的交互式定理证明架构" }, "dates": { "event": "1979-12-01", "first_public_claim": null, "paper_release": "1979-12-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Edinburgh LCF turned lessons from Stanford LCF into a durable proof-assistant architecture: a small trusted inference interface protected by an abstract theorem type, an ML metalanguage for extending proof procedures, and tactics/tacticals for programmable goal-directed proof. These ideas became architectural foundations for HOL, Isabelle and many later interactive theorem provers.", "zh-CN": "Edinburgh LCF 将 Stanford LCF 的实践经验发展为持久的证明助手架构：以抽象 theorem 类型保护小型可信推理接口，以 ML 元语言扩展证明过程，并用 tactics / tacticals 编排目标驱动证明。这些思想后来成为 HOL、Isabelle 等大量交互式定理证明器的架构基础。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "The Springer monograph Edinburgh LCF: A Mechanized Logic of Computation, published on 1 December 1979, documented the Edinburgh LCF system and its ML-based proof environment. Milner's retrospective account dates the Edinburgh LCF project to 1974 and explains that ML was created as a metalanguage for machine-assisted proof after experience with Stanford LCF.", "zh-CN": "Springer 专著 Edinburgh LCF: A Mechanized Logic of Computation 于 1979 年 12 月 1 日出版，系统记录 Edinburgh LCF 及其基于 ML 的证明环境。Milner 的历史回顾把 Edinburgh LCF 项目的启动时间定在 1974 年，并说明 ML 是在 Stanford LCF 实践基础上为机器辅助证明设计的元语言。" }, "summary": { "en": "Edinburgh LCF avoided retaining complete proof objects by exposing theorem values through a restricted abstract interface whose constructors corresponded to axioms and inference rules. Users could write higher-level proof procedures in the typed functional language ML, while tactics and tacticals supported reusable backward proof strategies.", "zh-CN": "Edinburgh LCF 不再依赖保存完整证明对象，而是通过受限的抽象接口产生 theorem 值，其构造操作对应公理与推理规则。用户可以在有类型函数式语言 ML 中编写高层证明过程，并利用 tactics 与 tacticals 复用和组合反向证明策略。" }, "why_it_matters": { "en": "This separation between a small trusted logical core and powerful untrusted proof automation became one of the central engineering patterns of proof assistants. It made extensible automation compatible with strong assurance and created the lineage from LCF to HOL and Isabelle that later supplied machine-readable formal environments for AI theorem proving.", "zh-CN": "这种“小型可信逻辑核心 + 强大但无需纳入可信基的证明自动化”分层成为证明助手最核心的工程范式之一，使可扩展自动化与高可信验证能够共存，并形成 LCF → HOL / Isabelle 的谱系，为后来的 AI 定理证明提供机器可读形式环境。" }, "ai_role": { "level": "human_ai_collaboration", "description": { "en": "Humans formulated goals and wrote or selected tactics, while the system executed tactic programs, performed inference and admitted theorem values only through the trusted logical interface.", "zh-CN": "人类提出目标并编写或选择 tactics，系统执行 tactic 程序与推理，并只允许通过可信逻辑接口产生 theorem 值。" } }, "human_contribution": { "description": { "en": "Robin Milner and the Edinburgh LCF team, including Michael Gordon, Christopher Wadsworth, Malcolm Newey and Lockwood Morris, designed the trusted architecture, ML metalanguage and tactic-based interaction model.", "zh-CN": "Robin Milner 与 Edinburgh LCF 团队，包括 Michael Gordon、Christopher Wadsworth、Malcolm Newey 和 Lockwood Morris，设计可信架构、ML 元语言与基于 tactic 的交互模式。" } }, "systems": [ "edinburgh-lcf", "lcf" ], "organizations": [ "university-of-edinburgh" ], "people": [ "robin-milner", "mike-gordon", "christopher-wadsworth", "malcolm-newey", "lockwood-morris" ], "problems": [ "interactive-theorem-proving", "program-verification" ], "methods": [ "trusted-kernel", "abstract-theorem-type", "ml", "tactics", "tacticals", "interactive-theorem-proving" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1979-12-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "Springer's archival monograph supplies an exact publication anchor for the mature Edinburgh LCF system; Milner's retrospective history distinguishes its 1974 project origin from Stanford LCF in 1971–1972.", "zh-CN": "Springer 档案专著为成熟 Edinburgh LCF 系统提供精确出版锚点；Milner 的历史回顾则明确区分其 1974 年项目起点与 1971–1972 年的 Stanford LCF。" } } ] }, "sources": [ { "id": "springer-edinburgh-lcf-1979", "tier": "S1", "type": "paper", "title": "Edinburgh LCF: A Mechanized Logic of Computation", "url": "https://doi.org/10.1007/3-540-09724-4", "primary": true, "published_date": "1979-12-01", "accessed_at": "2026-09-15" }, { "id": "milner-how-ml-evolved-1982", "tier": "S2", "type": "paper", "title": "How ML Evolved", "url": "https://www.pure.ed.ac.uk/ws/portalfiles/portal/17084823/Milner_R_1982_How_ML_Evolved.pdf", "primary": false, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "gordon-lcf-commentary-2015", "tier": "S3", "type": "independent_analysis", "title": "Tactics for mechanized reasoning — commentary on Milner's LCF architecture", "url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC4360087/", "primary": false, "published_date": "2015-04-13", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-1972-lcf" ], "successors": [ "evt-1988-hol", "evt-1988-isabelle" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "edinburgh-lcf", "lcf", "ml", "tactics", "trusted-kernel", "proof-assistant", "interactive-theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1977-am", "slug": "am-automated-mathematician", "title": { "en": "AM explores automated mathematical concept formation and conjecture discovery", "zh-CN": "AM 探索自动数学概念形成与猜想发现" }, "dates": { "event": "1977-08-22", "first_public_claim": "1977-08-22", "paper_release": "1977-08-22", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "discovery", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Douglas Lenat's AM made automated mathematical discovery an explicit AI research program by using heuristic search to invent and prioritize mathematical concepts and formulate conjectures.", "zh-CN": "Douglas Lenat 的 AM 把自动数学发现明确发展为 AI 研究方向，通过启发式搜索创造和筛选数学概念并形成猜想。" } }, "mathematical_novelty": { "type": "new_conjecture" }, "interfaces": [ "symbolic", "informal" ], "claim": { "en": "At IJCAI-77, Lenat described AM, a program that conducted elementary mathematical exploration by defining new concepts, studying their properties and formulating conjectures under hundreds of heuristic rules.", "zh-CN": "Lenat 在 IJCAI-77 介绍 AM：该程序在数百条启发式规则引导下定义新概念、研究其性质并形成猜想，从而执行初等数学探索。" }, "summary": { "en": "AM maintained an agenda of potentially interesting mathematical tasks and used general heuristics to decide which concepts, examples and conjectures to explore next.", "zh-CN": "AM 维护潜在有趣数学任务的 agenda，并利用通用启发式决定下一步探索哪些概念、例子与猜想。" }, "why_it_matters": { "en": "It is an early direct ancestor of modern AI-for-mathematical-discovery work because the machine was tasked not merely with proving supplied statements but with shaping what mathematical objects and conjectures to investigate.", "zh-CN": "它是现代 AI 数学发现的重要早期前史，因为机器不仅证明给定命题，还参与决定应该研究哪些数学对象与猜想。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "AM autonomously selected exploration tasks, generated concepts and formulated candidate conjectures using heuristic search.", "zh-CN": "AM 通过启发式搜索自主选择探索任务、生成概念并形成候选猜想。" } }, "human_contribution": { "description": { "en": "Douglas Lenat designed the representation, agenda mechanism and roughly 250 heuristic rules that structured AM's search.", "zh-CN": "Douglas Lenat 设计表示、agenda 机制以及约 250 条用于组织 AM 搜索的启发式规则。" } }, "systems": [ "am" ], "organizations": [ "stanford-ai-lab" ], "people": [ "douglas-lenat" ], "problems": [ "automated-mathematical-discovery" ], "methods": [ "heuristic-search", "concept-formation", "conjecture-generation" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1977-08-22", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The IJCAI-77 proceedings and later Artificial Intelligence article document AM and its heuristic mathematical-discovery behavior.", "zh-CN": "IJCAI-77 proceedings 与后续 Artificial Intelligence 论文记录了 AM 及其启发式数学发现行为。" } } ] }, "sources": [ { "id": "ijcai-am-1977", "tier": "S1", "type": "paper", "title": "Automated Theory Formation in Mathematics", "url": "https://www.ijcai.org/Proceedings/77-2/Papers/094.pdf", "primary": true, "published_date": "1977-08-22", "accessed_at": "2026-09-15" }, { "id": "artint-lenat-ubiquity-discovery", "tier": "S1", "type": "paper", "title": "The ubiquity of discovery", "url": "https://doi.org/10.1016/0004-3702(77)90024-8", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "automated-mathematician", "discovery", "conjecture-generation", "heuristic-search" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1977-wu-method", "slug": "wu-method-geometry-theorem-proving", "title": { "en": "Wen-Tsun Wu validates the algebraic method that becomes Wu's method for automated geometry theorem proving", "zh-CN": "吴文俊验证后来被称为“吴方法”的几何定理机器证明代数方法" }, "dates": { "event": "1977-02-18", "first_public_claim": null, "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Wu's method shifted automated geometry theorem proving from predominantly heuristic search toward an algebraic, algorithmic route: geometric hypotheses and conclusions are translated into polynomial conditions and treated with characteristic-set and elimination techniques. CADE later recognized Wu's work as groundbreaking, and its Herbrand Award record describes the method as a breakthrough that revitalized automated geometry theorem proving.", "zh-CN": "吴方法把自动几何定理证明从以启发式搜索为主的路线推进到代数化、算法化路线：将几何条件与结论转写为多项式条件，再利用特征列与消元技术处理。CADE 后来将吴文俊的工作明确评价为几何定理证明中的奠基性贡献，其 Herbrand Award 记录也将该方法视为重新推动自动几何定理证明的重要突破。" } }, "mathematical_novelty": { "type": "new_algorithm" }, "interfaces": [ "symbolic" ], "claim": { "en": "Retrospective Chinese Academy of Sciences accounts record that on Lunar New Year's Day in 1977, after several months of hand calculation, Wen-Tsun Wu first successfully verified the feasibility of his mechanical method for proving elementary-geometry theorems. An official 1977 holiday record independently fixes that Lunar New Year's Day to 18 February 1977. Wu published the foundational Chinese paper later that year in Scientia Sinica, volume 20, issue 6, pages 507-516; the English version appeared in 1978.", "zh-CN": "中国科学院的回顾性资料记载，经过数月手算后，吴文俊于 1977 年农历大年初一首次成功验证初等几何定理机械化证明方法的可行性；1977 年官方节假日档案独立确认当年农历新年首日为公历 2 月 18 日。吴文俊随后于同年在《中国科学》20 卷第 6 期 507–516 页发表奠基性中文论文，英文版于 1978 年发表。" }, "summary": { "en": "The method algebraizes elementary geometry: geometric configurations are encoded as polynomial equations and theorem proving is reduced to symbolic polynomial reasoning. Wu developed the route from Ritt-style characteristic-set ideas and constructive elimination, enabling mechanical proof procedures and explicit treatment of degenerate cases. Later computer implementations proved non-trivial geometry theorems and helped establish algebraic automated deduction in geometry as a durable research program.", "zh-CN": "该方法把初等几何代数化：将几何构型编码为多项式方程，并把定理证明转化为符号多项式推理。吴文俊在 Ritt 特征列思想与构造性消元基础上发展出机械化证明路线，并能显式处理退化情形。后续计算机实现证明了多项非平凡几何定理，使代数式自动几何推理成为长期研究方向。" }, "why_it_matters": { "en": "The event supplies a missing bridge in the Chronicle between Gelernter's earlier heuristic Geometry Theorem Machine and later mature symbolic-algebra approaches to automated deduction. It also illustrates an important historical form of AI4Math in which the central innovation was not a learned model but a mathematically designed algorithm that made a class of proof tasks mechanically executable.", "zh-CN": "该事件补上了 Chronicle 中从 Gelernter 早期启发式 Geometry Theorem Machine 到后来成熟符号代数自动演绎路线之间的重要桥梁。它也体现了一种关键的历史 AI4Math 形态：核心创新并非学习模型，而是把一类证明任务转化为可机械执行过程的数学算法。" }, "ai_role": { "level": "computation_only", "description": { "en": "The central contribution was a human-designed algorithm for mechanical reasoning. Wu first validated the procedure by hand; later implementations executed the algebraic proof procedure on computers. This record does not attribute mathematical discovery to an autonomous AI system.", "zh-CN": "核心贡献是由人类设计、面向机械推理的算法。吴文俊先以手算验证过程可行，后续实现再由计算机执行代数证明程序；本记录不把数学发现归因于自主 AI 系统。" } }, "human_contribution": { "description": { "en": "Wen-Tsun Wu formulated the algebraization strategy, developed the constructive polynomial machinery, manually tested the method, and subsequently led its computer implementation and broader mathematics-mechanization program.", "zh-CN": "吴文俊提出几何代数化路线，发展构造性多项式方法，以手算检验其可行性，并随后推动计算机实现及更广泛的数学机械化研究计划。" } }, "systems": [], "organizations": [ "chinese-academy-of-sciences" ], "people": [ "wen-tsun-wu" ], "problems": [ "euclidean-geometry-theorem-proving" ], "methods": [ "characteristic-set-method", "polynomial-elimination", "symbolic-reasoning", "automated-deduction" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "1977-02-18", "status": "claimed", "evidence_level": "E2", "note": { "en": "Chinese Academy of Sciences retrospective records date Wu's first successful hand verification to Lunar New Year's Day 1977; an official 1977 holiday calendar independently establishes that day as 18 February 1977. The exact day of the later journal publication is not inferred from issue-level metadata.", "zh-CN": "中国科学院回顾性资料把吴文俊首次成功手算验证定在 1977 年农历大年初一；1977 年官方节假日档案独立确认该日为公历 2 月 18 日。本记录不从只有期号精度的期刊元数据推断后续论文的具体出版日。" } } ] }, "sources": [ { "id": "cas-wu-method-lunar-new-year-1977", "tier": "S2", "type": "official_announcement", "title": "Chinese Academy of Sciences retrospective on Wen-Tsun Wu and Wu's method", "url": "https://www.cas.cn/zt/hyzt/ysdh21st/ysfc/202406/t20240621_5022393.shtml", "primary": true, "published_date": "2024-06-21", "accessed_at": "2026-09-15" }, { "id": "hk-grs-lunar-new-year-1977", "tier": "S2", "type": "other", "title": "Hong Kong Government Information Services — General Holidays for 1977", "url": "https://search.grs.gov.hk/repository/img?id=IKU2PV9X0p4gkvfn4VhffQ%3D%3D&ori=1", "primary": false, "published_date": "1976-01-02", "accessed_at": "2026-09-15" }, { "id": "amss-wu-mechanization-bibliography", "tier": "S2", "type": "official_announcement", "title": "Wen-Tsun Wu memorial bibliography — mathematics mechanization papers", "url": "https://www.amss.cas.cn/wwj/jnwz/201705/t20170506_4784450.html", "primary": true, "published_date": "2019-04-30", "accessed_at": "2026-09-15" }, { "id": "cade-herbrand-wu-1997", "tier": "S2", "type": "official_announcement", "title": "CADE Herbrand Award — Wen-Tsun Wu (1997)", "url": "https://cadeinc.org/Herbrand-Award", "primary": false, "published_date": null, "accessed_at": "2026-09-15" }, { "id": "amss-herbrand-wu-citation", "tier": "S2", "type": "official_announcement", "title": "1997 Herbrand Award citation for Wen-Tsun Wu", "url": "https://www.amss.cas.cn/wwj/xslz/201705/t20170506_4784301.html", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [ "evt-1960-geometry-theorem-machine" ], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "wu-method", "geometry", "theorem-proving", "symbolic-ai", "polynomial-methods", "mathematics-mechanization" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1973-mizar", "slug": "mizar-ideology", "title": { "en": "The Mizar program begins a long-running machine-readable formal mathematics project", "zh-CN": "Mizar 理念开启长期机器可读形式数学工程" }, "dates": { "event": "1973-11-14", "first_public_claim": "1973-11-14", "paper_release": null, "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "infrastructure", "field_building" ], "significance": { "tier": "H2", "rationale": { "en": "Mizar established a durable program for writing mathematics in a formal language close to mathematical practice and for accumulating a machine-checkable mathematical library.", "zh-CN": "Mizar 建立了长期工程：以贴近数学实践的形式语言书写数学，并持续积累机器可检查的数学知识库。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Mizar's official historical record dates Andrzej Trybulec's first public presentation of the Mizar ideology to 14 November 1973.", "zh-CN": "Mizar 官方历史记录把 Andrzej Trybulec 首次公开介绍 Mizar 理念的日期标为 1973 年 11 月 14 日。" }, "summary": { "en": "Mizar developed a formal mathematical language, checker and library model aimed at building a cumulative body of computer-verifiable mathematics.", "zh-CN": "Mizar 发展形式数学语言、检查器与数学库模式，目标是形成可累积的计算机可验证数学体系。" }, "why_it_matters": { "en": "The Mizar Mathematical Library later became a major formal corpus for automated reasoning and machine-learning research, including DeepMath and neural autoformalization.", "zh-CN": "Mizar Mathematical Library 后来成为自动推理与机器学习研究的重要形式语料，包括 DeepMath 与神经自动形式化路线。" }, "ai_role": { "level": "computation_only", "description": { "en": "The system mechanically checks formal mathematical texts; the historical milestone is the formal knowledge infrastructure rather than autonomous discovery.", "zh-CN": "系统机械检查形式数学文本；该历史节点的核心是形式知识基础设施，而非自主发现。" } }, "human_contribution": { "description": { "en": "Andrzej Trybulec and the Mizar community designed the language, verification discipline and growing formal library.", "zh-CN": "Andrzej Trybulec 与 Mizar 社群设计语言、验证规范并建设持续增长的形式数学库。" } }, "systems": [ "mizar" ], "organizations": [], "people": [ "andrzej-trybulec" ], "problems": [ "formal-mathematical-knowledge" ], "methods": [ "formalization", "proof-checking", "mathematical-library" ], "verification": { "evidence_level": "E2", "status": "claimed", "formal_assurance": "none", "history": [ { "date": "1973-11-14", "status": "claimed", "evidence_level": "E2", "note": { "en": "The official Mizar historical archive records the first public presentation date and the project's origins.", "zh-CN": "Mizar 官方历史档案记录了首次公开介绍日期与项目起源。" } } ] }, "sources": [ { "id": "mizar-official-history", "tier": "S2", "type": "official_announcement", "title": "Mizar project history", "url": "https://mizar.uwb.edu.pl/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "mizar", "formalization", "mathematical-library", "proof-checking" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1973-pltp", "slug": "pltp-boyer-moore-induction", "title": { "en": "The Edinburgh Pure Lisp Theorem Prover brings automated induction to program reasoning", "zh-CN": "Edinburgh Pure Lisp Theorem Prover 将自动归纳推理用于程序性质证明" }, "dates": { "event": "1973-08-20", "first_public_claim": "1973-08-20", "paper_release": "1973-08-20", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Boyer and Moore's PLTP established a durable automated-induction lineage for reasoning about recursive Lisp functions, preceding the later Boyer–Moore prover, NQTHM and ACL2.", "zh-CN": "Boyer 与 Moore 的 PLTP 建立了面向递归 Lisp 函数的自动归纳推理谱系，并成为后来的 Boyer–Moore prover、NQTHM 与 ACL2 的前史。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Boyer and Moore presented “Proving Theorems about LISP Functions” at IJCAI-73, documenting the Edinburgh Pure Lisp Theorem Prover developed in 1972–1973 and its automated use of induction, rewriting and symbolic evaluation.", "zh-CN": "Boyer 与 Moore 在 IJCAI-73 发表“Proving Theorems about LISP Functions”，公开记录 1972–1973 年开发的 Edinburgh Pure Lisp Theorem Prover 及其自动归纳、重写与符号求值方法。" }, "summary": { "en": "PLTP targeted properties of recursively defined programs that resolution-based first-order provers handled poorly, using domain-specific proof procedures centered on simplification and induction.", "zh-CN": "PLTP 面向基于归结的一阶证明器难以处理的递归程序性质，采用以化简与归纳为核心的专门证明过程。" }, "why_it_matters": { "en": "It established a long-running architecture for automated inductive theorem proving and program verification that evolved into influential later systems.", "zh-CN": "它建立了长期发展的自动归纳定理证明与程序验证架构，并演化为多个重要后续系统。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The prover automatically simplified formulas, selected induction schemes and searched for proofs of recursive-function properties.", "zh-CN": "证明器自动化简公式、选择归纳方案并搜索递归函数性质的证明。" } }, "human_contribution": { "description": { "en": "Robert Boyer and J Strother Moore designed and implemented the logic, heuristics and proof procedures.", "zh-CN": "Robert Boyer 与 J Strother Moore 设计并实现逻辑、启发式与证明过程。" } }, "systems": [ "pltp" ], "organizations": [ "university-of-edinburgh" ], "people": [ "robert-s-boyer", "j-strother-moore" ], "problems": [ "inductive-theorem-proving", "program-verification" ], "methods": [ "mathematical-induction", "rewriting", "symbolic-evaluation" ], "verification": { "evidence_level": "E3", "status": "paper_released", "formal_assurance": "artifact_available", "history": [ { "date": "1973-08-20", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The IJCAI-73 paper documents PLTP and its theorem-proving methods.", "zh-CN": "IJCAI-73 论文记录了 PLTP 及其定理证明方法。" } }, { "date": "2026-09-15", "status": "paper_released", "evidence_level": "E3", "note": { "en": "The UT Austin PLTP archive preserves original 1973 source listings and modern transcriptions/reconstructions.", "zh-CN": "UT Austin 的 PLTP 档案保存 1973 年原始源代码清单以及现代转录与重建版本。" } } ] }, "sources": [ { "id": "ut-pltp-archive", "tier": "S1", "type": "repository", "title": "The PLTP Archive", "url": "https://www.cs.utexas.edu/~moore/best-ideas/pltp/index.html", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [ { "id": "pltp-1973-source-archive", "kind": "code", "title": "PLTP 1973 source listings and reconstructions", "url": "https://www.cs.utexas.edu/~moore/best-ideas/pltp/index.html" } ], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "boyer-moore", "pltp", "induction", "theorem-proving", "program-verification" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1972-lcf", "slug": "lcf-proof-checker", "title": { "en": "Stanford LCF demonstrates interactive machine checking for Scott's Logic for Computable Functions", "zh-CN": "Stanford LCF 展示 Scott 可计算函数逻辑的交互式机器证明检查" }, "dates": { "event": "1972-01-01", "first_public_claim": "1972-01-01", "paper_release": "1972-01-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "infrastructure", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Stanford LCF implemented Dana Scott's Logic for Computable Functions as an interactive proof checker with subgoaling and simplification, establishing practical experience that directly motivated the later Edinburgh LCF architecture.", "zh-CN": "Stanford LCF 将 Dana Scott 的 Logic for Computable Functions 实现为带有子目标分解与化简机制的交互式证明检查器，为后来 Edinburgh LCF 的架构创新提供了直接实践基础。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Robin Milner's January 1972 publication described an implemented proof checker for Scott's Logic for Computable Functions and showed formal reasoning about recursively defined programs; later historical accounts identify this system as Stanford LCF, developed at Stanford in 1971–1972 with Richard Weyhrauch and Malcolm Newey.", "zh-CN": "Robin Milner 于 1972 年 1 月发表的论文描述了 Scott 的 Logic for Computable Functions 的已实现证明检查器，并展示了对递归定义程序的形式推理；后来的历史资料将这一系统识别为 Stanford LCF，由 Milner、Richard Weyhrauch 与 Malcolm Newey 于 1971–1972 年在 Stanford 开发。" }, "summary": { "en": "Stanford LCF let users state proof goals, decompose them into subgoals and apply simplification and inference commands while the machine checked the resulting formal derivations. It predated the extensible ML metalanguage, abstract theorem type and programmable tactics that characterized Edinburgh LCF.", "zh-CN": "Stanford LCF 允许用户提出证明目标、分解子目标，并通过化简与推理命令构造由机器检查的形式推导。它早于 Edinburgh LCF 中可扩展的 ML 元语言、抽象 theorem 类型与可编程 tactics。" }, "why_it_matters": { "en": "The system made interactive machine-assisted proof concrete and exposed limitations in memory use and fixed proof commands. Those limitations became design targets for Edinburgh LCF, which in turn shaped the trusted-kernel architecture of many later proof assistants.", "zh-CN": "该系统把交互式机器辅助证明落实为可运行工具，同时暴露了证明对象占用内存以及证明命令固定等限制；这些问题随后成为 Edinburgh LCF 的直接设计目标，并间接塑造大量后续证明助手的可信内核架构。" }, "ai_role": { "level": "computation_only", "description": { "en": "The machine checked formal derivations and provided subgoaling and simplification support, while users supplied substantial proof direction.", "zh-CN": "机器负责检查形式推导并提供子目标分解与化简支持，证明方向仍主要由用户给出。" } }, "human_contribution": { "description": { "en": "Robin Milner, Richard Weyhrauch, Malcolm Newey and collaborators developed the Stanford LCF proof-checking system and its applications to reasoning about programs.", "zh-CN": "Robin Milner、Richard Weyhrauch、Malcolm Newey 与合作者开发 Stanford LCF 证明检查系统及其程序推理应用。" } }, "systems": [ "stanford-lcf", "lcf" ], "organizations": [ "stanford-university" ], "people": [ "robin-milner", "richard-weyhrauch", "malcolm-newey" ], "problems": [ "program-verification" ], "methods": [ "proof-checking", "interactive-theorem-proving", "subgoaling", "simplification", "typed-lambda-calculus" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1972-01-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The ACM publication documents the implemented proof checker, while Mike Gordon's later historical account distinguishes Stanford LCF from its Edinburgh successor and describes the fixed-command and proof-storage limitations that motivated the redesign.", "zh-CN": "ACM 论文记录了已实现的证明检查器；Mike Gordon 后来的历史回顾则区分 Stanford LCF 与其 Edinburgh 后继系统，并说明固定证明命令与保存完整证明带来的限制如何推动后续重构。" } } ] }, "sources": [ { "id": "acm-stanford-lcf-1972", "tier": "S1", "type": "paper", "title": "Implementation and Applications of Scott's Logic for Computable Functions", "url": "https://doi.org/10.1145/800235.807067", "primary": true, "published_date": "1972-01-01", "accessed_at": "2026-09-15" }, { "id": "gordon-lcf-hol-history-2000", "tier": "S2", "type": "paper", "title": "From LCF to HOL: A Short History", "url": "https://www.cl.cam.ac.uk/archive/mjcg/papers/HolHistory.pdf", "primary": false, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-1979-edinburgh-lcf" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "stanford-lcf", "lcf", "proof-assistant", "proof-checking", "formal-methods" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [ { "date": "2026-09-15", "summary": { "en": "The record was narrowed from a generic LCF/trusted-kernel account to Stanford LCF. ML, the abstract theorem type and programmable tactics belong to the later Edinburgh LCF lineage rather than the 1972 Stanford system.", "zh-CN": "本记录由笼统的 LCF / trusted-kernel 叙述校准为 Stanford LCF；ML、抽象 theorem 类型与可编程 tactics 属于后来的 Edinburgh LCF 谱系，而非 1972 年 Stanford 系统。" }, "source_ids": [ "acm-stanford-lcf-1972", "gordon-lcf-hol-history-2000" ] } ] }, { "schema_version": 1, "id": "evt-1971-macsyma", "slug": "macsyma-symbolic-mathematics", "title": { "en": "MACSYMA consolidates symbolic mathematical manipulation into an AI-era system", "zh-CN": "MACSYMA 将符号数学操作整合为 AI 时代的通用系统" }, "dates": { "event": "1971-03-23", "first_public_claim": "1971-03-23", "paper_release": "1971-03-23", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "MACSYMA turned a broad range of symbolic algebra and calculus operations into a reusable computer mathematics system developed within MIT's Project MAC AI environment, forming an important bridge between symbolic AI and computer algebra.", "zh-CN": "MACSYMA 把广泛的符号代数与微积分操作整合为可复用的计算机数学系统，并诞生于 MIT Project MAC 的 AI 研究环境，成为符号 AI 与计算机代数之间的重要桥梁。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "symbolic" ], "claim": { "en": "The 23 March 1971 system paper documented MACSYMA as a Project MAC system for symbolic manipulation of algebraic expressions, after development had begun in the late 1960s.", "zh-CN": "1971 年 3 月 23 日的系统论文公开记录 MACSYMA：Project MAC 开发的代数表达式符号操作系统，其研发始于 1960 年代末。" }, "summary": { "en": "MACSYMA integrated rational functions, algebraic simplification, calculus and related symbolic operations within an interactive extensible system.", "zh-CN": "MACSYMA 在可交互、可扩展系统中整合有理函数、代数化简、微积分及相关符号运算。" }, "why_it_matters": { "en": "It demonstrated that substantial bodies of mathematical manipulation could be delegated to general-purpose symbolic software and influenced the subsequent computer-algebra ecosystem.", "zh-CN": "它展示了大规模数学符号操作可以交由通用软件完成，并影响后续计算机代数生态。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The system automatically carried out symbolic mathematical transformations requested by users.", "zh-CN": "系统自动执行用户请求的符号数学变换。" } }, "human_contribution": { "description": { "en": "MIT researchers designed and implemented the algebraic representations, algorithms, simplification rules and interactive system.", "zh-CN": "MIT 研究者设计并实现代数表示、算法、化简规则与交互系统。" } }, "systems": [ "macsyma" ], "organizations": [ "mit-project-mac" ], "people": [ "william-a-martin", "richard-fateman" ], "problems": [ "symbolic-mathematics" ], "methods": [ "computer-algebra", "symbolic-manipulation", "algebraic-simplification" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1971-03-23", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The ACM SYMSAC system paper documents MACSYMA's goals, design and achieved symbolic capabilities.", "zh-CN": "ACM SYMSAC 系统论文记录了 MACSYMA 的目标、设计与已实现符号能力。" } } ] }, "sources": [ { "id": "acm-macsyma-system-1971", "tier": "S1", "type": "paper", "title": "The MACSYMA system", "url": "https://doi.org/10.1145/800204.806267", "primary": true, "published_date": "1971-03-23", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "macsyma", "symbolic-mathematics", "computer-algebra", "project-mac" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1968-automath", "slug": "automath-language", "title": { "en": "Automath establishes a language for machine-checkable mathematics", "zh-CN": "Automath 建立面向机器检查数学的形式语言" }, "dates": { "event": "1968-12-16", "first_public_claim": "1968-12-16", "paper_release": "1968-12-16", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "formalization", "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Automath was a foundational early effort to encode substantial mathematics in a formal language whose derivations could be checked mechanically, anticipating dependent-type proof assistants and large formal libraries.", "zh-CN": "Automath 是把大规模数学编码进可由机器检查推导的形式语言的奠基性早期尝试，预示了依赖类型证明助手与大型形式数学库。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "N. G. de Bruijn presented Automath as a language for expressing mathematical texts in a form suitable for automatic checking; the 1968 Symposium on Automatic Demonstration provides a precise public anchor for the system's early record.", "zh-CN": "N. G. de Bruijn 将 Automath 提出为一种把数学文本表达成适合自动检查形式的语言；1968 年 Automatic Demonstration Symposium 为其早期公开记录提供了精确时间锚点。" }, "summary": { "en": "Automath represented definitions, propositions and proofs in a highly explicit typed formal language so a computer could verify the correctness of derivations.", "zh-CN": "Automath 以高度显式的有类型形式语言表示定义、命题与证明，使计算机能够检查推导的正确性。" }, "why_it_matters": { "en": "It helped establish the idea that whole mathematical texts—not only isolated logical formulas—could be represented and mechanically checked.", "zh-CN": "它推动了“完整数学文本而非孤立逻辑公式也可以形式表示并由机器检查”的理念。" }, "ai_role": { "level": "computation_only", "description": { "en": "Computers checked formally encoded mathematical derivations; proof discovery was not the central AI role.", "zh-CN": "计算机负责检查形式编码的数学推导；自动发现证明并非核心 AI 角色。" } }, "human_contribution": { "description": { "en": "De Bruijn designed the formal language and the methodology for encoding mathematical texts for mechanical checking.", "zh-CN": "de Bruijn 设计形式语言及把数学文本编码为可机械检查表示的方法。" } }, "systems": [ "automath" ], "organizations": [ "eindhoven-university-of-technology" ], "people": [ "nicolaas-govert-de-bruijn" ], "problems": [ "formal-mathematical-knowledge" ], "methods": [ "dependent-types", "proof-checking", "formalization" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1968-12-16", "status": "paper_released", "evidence_level": "E2", "note": { "en": "TU/e and the Automatic Demonstration proceedings establish the early Automath language and its purpose.", "zh-CN": "TU/e 与 Automatic Demonstration 会议文献确认了早期 Automath 语言及其目标。" } } ] }, "sources": [ { "id": "tue-automath-language-1968", "tier": "S1", "type": "paper", "title": "AUTOMATH, a language for mathematics", "url": "https://research.tue.nl/en/publications/automath-a-language-for-mathematics/", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "automath", "formalization", "proof-checking", "formal-mathematics" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1965-resolution-principle", "slug": "resolution-principle", "title": { "en": "Robinson's resolution principle establishes a machine-oriented foundation for automated deduction", "zh-CN": "Robinson 归结原理建立面向机器的自动演绎基础" }, "dates": { "event": "1965-01-01", "first_public_claim": "1965-01-01", "paper_release": "1965-01-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "infrastructure" ], "significance": { "tier": "H2", "rationale": { "en": "Robinson's resolution principle supplied a machine-oriented inference rule and unification-centered framework that became foundational to automated first-order theorem proving.", "zh-CN": "Robinson 的归结原理提供面向机器的推理规则与以合一为核心的框架，成为一阶自动定理证明的基础方法之一。" } }, "mathematical_novelty": { "type": "new_algorithm" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "J. A. Robinson introduced a resolution-based procedure for first-order predicate logic designed to improve the efficiency and practical applicability of machine theorem proving.", "zh-CN": "J. A. Robinson 提出面向一阶谓词逻辑的归结式过程，旨在提升机器定理证明的效率与实际适用范围。" }, "summary": { "en": "The method combines substitution through unification with a single resolution inference scheme, replacing less efficient alternating procedures used in earlier machine theorem proving.", "zh-CN": "该方法通过合一处理代换，并使用统一的归结推理模式，取代早期机器定理证明中效率较低的交替过程。" }, "why_it_matters": { "en": "Resolution became one of the central algorithmic foundations of automated deduction, logic programming and many later theorem-proving systems.", "zh-CN": "归结后来成为自动演绎、逻辑程序设计及大量后续定理证明系统的核心算法基础之一。" }, "ai_role": { "level": "computation_only", "description": { "en": "The event concerns an algorithmic inference method designed for machine reasoning rather than an AI system producing a new mathematical theorem.", "zh-CN": "该事件的核心是为机器推理设计的算法推理方法，而非 AI 系统产生新的数学定理。" } }, "human_contribution": { "description": { "en": "J. A. Robinson developed and analyzed the resolution principle and its machine-oriented logical formulation.", "zh-CN": "J. A. Robinson 提出并分析归结原理及其面向机器的逻辑形式。" } }, "systems": [], "organizations": [ "argonne-national-laboratory" ], "people": [ "j-a-robinson" ], "problems": [ "first-order-theorem-proving" ], "methods": [ "resolution", "unification", "automated-deduction" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1965-01-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The JACM research record establishes the resolution principle and its machine-theorem-proving motivation.", "zh-CN": "JACM 研究记录确认了归结原理及其机器定理证明动机。" } } ] }, "sources": [ { "id": "acm-robinson-resolution-1965", "tier": "S1", "type": "paper", "title": "A Machine-Oriented Logic Based on the Resolution Principle", "url": "https://doi.org/10.1145/321250.321253", "primary": true, "published_date": "1965-01-01", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "resolution", "unification", "automated-deduction", "theorem-proving" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1961-saint", "slug": "saint-symbolic-integration", "title": { "en": "SAINT applies heuristic AI to symbolic integration", "zh-CN": "SAINT 将启发式人工智能用于符号积分" }, "dates": { "event": "1961-05-10", "first_public_claim": "1961-05-10", "paper_release": "1961-05-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "system" ], "significance": { "tier": "H2", "rationale": { "en": "SAINT was an early AI system for mathematical problem solving that used heuristic search to perform symbolic integration rather than relying only on a fixed algebraic procedure.", "zh-CN": "SAINT 是早期 AI 数学问题求解系统之一，通过启发式搜索执行符号积分，而非仅依赖固定代数算法。" } }, "mathematical_novelty": { "type": "tooling_only" }, "interfaces": [ "symbolic" ], "claim": { "en": "James Slagle's Symbolic Automatic INTegrator applied heuristic problem-solving strategies to freshman-calculus integration problems and documented the system in a Lincoln Laboratory report dated 10 May 1961.", "zh-CN": "James Slagle 的 Symbolic Automatic INTegrator 将启发式问题求解策略用于大学基础微积分积分题，并在 1961 年 5 月 10 日的 Lincoln Laboratory 报告中记录该系统。" }, "summary": { "en": "SAINT represented integration as a search problem, using rules of thumb to choose transformations and substitutions that reduced an integral toward solvable forms.", "zh-CN": "SAINT 将积分表示为搜索问题，利用经验规则选择变换与代换，把积分逐步化为可求解形式。" }, "why_it_matters": { "en": "It is an early bridge between symbolic mathematics and AI-style heuristic reasoning, anticipating later symbolic mathematical problem-solving systems.", "zh-CN": "它是符号数学与 AI 式启发推理之间的早期桥梁，并预示了后来的符号数学问题求解系统。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The program chose integration transformations through automated heuristic search.", "zh-CN": "程序通过自动启发式搜索选择积分变换。" } }, "human_contribution": { "description": { "en": "James Slagle designed the heuristic knowledge, search strategy, implementation and evaluation.", "zh-CN": "James Slagle 设计启发知识、搜索策略、实现与评测。" } }, "systems": [ "saint" ], "organizations": [ "mit-lincoln-laboratory" ], "people": [ "james-slagle" ], "problems": [ "symbolic-integration" ], "methods": [ "heuristic-search", "symbolic-computation" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1961-05-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The Lincoln Laboratory report and later JACM paper document SAINT and its integration experiments.", "zh-CN": "Lincoln Laboratory 报告与后续 JACM 论文记录了 SAINT 及其积分实验。" } } ] }, "sources": [ { "id": "acm-saint-symbolic-integration", "tier": "S1", "type": "paper", "title": "A Heuristic Program that Solves Symbolic Integration Problems in Freshman Calculus", "url": "https://doi.org/10.1145/321186.321193", "primary": true, "published_date": null, "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "saint", "symbolic-integration", "heuristic-search", "symbolic-ai" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1960-geometry-theorem-machine", "slug": "geometry-theorem-machine", "title": { "en": "The Geometry Theorem Machine demonstrates heuristic proof search in Euclidean geometry", "zh-CN": "Geometry Theorem Machine 展示欧氏几何中的启发式证明搜索" }, "dates": { "event": "1960-05-03", "first_public_claim": "1960-05-03", "paper_release": "1960-05-03", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Gelernter's Geometry Theorem Machine extended early symbolic AI from propositional-style proof search to diagram-grounded Euclidean geometry and documented machine solutions to textbook and examination problems.", "zh-CN": "Gelernter 的 Geometry Theorem Machine 将早期符号 AI 从命题式证明搜索推进到结合图形信息的欧氏几何，并记录了机器解决教材与考试几何题的能力。" } }, "mathematical_novelty": { "type": "rediscovery" }, "interfaces": [ "symbolic", "hybrid" ], "claim": { "en": "The 1960 public evaluation documented that the IBM 704 Geometry Theorem Machine had begun proving elementary Euclidean geometry theorems in spring 1959 and subsequently solved a range of textbook and examination problems.", "zh-CN": "1960 年公开评估记录表明，IBM 704 上的 Geometry Theorem Machine 在 1959 年春已开始证明初等欧氏几何定理，随后解决了多类教材与考试问题。" }, "summary": { "en": "The system combined symbolic deduction with geometric information to prune implausible proof paths, demonstrating an early form of domain-informed heuristic reasoning.", "zh-CN": "系统把符号演绎与几何信息结合，用于剪除不合理的证明路径，展示了早期的领域知识驱动启发式推理。" }, "why_it_matters": { "en": "It broadened the scope of AI theorem proving beyond formal logic exercises and showed how mathematical structure and auxiliary representations could guide search.", "zh-CN": "它把 AI 定理证明从形式逻辑练习扩展到几何问题，并展示数学结构与辅助表示如何引导搜索。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The program selected deductions and searched for geometry proofs using symbolic and geometric heuristics.", "zh-CN": "程序利用符号与几何启发式自动选择推导并搜索几何证明。" } }, "human_contribution": { "description": { "en": "Herbert Gelernter and collaborators designed the representation, heuristics, implementation and evaluation problems.", "zh-CN": "Herbert Gelernter 与合作者设计问题表示、启发式、实现与评测题目。" } }, "systems": [ "geometry-theorem-machine" ], "organizations": [ "ibm-research" ], "people": [ "herbert-gelernter" ], "problems": [ "euclidean-geometry-theorem-proving" ], "methods": [ "heuristic-search", "symbolic-reasoning", "geometric-reasoning" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1960-05-03", "status": "paper_released", "evidence_level": "E2", "note": { "en": "IBM and the published research record document the system and its 1959–1960 geometry experiments.", "zh-CN": "IBM 与公开研究记录确认了该系统及其 1959–1960 年几何实验。" } } ] }, "sources": [ { "id": "ibm-geometry-theorem-machine-1960", "tier": "S1", "type": "paper", "title": "Empirical Explorations of the Geometry Theorem Machine", "url": "https://research.ibm.com/publications/empirical-explorations-of-the-geometry-theorem-machine", "primary": true, "published_date": "1960-05-03", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [ "evt-1977-wu-method" ], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "geometry", "theorem-proving", "symbolic-ai", "heuristic-search" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1956-logic-theorist", "slug": "logic-theorist", "title": { "en": "Logic Theorist demonstrates machine-generated proofs in symbolic logic", "zh-CN": "Logic Theorist 展示机器生成的符号逻辑证明" }, "dates": { "event": "1956-09-10", "first_public_claim": "1956-09-10", "paper_release": "1956-09-10", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "proof", "system" ], "significance": { "tier": "H2", "rationale": { "en": "Logic Theorist is a foundational early example of artificial intelligence applied directly to mathematical proof, using heuristic search to construct proofs of symbolic-logic propositions.", "zh-CN": "Logic Theorist 是人工智能直接用于数学证明的奠基性早期案例之一，通过启发式搜索构造符号逻辑命题的证明。" } }, "mathematical_novelty": { "type": "rediscovery" }, "interfaces": [ "formal", "symbolic" ], "claim": { "en": "Newell, Shaw and Simon presented the Logic Theory Machine in 1956 as a program that searched for proofs of propositions from Principia Mathematica using symbolic representations and heuristics.", "zh-CN": "Newell、Shaw 与 Simon 于 1956 年公开 Logic Theory Machine，通过符号表示与启发式搜索为《Principia Mathematica》中的命题寻找证明。" }, "summary": { "en": "The system encoded logical expressions and searched a space of permissible transformations, prioritizing promising branches with heuristics rather than exhaustive enumeration.", "zh-CN": "系统编码逻辑表达式并搜索允许的变换空间，利用启发式优先探索更有希望的分支，而非完全穷举。" }, "why_it_matters": { "en": "It established mathematical theorem proving as one of the earliest concrete demonstrations of symbolic AI and set a durable precedent for treating proof search as intelligent problem solving.", "zh-CN": "它把数学定理证明确立为符号 AI 最早的具体展示场景之一，并为把证明搜索视作智能问题求解建立了长期先例。" }, "ai_role": { "level": "autonomous_primary", "description": { "en": "The program selected transformations and assembled proofs through automated heuristic search.", "zh-CN": "程序通过自动启发式搜索选择变换并组装证明。" } }, "human_contribution": { "description": { "en": "Researchers designed the representation, heuristics, search procedure and evaluation corpus.", "zh-CN": "研究者设计符号表示、启发式、搜索过程与评测命题。" } }, "systems": [ "logic-theorist" ], "organizations": [ "rand-corporation", "carnegie-tech" ], "people": [ "allen-newell", "cliff-shaw", "herbert-simon" ], "problems": [ "symbolic-logic-theorem-proving" ], "methods": [ "heuristic-search", "symbolic-reasoning", "proof-search" ], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "1956-09-10", "status": "paper_released", "evidence_level": "E2", "note": { "en": "RAND P-868 records the 1956 Logic Theory Machine and its symposium presentation.", "zh-CN": "RAND P-868 记录了 1956 年 Logic Theory Machine 及其研讨会发表。" } } ] }, "sources": [ { "id": "rand-logic-theory-machine-p868", "tier": "S1", "type": "paper", "title": "The Logic Theory Machine — A Complex Information Processing System", "url": "https://www.rand.org/pubs/papers/P868.html", "primary": true, "published_date": "1956-09-10", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": true, "significance": "primary" }, "tags": [ "logic-theorist", "symbolic-ai", "theorem-proving", "heuristic-search" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] }, { "schema_version": 1, "id": "evt-1955-dartmouth-ai-proposal", "slug": "dartmouth-ai-proposal", "title": { "en": "The Dartmouth proposal frames artificial intelligence as a research program", "zh-CN": "达特茅斯提案将“人工智能”明确提出为研究计划" }, "dates": { "event": "1955-08-31", "first_public_claim": "1955-08-31", "paper_release": "2006-12-01", "artifact_release": null, "independently_verified": null, "added_to_chronicle": "2026-09-15", "last_updated": "2026-09-15" }, "event_types": [ "field_building" ], "significance": { "tier": "H3", "rationale": { "en": "The Dartmouth proposal is broad AI history rather than a mathematics-specific result, but it supplies the field-formation context from which symbolic reasoning, theorem proving and machine mathematical problem solving soon emerged.", "zh-CN": "达特茅斯提案属于广义人工智能史而非数学专属成果，但它提供了符号推理、自动定理证明与机器数学求解随后发展的学科起点背景。" } }, "mathematical_novelty": { "type": "not_applicable" }, "interfaces": [ "not_applicable" ], "claim": { "en": "The proposal dated 31 August 1955 proposed a 1956 Dartmouth summer research project under the name “artificial intelligence” and treated learning, abstraction, reasoning and problem solving as machine-research problems.", "zh-CN": "1955 年 8 月 31 日的提案为 1956 年达特茅斯夏季研究计划提出“人工智能”这一名称，并把学习、抽象、推理与问题求解作为机器智能研究问题。" }, "summary": { "en": "The proposal did not establish AI4Math as a separate field. It established the broader AI research frame within which mathematical reasoning became one of the earliest domains for testing machine intelligence.", "zh-CN": "该提案并未建立独立的 AI4Math 领域，但确立了更广义的 AI 研究框架，而数学推理很快成为检验机器智能的早期核心场景之一。" }, "why_it_matters": { "en": "It provides the historical vocabulary and institutional starting point for understanding why Logic Theorist and other early mathematical reasoning programs were regarded as artificial-intelligence research.", "zh-CN": "它提供了理解 Logic Theorist 等早期数学推理程序为何被视为人工智能研究的历史术语与制度起点。" }, "ai_role": { "level": "not_applicable", "description": { "en": "This is a field-formation event; no AI system performed mathematical work in the event itself.", "zh-CN": "这是领域形成事件；事件本身没有 AI 系统执行数学任务。" } }, "human_contribution": { "description": { "en": "John McCarthy, Marvin Minsky, Nathaniel Rochester and Claude Shannon formulated the proposal and organized the research program.", "zh-CN": "John McCarthy、Marvin Minsky、Nathaniel Rochester 与 Claude Shannon 制订提案并组织研究计划。" } }, "systems": [], "organizations": [ "dartmouth-college" ], "people": [ "john-mccarthy", "marvin-minsky", "nathaniel-rochester", "claude-shannon" ], "problems": [], "methods": [], "verification": { "evidence_level": "E2", "status": "paper_released", "formal_assurance": "none", "history": [ { "date": "2006-12-01", "status": "paper_released", "evidence_level": "E2", "note": { "en": "The AI Magazine archival publication reproduces and dates the original Dartmouth proposal.", "zh-CN": "AI Magazine 的档案性发表重现并明确标注了原始达特茅斯提案日期。" } } ] }, "sources": [ { "id": "aimag-dartmouth-proposal", "tier": "S1", "type": "paper", "title": "A Proposal for the Dartmouth Summer Research Project on Artificial Intelligence", "url": "https://doi.org/10.1609/aimag.v27i4.1904", "primary": true, "published_date": "2006-12-01", "accessed_at": "2026-09-15" } ], "artifacts": [], "relationships": { "predecessors": [], "successors": [], "related": [] }, "timeline": { "featured": false, "significance": "context" }, "tags": [ "artificial-intelligence", "dartmouth", "field-formation", "history-of-ai" ], "editorial": { "created_at": "2026-09-15", "last_reviewed": "2026-09-15", "reviewers": [ "Charlie-Wang-03" ] }, "corrections": [] } ] }