{
  "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": []
}