{ "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" ] } ] }