OpenAI Claims Navier-Stokes Proof and Substantial Progress on a Second Millennium Prize Problem

OpenAI 宣称已解决七大千禧年大奖难题之一的 Navier-Stokes 方程问题，并表示在另一个千禧难题上取得实质性进展，相关成果「正在斟酌如何妥善分享」。证明由约 1 万个 agent 组成的集群产出 forced blowup（强制爆破）构造，并附带 Lean 4 机器可验证的形式化证明；据 John D. Cook 估算，该形式化验证仅耗时约 17 小时，远低于传统人工形式化的速度。NYT 报道披露 OpenAI 抢先于 NYU 数学家 Tristan Buckmaster 团队发布了结果。

已确认

• OpenAI 在周三晚间声明及对《纽约时报》的表态中称，已完成 Navier-Stokes 存在性与光滑性问题的证明，并在另一个未指明的千禧年大奖难题上取得实质性进展，正考虑如何公布
• 证明以约 1 万个 agent 集群产出 forced blowup 构造，涡旋不断加速旋转并向极小区域坍缩，总动能保持有界，同时发布 Lean 4 形式化证明（验证约 17 小时）
• 《纽约时报》报道，NYU 的 Tristan Buckmaster 与合作者整个 8 月在 Navier-Stokes 上取得重大进展，但 OpenAI 在不到一周内抢先公布；Buckmaster 与 Levent Alpöge 的独立工作同样重度依赖 Lean 验证
• Clay 研究所七大千禧难题每个悬赏 100 万美元，庞加莱猜想已被解决

尚未确认

• 第二个千禧难题具体是哪一道、成果内容如何，OpenAI 均未披露
• 网友 ChrisGPT 分析称 OpenAI 内部模型给出了解的构造性证明且经得起推敲，但这属于个人观点，仍待官方审核流程
• 用户 l4rz 转述匿名帖称该证明本质是「逆问题」解法：先选定平均流、反推所需应力、再构造振荡解；其真实性无法核实
• 围绕构造的争议：被引用的分析指出 OpenAI 用特制光滑外力驱动有限时间奇点，并论证这符合 Clay 陈述中 C、D 两种允许受力的破裂情形，但若验证不通过则不算真正解开原题

为什么重要

• 若证明成立，这将是 AI 系统攻克顶级数学难题的标志性案例，直接关联递归自我改进讨论：Andy Masley 等人认为 AI 若能持续解千禧难题，将同样加速 AI 研究本身；robleclerc 则反问，能解千禧难题的 AI 也应能缓解 AI 安全风险
• Lance Fortnow 与 Csaba Szepesvari 均注意到两组 Navier-Stokes 工作都重度依赖 Lean 形式化，讨论这是否会成为数学发表的新门槛
• 数学界反应分化：PDE 分析师 Scott Armstrong 以社区口吻「求饶」，调侃组合数学等其他领域将被逐一「针对」

2026-09-10 ~ 2026-09-11 · 21 related posts

Full story(7 episodes)→

• Episode 1: Rumors claim GPT-6 cracks Navier-Stokes, credibility doubtful(2026-09-05, 2 posts)
• Episode 2: OpenAI Claims 10,000 Agents Solved Navier-Stokes in 88 Hours(2026-09-09, 13 posts)
• Episode 3: Existence Proof Effect: Rumor of Solvability Drove OpenAI's Navier-Stokes Attempt(2026-09-09, 3 posts)
• Episode 4: Rumors swirl that OpenAI's internal model Bel is cracking Millennium Prize problems(2026-09-10, 27 posts)
• Episode 5: OpenAI Claims Navier-Stokes Proof and Substantial Progress on a Second Millennium Prize Problem(2026-09-10, 21 posts)
• Episode 6: AI Circles Speculate Millennium Prize Problems May Fall to AI(2026-09-11, 2 posts)
• Episode 7: Report: OpenAI's internal model targets Riemann Hypothesis and P vs NP(2026-09-11, 4 posts)

• OpenAI and Alpöge-Buckmaster both leaned on Lean for Navier-Stokes claims — fortnow · 2026-09-10
• Lean verification in Navier-Stokes announcements: is formal proof checking the new publishing bar? — CsabaSzepesvari · 2026-09-10
• OpenAI claims Navier-Stokes breakthrough, says another Millennium Prize problem near — basedjensen · 2026-09-10
• OpenAI says it has made substantial progress on another Millennium Prize problem — ilkamoi · 2026-09-11
• After Navier-Stokes, researchers report substantial progress on another Millennium Prize problem — soumitrashukla9 · 2026-09-11
• Report: OpenAI Confirms Substantial Progress on Hodge Conjecture Within Five Days — AI寒武纪 · 2026-09-11
• If AI can crack Millennium Prize problems, it can mitigate AI risk too — robleclerc · 2026-09-11
• OpenAI confirms progress on second Millennium Prize problem, sparking RSI debate — AndyMasley · 2026-09-11
• NYT: OpenAI Claims Substantial Progress on a Second Millennium Prize Problem — rohanpaul_ai · 2026-09-11
• PDE Mathematicians Joke-Beg OpenAI to Solve Another Millennium Problem Next — jasondeanlee · 2026-09-11
• OpenAI Paper Constructs Finite-Time Blowup for Navier–Stokes, Verified in Lean by GPT-6 Astra — burny_tech · 2026-09-11
• OpenAI's Navier-Stokes proof: Lean 4 verification in 17 hours vs 132,800 person-hours — jedisct1 · 2026-09-11
• ChatGPT predicted in May that Navier-Stokes would be the next Millennium problem solved — Alert_Cookie_633 · 2026-09-11
• OpenAI's Navier–Stokes Claim Under Scrutiny: Forced Singularity Isn't a Full Millennium Proof — basedjensen · 2026-09-11
• Unverified: Anonymous Account Claims OpenAI Solved the Navier-Stokes Millennium Problem — l4rz · 2026-09-11
• [source] OpenAI claims ~10k-agent swarm produced forced Navier-Stokes blowup proof with Lean formalization — thursdai_pod · 2026-09-11

5 near-duplicate retellings: socoolandawesome · Dr_Singularity · Dr_Singularity · rohanpaul_ai · QuintinPope5