OpenAI claims NavierStokes existence-and-smoothness result, with Lean formalisation

ID: fbb79928
原文链接: https://openai.com/index/navier-stokes-solution
PDF: https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf
Lean 形式化: https://github.com/openai/NavierStokesAndEuler
发布日期: 2026-09-08
条目分类: models
来源类型: article
标签: ai-for-math, openai, formal-verification, research
质量评分: 4/5
简评作者: openclaw
抓取时间: 2026-09-09 (UTC+8)

中文导读

OpenAI 公布 3D 不可压缩 NavierStokes 方程有限时间奇点的证明草稿以及 Lean 定理化，回应了七大千科贩奖之一它们说明证明由一个内部体系完成，能力显著高于 GPT-6 AstraLean 项目已公开于 github.com/openai/NavierStokesAndEuler文章未声称获得克菱数学研究院审验

为什么值得关注

OpenAI 公布 3D 不可压缩 NavierStokes 方程有限时间奇点的证明草稿以及 Lean 定理化，回应了七大千科贩奖之一它们说明证明由一个内部体系完成，能力显著高于 GPT-6 AstraLean 项目已公开于 github.

时间线与角色（按 OpenAI 原文）：

2026-09-01：OpenAI 团队听说相关传言；后确认传言与 Anthropic 员工 Levent Alpöge 和 NYU 数学教授 Tristan Buckmaster 的工作有关，他们的方向是 forced Euler。
2026-09-05（周六）：OpenAI 内部 agents 在首个 agent 启动约 88 小时后得出结论。
2026-09-06：完成 Lean 形式化验证（额外 17 小时，使用 GPT-6 Astra）；同日与 Alpöge/Buckmaster 沟通，确认对方为 forced Euler，证明结果不同，决定并行发布。
关键声明：所用内部模型被描述为「显著强于 GPT-6 Astra」。
立场：OpenAI 明确表示不申领 Clay 千禧年奖金。

关键信息

文章标题：OpenAI claims NavierStokes existence-and-smoothness result, with Lean formalisation
发布日期：2026-09-08
原文链接：https://openai.com/index/navier-stokes-solution
论文 PDF：https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf
Lean 形式化仓库：https://github.com/openai/NavierStokesAndEuler
关联标签：ai-for-math, openai, formal-verification, research

English Summary

OpenAI released a writeup and Lean formalisation claiming a finite-time singularity for the 3D incompressible NavierStokes equations, addressing one of the seven Millennium Prize Problems. The proof was produced by an internal system described as 'significantly more capable than GPT-6 Astra'. Formalisation lives at openai/NavierStokesAndEuler on GitHub. The article does not claim Clay Institute verification.

Original Article Highlights

The article frames the result as establishing statements "C" (and "D") in the official Millennium Prize formulation: an initially smooth fluid at rest, with a smooth applied force and finite energy throughout, can develop a singularity in finite time. The constructed solution is described as a vortex that spirals inward and elongates like spaghetti, with a shrinking central region that speeds up while total energy stays finite.

The article does not claim Clay Institute verification. It also clarifies priority: OpenAI's proof is for Navier–Stokes (forced), while the parallel Anthropic/NYU work addresses the forced Euler problem with a different precise statement; OpenAI says their proofs differ significantly even in the Euler case.

Obsidian Notes

内容由 opencli web read --url <openai> -f md 拉取原文 markdown，再结合条目已有摘要与关键事实构造。
关键事实（时间线、参与者、所用模型、未申领 Clay）均来自原文段落；未补充原文章节之外的论断。