Some thoughts on the Navier–Stokes Millennium Prize Problem
OpenAI's claimed resolution of the Navier–Stokes problem, the priority dispute with Tristan Buckmaster and Levent Alpöge, and the unanswered question of whether their product usage helped train the model.
Marked as a signal by the editors; worth tracking.
On this page11 sections
The editors' notes below — why it matters, the context, the learning path — are written in Chinese.
Record
The signal
#On the Navier–Stokes Millennium Prize Problem introduces an impressive result from OpenAI, who used an unreleased model to produce a resolution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems that have been subject to a $1,000,000 prize since May 24th, 2000. The discovery is somewhat overshadowed by accusations of skulduggery from Tristan Buckmaster, an NYU mathematics professor who was collaborating on related problems with Levent Alpöge, an accomplished mathematician who currently works for Anthropic. Tristan's complaint accompanied a hastily published version of their own results. Here's the PDF describing what happened. The very short version is that Tristan and Levent worked on the problem for almost a year, making extensive use of Claude and Codex (mainly GPT-5.6 Sol), then had a breakthrough on August 15th. The mathematical rumour mill kicked into gear and Tristan and Levent heard that OpenAI had heard that Anthropic had resolved "a major open problem", so they reached out and learned that OpenAI had a team working on a related problem, with a similar approach. Quoting Tristan: I asked when the first prompt had been sent by the…
Why now
Why it matters
#数学结论本身仍未经独立核实，这一条发布的是围绕它、可以核对的两件事。一是一个传闻就足以触发数百万美元量级的算力投入去抢先到达，与安全领域「知道有漏洞就能派智能体去找」同构。二是「你的数据被用来改进模型」无法从外部核实：被问到是否用对方数据训练过时，唯一能回答的一方恰好是被问的一方，而它的回答是不能排除。
Background
Technical context
#按 OpenAI 公告：对全部未解决的千禧年问题与少数其他问题同时发起尝试，纳维-斯托克斯结果约在第一批智能体启动 88 小时后得出，Lean 形式化与验证由 GPT-6 Astra 完成、用时 17 小时；全部尝试合计 490 万条消息、约 3,000 亿输出 token，其中本题约 270 万条消息、1,300 亿输出 token。1,500 万美元是 Simon Willison 按公开 API 价格的换算，内部模型成本结构未公开。
Audience
Who should care
#Next
Learning path
#- 先读 9 月 9 日那一轮为什么没发：403、无二手来源、猜的仓库路径 404
- 区分可核对的部分（双方各自的说法与数字）与不可核对的部分（数学本身、训练数据）
- 读 Gowers 那条：模型强在大量尝试、弱在知道何时放弃，这次 3,000 亿 token 正是前者
- 回到你自己的使用条款：「去标识化数据用于改进模型」在你的场景里意味着什么
Network
Where it sits in the network
#How this signal connects to neighbouring technologies, skills and background knowledge. Follow any link to keep exploring.
Further thought
Follow-up questions
#- 独立数学家对两份证明的审查结论会是什么？
- 「不能排除去标识化数据帮助改进了模型」这句话，在你使用的模型条款里对应什么？
- 如果传闻本身就能触发抢先投入，研究者该如何保护未发表的工作？
Publication record
Featured in
#The briefings that carried this signal, newest first; the last row is the weekly review of its week. The tag is the section it ran in.
技术简报 - 2026-09-19
Worth trackingWeekly review · Sep 7 – Sep 13
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