OpenAI claims Navier-Stokes blow-up proof; mathematicians dispute credit
OpenAI said an internal model beyond GPT-6 Astra, run as about 10,000 parallel agents for 88 hours, proved that a smooth forced 3D fluid starting at rest can develop a finite-time singularity, which would answer the Millennium Prize problem in the negative; it released a Lean check and a companion Euler result. NYU's Tristan Buckmaster said the approach followed unpublished work by him and Anthropic's Levent Alpöge and alleged pressure over authorship; OpenAI denies seeing it and will not claim the prize, and no independent acceptance has yet been reported.
Why it matters
It is the biggest AI maths claim yet and a test of credit, data use and verification norms when frontier labs do research.
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- DevelopmentOpenAI publishes a batch of new maths results from an internal model, with Lean proofs6 Oct 2026 · Research · USLed to: Comes after the disputed Navier-Stokes claim, with more transparency about method
- DevelopmentOpenAI model disproves Erdős's 1946 unit-distance conjecture20 May 2026 · Research · USFollows from: Escalation from an Erdős problem to a Millennium problem
- DevelopmentClaude completes first end-to-end Lean formal proof of Fermat's Last Theorem4 Sep 2026 · Research · US, GBContrasts with: Formal verification of a known proof versus a new claimed proof
What led here
Earlier developments on the same thread
- DevelopmentDeepMind study: most AI 'solutions' to open Erdős problems were already in the literature29 Jan 2026 · Research · GB, US
- DevelopmentOpenAI, Anthropic and Google offer frontier AI to US agencies for about $1 via GSA6 Aug 2025 · Procurement · US
- DevelopmentGemini Deep Think earns officially graded gold-medal score at IMO 202521 Jul 2025 · Research · GB, US
- DevelopmentGoogle DeepMind's AlphaEvolve agent improves algorithms and open maths bounds14 May 2025 · Research · GB, US
What happened next
Later developments on the same thread
- DevelopmentOpenAI ties large reasoning-distillation campaign to people linked to Moonshot AI30 Sep 2026 · Incident · US, CN
Same story elsewhere
What other countries and bodies did on this
- DevelopmentAI systems from Huawei and Xiaohongshu reported to score 42/42 at IMO 202623 Jul 2026 · Research · CN, INTL
- DevelopmentIndia hosts AI Impact Summit in New Delhi, first in the series in the Global South16 Feb 2026 · Statement · IN, INTL
- DevelopmentEU publishes General-Purpose AI Code of Practice ahead of AI Act model duties10 Jul 2025 · Rule change · EU
- DevelopmentDeepSeek releases R1 reasoning model with open weights under MIT licence20 Jan 2025 · Model release · CN
Threads by topic: Mathematics Frontier models