The mathematicians’ statement is relayed by Hacker News.
Tristan Buckmaster and Levent Alpöge claimed that they proved that a singularity, a situation in which a quantity becomes infinite, forms in finite time in the three-dimensional incompressible Euler equation. TechCrunch identifies Buckmaster as an NYU mathematics professor and reports that he announced three proofs.
Scientific American reports that three mathematicians published a proof showing that the singularity disappears if the external force is removed.
Scientific American concludes that OpenAI’s approach cannot be extended to the full problem without a specially constructed external force.
Claim check:
- Tristan Buckmaster and Levent Alpöge claimed that they proved that a singularity forms in finite time in the three-dimensional incompressible Euler equation. (confirmed only by the carrying publication: evidence; «Tristan Buckmaster and Levent Alpoge claim to have proven finite-time blowup for 3D incompressible Euler using LLMs»)
- TechCrunch identifies Buckmaster as an NYU mathematics professor and reports that he announced three proofs. (confirmed by the publication itself: evidence; «NYU mathematics professor Tristan Buckmaster announced three proofs on Tuesday»)
- Scientific American reports that three mathematicians published a proof showing that the singularity disappears if the external force is removed. (confirmed by the publication itself: evidence; «the new work released last Thursday shows unequivocally that if the force is removed, the blowup will disappear.»)
- Scientific American concludes that OpenAI’s approach cannot be extended to the full problem without a specially constructed external force. (confirmed by the publication itself: evidence; «OpenAI’s method can never work, in fact, without using a very contrived equation for the force»)
Publications:
- https://mastodon.social/@tristanbuckmaster/117233413705701198
- https://reddit.com/r/codex/s/psWHRr9864
- https://firstpost.com/tech/has-openai-model-solved-80-year-old-navier-stokes-problem-mathematician-raises-questions-14044080.html
- https://nytimes.com/2026/09/08/science/what-is-navier-stokes.html
- https://lesswrong.com/posts/yekQKwmQJNk7thDtQ/openai-have-solved-the-navier-stokes-problem-with-a
- https://techcrunch.com/2026/09/08/openai-fought-dirty-on-career-making-math-problem-says-nyu-mathematician
- https://nytimes.com/2026/09/08/science/openai-proof-millennium-problem.html
- https://simonwillison.net/2026/Sep/8/on-navier-stokes
- https://latent.space/p/ainews-openai-reports-navier-stokes
- https://science.org/content/article/how-ai-math-breakthrough-ignited-controversy
- https://lesswrong.com/posts/ZGme2YKjjAdBPtxsp/it-s-fair-to-say-we-now-have-a-country-of-geniuses-in-a
- https://scottaaronson.blog/?p=10062
- https://wired.com/story/mathematicians-cant-quit-ai
- https://terrytao.wordpress.com/2026/09/21/advisory-group-on-mathematics-and-artificial-intelligence
- https://techcrunch.com/2026/09/21/openai-forms-math-advisory-group-as-its-ai-resolves-more-than-100-open-problems
- https://scientificamerican.com/article/did-openai-solve-the-wrong-navier-stokes-problem
Primary sources:
- https://cims.nyu.edu/~tristanb/statement.pdf
- https://cims.nyu.edu/~tristanb/euler.pdf
- https://cims.nyu.edu/~tristanb/ipm.pdf
- https://cims.nyu.edu/~tristanb/boussinesq.pdf
- https://help.openai.com/en/articles/5722486-how-your-data-is-used-to-improve-model-performance
- https://openai.com/index/navier-stokes-solution
- https://claymath.org/millennium-problems
- https://x.com/openai/status/2097374640582668336?s=12
- https://twitter.com/sama/status/2097385167002415140
- https://openai.com/index/previewing-ultrafast
- https://openai.com/index/hugging-face-incident-and-the-road-ahead
- https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8a9a/navier-stokes.pdf
- https://linkedin.com/posts/sebastien-bubeck-6b558a1a5_i-would-like-to-clarify-a-few-things-1-activity-7503148080888893440-Ny3E
- https://eccc.weizmann.ac.il/report/2026/155
- https://arxiv.org/abs/2608.11195
- https://www.anthropic.com/research/formalizing-fermats-last-theorem
- https://arxiv.org/abs/2609.02865
- https://arxiv.org/abs/2609.13032
- https://arxiv.org/abs/2607.29686
- https://arxiv.org/abs/2608.19158
- https://mathandai.org/
- https://openai.com/index/advisory-group-on-mathematics-and-ai
- https://agmai.org/
- https://arxiv.org/html/2609.20803v1
- https://claymath.org/wp-content/uploads/2022/06/navierstokes.pdf
score 56.9 out of 100 · kind: announcement · update 17