We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.
Rules for the Millennium Prize Problems
The revised rules for the Millennium Prize Problems were adopted by the Board of Directors of the Clay Mathematics Institute on 26 September, 2018. Please read this document carefully before contacting CMI about a proposed solution. In particular, please note that:
NIK on Twitter / X
>sam altman: "we tried this because there were rumor on the internet">rumor: math professor close to solving navier-stokes>the professor: using codex for a year>openai: has all his logs>checked every codex session tagged to N-S>found the most promising one>spun up 10,000… pic.twitter.com/RInlP88gmA— NIK (@ns123abc) September 8, 2026
Navier-Stokes Equation - Clay Mathematics Institute
This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
GitHub - openai/NavierStokesAndEuler at 8937a8f4cbc7abaab5e9e97d1cc7f5d2319d9538
Lean certificates accompanying Navier-Stokes and Euler results - openai/NavierStokesAndEuler
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Bartosz Naskręcki on Twitter / X
Congrats to @LechMazur for the solution and to Terence Tao for the digestion and storytelling. You see the trend. Mathematicians are still needed if we want to make any sense of the formal proofs. For now... Maybe the next gen LLMs will simply read allthe blogs of Terry and… https://t.co/yXiISCrNAF— Bartosz Naskręcki (@nasqret) August 13, 2026
Daron Acemoglu on Twitter / X
I recommend Columbia mathematician Michael Harris’s wide-ranging, informative and thought-provoking essay in Boston Review on AI and mathematics:https://t.co/txwAd8ri4xHarris rightly worries about the possible negative effects of AI-generated proofs and mathematics on…— Daron Acemoglu (@DAcemogluMIT) June 16, 2026
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Michael Truell on Twitter / X
We believe Cursor discovered a novel solution to Problem Six of the First Proof challenge, a set of math research problems that approximate the work of Stanford, MIT, Berkeley academics. Cursor's solution yields stronger results than the official, human-written solution.…— Michael Truell (@mntruell) March 3, 2026
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