OpenAI claims an AI solution to the Navier–Stokes Millennium Prize problem
An internal OpenAI system produced a proof, formalized in Lean, that 3D fluid equations can blow up in finite time. It came 12 hours after related work by mathematicians, and credit is disputed.
OpenAI says the proof shows an initially smooth fluid with a smooth applied force can develop a singularity in finite time, settling the problem in the negative. It used a model it calls “significantly more capable than GPT-6 Astra”; Quanta reports about 10,000 agents ran for 88 hours. Charles Fefferman, who wrote the Clay Institute’s problem statement, welcomed the result.
Hours earlier, Tristan Buckmaster of NYU and Levent Alpöge of Anthropic had announced AI-assisted results on closely related problems. Buckmaster suggested OpenAI benefited from their work; OpenAI says it did not see it. Clay rules require two years after publication before any prize.
Index treatment. None yet. Lab claims do not move the Index. If mathematicians accept the proof, Research-level mathematics moves in a new entry citing that acceptance.