OpenAI says an internal AI model has generated a solution to the Navier-Stokes existence and smoothness problem, one of mathematics’ seven Millennium Prize Problems.
The company released a 165-page proof and a formalization in Lean, but said it would not pursue the associated $1 million prize.
According to OpenAI, about 10,000 AI agents worked in parallel for 88 hours to develop the proposed solution, which describes a possible finite-time blowup in fluid equations.
The proof was checked using Lean, a system designed to verify mathematical reasoning. OpenAI said no specific user data was accessed, while acknowledging that de-identified product data could not be ruled out in model training. Independent mathematical scrutiny will be needed to determine whether the claimed solution is valid.
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OpenAI Says It Has Solved a Millennium Prize Problem—a Holy Grail of Math https://t.co/o1DPiW1jbR
— WSJ Business News (@WSJbusiness) September 8, 2026
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