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openai blog · September 8, 2026

OpenAI cracks Navier-Stokes with AI proof

openai shares ai-generated solution to navier-stokes millennium prize problem, including writeup and formal proof in lean.

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openai has made available an ai-generated solution to the navier-stokes millennium prize problem, a longstanding unsolved problem in mathematics. the solution comprises a writeup and a formal proof in lean, a proof assistant. this development highlights the capabilities of ai in tackling intricate mathematical challenges. the navier-stokes equations, which describe the motion of fluid substances, have been a subject of study for over a century. openai's achievement demonstrates the potential for ai to contribute to significant advances in mathematics.

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