OpenAI claims to have solved a Millennium Prize Problem

OpenAI claims to have solved a Millennium Prize Problem — no proof yet

Mathematician Tristan Buckmaster said OpenAI told him an internal model produced a blow-up proof for the Navier–Stokes equations with an external force, but the document has not been published, there is no independent verification, and the Clay Mathematics Institute still lists the problem as unsolved.

Compiled by Sergey KostenchukPublished 2026-09-08Updated 2026-09-18

2026-09-08 Research OpenAI

🤖 OpenAI claims to have solved a Millennium Prize Problem — but there is no proof

Mathematician Tristan Buckmaster (NYU Courant) said: On September 6, during calls with OpenAI’s head of math Sébastien Bubeck, he was told that an internal model had produced a “blow-up” proof for the Navier–Stokes equations with an external force — about 100 pages. The document has not been published, there is no verification, and the Clay Mathematics Institute lists the problem as unsolved.

🌍 If confirmed, this would be the first time an AI has solved a Millennium Prize Problem with a $1 million prize. The mechanism has already been demonstrated: a human using an LLM (Claude, OpenAI Codex) took a “forced” blow-up program to the Euler equations in a month; the first result was verified in Lean.

👤 It is too early to declare victory: no one has seen the proof, and the external force is a possible loophole in the Clay condition. Watch for OpenAI’s preprint and Lean certificate, and the Clay Mathematics Institute’s position.

Source 1: https://cims.nyu.edu/~tristanb/statement.pdf

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