One of the options OpenAI put to Tristan Buckmaster would have stripped his collaborator's name from the credit, he says. The proof itself has not been independently verified.

OpenAI has published what it says is a solution to the Navier-Stokes problem — one of the seven Millennium Prize Problems, each carrying a $1 million award from the Clay Mathematics Institute — with a Lean formalization a computer can check. Its answer is that smooth flow can break down.

On September 7, 2026, NYU mathematics professor Tristan Buckmaster and his Anthropic co-author Levent Alpöge posted three preprints establishing the same kind of breakdown for simpler fluid equations. Navier-Stokes itself was not among them.

In the statement he issued with them, Buckmaster said OpenAI had been running an effort alongside theirs that drew on their work while it was still unpublished.

They got in touch and were told OpenAI already had a complete proof. When they pressed on when the work had started, the replies grew vaguer; the first prompt, it emerged, had gone in only days after news of their work reached the company.

The route the two had taken was one hardly anyone else was known to be pursuing, he wrote, and not somewhere a model lands within days of being handed the problem statement.

OpenAI then put two choices to him, on his telling: publish and let the company release its own proof a day later, or publish and then — alone, with Alpöge's credit taken off — write up a paper crediting the solution to OpenAI's model, keeping the prize the company said it would not claim.

OpenAI's own post puts the start of the work at September 1, prompted by talk that two Millennium Prize Problems had been solved, and says it proposed a simultaneous joint announcement crediting the mathematicians' priority.

The week-long effort ran to 300 billion output tokens, around $22.5 million of compute at list rates.

Buckmaster raised a further worry: he had leaned heavily on Codex while assembling the project, and what he did there might have fed into OpenAI's attempt.

OpenAI said its researchers and agents saw none of the mathematicians' work before publication and that no specific user's data was accessed, argued that the two sets of proofs differ substantially, and recognized their priority on the result they had proved.

Buckmaster's letter closes by saying he is not accusing anyone. He has not seen the proof, he writes, and if the model genuinely closed the gap that should be announced publicly, with the credit record kept accurate.