NYU mathematician alleges OpenAI raced to solve Navier-Stokes problem using leaked details of his approach

Tristan Buckmaster and Levent Alpöge announced proofs related to the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize problems carrying a $1 million bounty from the Clay Mathematics Institute. Their approach used both OpenAI's Codex and Anthropic's Claude models. Alpöge is employed by Anthropic but was not conducting the research on the company's behalf. The specific route they took, through a smooth force, options c and d in Fefferman's statement of the problem, was, according to Buckmaster, one that almost nobody else was pursuing, making it unlikely someone would arrive at it independently in a few days.

The controversy arose when Buckmaster learned that information about their progress had reached OpenAI. When contacted, OpenAI reportedly claimed to have already achieved a full proof of the central problem. Buckmaster says follow-up questions about when OpenAI began its research and how much human input was involved became evasive, and it eventually emerged that a team had been working on the problem with substantial compute. He states that the first prompt was sent in the past few days, after information about their work had reached OpenAI, suggesting OpenAI used its compute advantage to reach a formal proof first using the same approach.

Sebastian Bubeck, who leads OpenAI's mathematical research, denies the claims, calling them false and inflammatory, and says he followed academic norms. Buckmaster alleges that Bubeck asked him to remove Alpöge's credit as part of a proposed compromise, and that when Buckmaster pushed to make the dispute public, Bubeck said: Why would you ruin your career? and If you don't want me to be nice, then I don't have to be nice. These are attributed quotes from Buckmaster's statement, not independently corroborated.

A separate concern is data leakage through Codex. Buckmaster used Codex extensively, and OpenAI reserves the right to train models on Codex interactions, though users can opt out. If OpenAI's team used a model trained on Buckmaster's Codex sessions, it could have surfaced his approach when given a similar problem. OpenAI did not respond to a request for comment on this possibility. Buckmaster explicitly states he has not seen OpenAI's proof, does not know what their model did, and is not accusing anyone, rather, he is documenting what he was told and what was proposed to him to prevent a false narrative from forming through announcements alone.

Only one feed carried this story, so the allegations remain uncorroborated by independent reporting. The dispute nonetheless highlights a structural risk for anyone using a provider's AI tools on sensitive intellectual work: the same provider may compete in that domain and may train on the interactions. The episode also illustrates how AI labs' incentives around mathematical breakthroughs can collide with academic norms of priority, credit, and transparency. Until OpenAI releases its proof or a fuller statement from Bubeck, the technical claims on either side cannot be evaluated.