NYU mathematician says OpenAI raced him to the Navier-Stokes Millennium Prize proof

NYU mathematics professor Tristan Buckmaster announced three proofs this week, among them a preliminary result on the Navier-Stokes existence and smoothness problem — one of the seven Millennium Prize problems, each backed by a $1 million bounty from the Clay Mathematics Institute. According to TechCrunch, the results are significant on their own, but the announcement was shadowed by an unusual controversy over how OpenAI came to pursue the very same problem at the very same time.

Buckmaster's collaborator was Levent Alpöge, a mathematician employed by Anthropic, though not conducting the research on that company's behalf. The pair worked with a mix of AI models — primarily OpenAI's Codex, alongside Anthropic's Claude.

What Buckmaster alleges

As the two were finalizing their results, Buckmaster says they learned that information about their progress had been passed to OpenAI. When they contacted the lab, they were told OpenAI had already achieved a full proof of the central problem. But when Buckmaster asked follow-up questions about when the research had started and how much human input was involved, he says the answers grew evasive.

According to his account, it eventually emerged that an entire OpenAI team had been working on the problem using what he described as an enormous amount of compute — and that the first prompt had been sent only in the preceding days, after word of the mathematicians' work had reached OpenAI. TechCrunch notes that if this timeline holds, it would suggest the OpenAI team concluded the pair's approach was the promising one and leaned on its computing resources to reach a formal proof first.

Sebastian Bubeck, who leads OpenAI's mathematical research, rejects the account. In a post responding to Buckmaster's statement, quoted by TechCrunch, he called the claims "false and inflammatory" and said he had entered the discussion "following academic norms," adding that he would issue a more complete statement soon.

A rare route to a famous problem

Part of what made the timing suspicious, in Buckmaster's view, is how unusual his chosen line of attack was. The path to the Clay problem through a smooth force — options c and d in Fefferman's statement of the problem, a direction he credits to mathematicians he names only as Luis and Diego — was the one he and Alpöge had quietly selected, and by his account almost nobody else was pursuing it. As he put it, it is not a direction anyone arrives at within days simply by handing a model the problem statement.

Pressure over credit

Buckmaster also claims Alpöge's affiliation with a rival lab was a sore point for OpenAI, and that Bubeck asked him to remove Alpöge's credit as part of a proposed compromise. When Buckmaster pushed to take the dispute public, he says Bubeck responded, "Why would you ruin your career?" — and, after further pushback, "If you don't want me to be nice, then I don't have to be nice."

The Codex data question

Perhaps the most consequential allegation concerns the tools themselves. Because Buckmaster used Codex heavily throughout the project, he raised the possibility that his own interactions informed OpenAI's effort. OpenAI reserves the right to train its models on Codex conversations, though users can opt out. If OpenAI's team ran a model trained on Buckmaster's sessions, TechCrunch observes, it could plausibly have surfaced his work when given a similar problem. OpenAI reportedly did not respond to a request for comment on that possibility, and no evidence has been presented that it occurred.

Buckmaster himself is careful on this point. He writes that he has not seen OpenAI's proof, does not know what its model did or how, and does not know whether his data was used. "I am not accusing anyone of anything," his statement reads. "I am stating what I was told, when, and what was proposed to me. I am stating it because the alternative is to let a sequence of announcements say something I know to be false."

Why it matters

The dispute is a preview of the credit problems AI-assisted research now poses. A lab with vast compute can, in principle, learn of an academic's promising approach and formalize it faster than the people who conceived it — a dynamic the Millennium Prize framework, built around human mathematicians, was never designed to referee. It also raises a data-leakage concern unique to AI tooling: researchers who use an assistant like Codex may effectively be sharing live research strategies with the company that builds it, including teams racing them to the same result. With OpenAI promising a fuller response, the factual record remains contested. Buckmaster's chosen remedy — publishing exactly what he was told and when — may become a template for researchers who find themselves in similar positions.