Breakthrough on a Million-Dollar Math Problem
NYU mathematics professor Tristan Buckmaster, alongside Anthropic researcher Levent Alpöge, revealed three proofs tied to the Navier-Stokes existence and smoothness problem — one of seven Millennium Prize problems, each carrying a $1 million reward from the Clay Mathematics Institute. The duo relied on OpenAI’s Codex and Anthropic’s Claude models to assemble their work, marking another milestone in the growing role of AI in advanced mathematical research.
Accusations of Premature Racing
Buckmaster claims that while he and Alpöge were finalizing their results, details about their progress reached OpenAI. He says the lab then disclosed having achieved a full proof of the central problem — but grew evasive when asked about the timeline of their research and the extent of human involvement.
« It emerged that an entire team had been working on the problem, and that an insane amount of compute had been used, » Buckmaster stated. He believes OpenAI’s team recognized the validity of his approach and leveraged its computing advantage to formalize a proof first.
OpenAI Pushes Back
Sebastian Bubeck, who leads mathematical research at OpenAI, called the allegations « false and inflammatory. » He said he entered the discussion following standard academic practices and expressed disappointment at the public dispute. Bubeck promised a more detailed statement but has not yet provided one. OpenAI did not respond to a request for comment on whether Buckmaster’s Codex interactions could have informed its own efforts.
A Rare Approach Raises Eyebrows
The specific tactic Buckmaster and Alpöge used — targeting the smooth force options c and d outlined by mathematician Charles Fefferman — is uncommon among researchers. Buckmaster found it suspicious that OpenAI independently converged on the same narrow path shortly after learning of his work.
« Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement, » he wrote.
Credit, Data, and Career Pressures
Buckmaster also alleged that Bubeck asked Alpöge to remove his name from a proposed compromise — an uncomfortable request given Alpöge’s affiliation with Anthropic, a rival lab. When Buckmaster insisted on going public, he says Bubeck warned: « Why would you ruin your career? » and later added: « If you don’t want me to be nice, then I don’t have to be nice. »
Buckmaster raised a separate concern about data leakage: because he used Codex extensively, OpenAI could theoretically have trained models on his interactions, potentially regurgitating his ideas when confronted with a similar problem. Users can opt out of Codex training, but the default settings remain a point of contention.
What This Means for AI Research
The dispute highlights unresolved questions about transparency, intellectual property, and competition as AI tools become central to scientific discovery. Buckmaster said he chose to go public not to accuse anyone, but to prevent a narrative he knows to be false from taking hold. « I am stating it because the alternative is to let a sequence of announcements say something I know to be false, » he wrote.
