When a researcher tells you “why would you ruin your career?” you’re probably onto something worth publishing. That’s the position NYU mathematician Tristan Buckmaster found himself in after alleging that OpenAI used knowledge of his unpublished work to race him to a solution on one of the most famous unsolved problems in mathematics.
According to TechCrunch, Buckmaster and Anthropic mathematician Levent Alpöge announced three proofs Tuesday, including a preliminary result on the Navier-Stokes existence and smoothness problem. That’s one of seven Millennium Prize problems, each carrying a $1 million bounty from the Clay Mathematics Institute. The Navier-Stokes equations are central to fluid mechanics but remain poorly understood at a theoretical level. A verified solution would be a major event in mathematical physics, full stop.
The work itself is significant. But Buckmaster’s statement came with something extra: a detailed allegation that while he and Alpöge were finalizing their results, information about their progress had been passed to OpenAI. He says that when he contacted OpenAI, he was told the company had already reached a full proof. When he asked when the research had started and how much human input was involved, he says the answers got evasive. He was eventually told the first prompt had been sent “in the past few days” after information about his work had reached the lab.
That timeline matters a lot. Buckmaster’s approach to the problem was deliberately obscure. The specific route he and Alpöge chose through Fefferman’s formulation is not a direction most researchers pursue. “Almost nobody else I know of was working on it,” he wrote. “It is not the direction one arrives at in a few days by giving a model the problem statement.” The implication is that OpenAI’s team saw enough about his approach to recognize it was promising, then used its compute advantage to push through a formal proof before he could publish.
OpenAI’s head of mathematical research Sebastian Bubeck called those claims “false and inflammatory” and said he would issue a fuller response. But the allegations don’t stop at research priority. Buckmaster says Bubeck asked him to remove Alpöge’s credit as part of a proposed compromise, likely because Alpöge is employed by Anthropic. He also says Bubeck told him: “If you don’t want me to be nice, then I don’t have to be nice.” OpenAI has not publicly addressed those specific claims.
There’s also a data angle that hasn’t gotten enough attention. Buckmaster used OpenAI’s Codex extensively in assembling the research. OpenAI’s terms allow it to train on Codex interactions unless users opt out. If models trained on Buckmaster’s own sessions were later used by OpenAI’s internal team on the same problem, there’s a plausible path by which his work could have fed back into a competing effort without anyone technically “stealing” anything. OpenAI did not respond to questions about that possibility.
This dispute lands at a particularly charged moment. AI labs are increasingly positioning math as a benchmark for general reasoning ability, and there’s real competitive pressure to demonstrate that their models can do serious research, not just assist with it. OpenAI, Google DeepMind, and others have all been investing in mathematical AI. A verified Millennium Prize result would be an enormous credibility marker, worth far more than the $1 million prize itself.
But what this situation exposes is that the incentive structures around AI-assisted research are still badly undefined. Who owns a result when it’s produced by a model? What obligations does a lab have when its systems may have learned from a user’s private work? And when an AI team races an independent researcher to a result using that researcher’s likely data, is that competition or something else?
Buckmaster says he has not seen OpenAI’s proof and isn’t formally accusing anyone of misconduct. He’s publishing what he was told, when, and what was proposed to him. That’s a careful way to put it. But the picture it paints is one that the broader research community, and anyone using AI tools to do original work, should think hard about.
