OpenAI claims Navier-Stokes Millennium Prize solution amid rivalry and data disputes

OpenAI claims a Millennium Prize breakthrough

OpenAI has announced that an advanced, unreleased model produced a solution to the Navier-Stokes problem, one of the seven Millennium Prize problems set out by the Clay Mathematics Institute in 2000, each carrying a $1 million award. According to figures the company gave The Verge, the effort took roughly 10,000 AI agents, tens of millions of dollars of compute and 88 hours of run time. The problem concerns the flow of fluids and has resisted resolution for generations; since the prizes were established, only one of the seven, the Poincaré conjecture, has been solved.

The claim has not been met with unreserved celebration. The Verge reports that it spoke with more than a dozen mathematicians who described a field shaken by the company's conduct, with many seeing a well-resourced newcomer treating mathematics as a contest to be won rather than a discipline to be advanced.

A race OpenAI did not expect

According to The Verge, OpenAI says it heard that researchers were making progress on Millennium Prize problems and decided to test whether one of its unreleased models could make headway too. In doing so, it discovered who it was competing with: Tristan Buckmaster, a professor at NYU, and Levent Alpöge, a researcher at Anthropic. The pair had been pursuing Navier-Stokes among other lines of research but had not completed a proof.

The two sides disagree on some details but broadly agree on the sequence of events, The Verge reports. Buckmaster said that after learning OpenAI was racing toward its own solution, he contacted the company, and that discussions with OpenAI researcher Sébastien Bubeck turned contentious and, in his view, threatening. He said he was offered effectively unlimited compute to finish his own proof, along with sole authorship of OpenAI's paper, on condition that Alpöge be excluded. Buckmaster described the proposal to The Verge as an attempt to cast aside his collaborator, called it a bribe, and rejected it.

Bubeck has disputed that characterisation in an interview with The New York Times and on social media, while confirming that he offered OpenAI's resources for Buckmaster to complete his proof or take over the company's write-up. He said OpenAI has made similar arrangements with other mathematicians, whom he did not name, and framed the obstacle as Alpöge's employment at a rival lab, asking how an internal OpenAI project could include an Anthropic employee. Alpöge has said his work with Buckmaster was a personal collaboration independent of his Anthropic role.

Questions over Codex data

Buckmaster had been using Codex, one of OpenAI's tools, in his own work on the problem, and he has questioned whether that usage could have contributed to the company's success. According to The Verge, OpenAI initially acknowledged it could not rule out that data derived from his use of its products had been used to improve the model, while maintaining that no person or agent accessed his specific user data. Spokesperson Laurance Fauconnet later told the publication it was impossible for Buckmaster's prompts in recent months to have influenced the system in any way, including training. Buckmaster said such assurances deserve deep skepticism given the company's behaviour.

Buckmaster ultimately took his work and his account of the episode public, coordinating with colleagues who checked his mathematics and helped him reach out to lawyers. He told The Verge that his earlier stint collaborating with Google DeepMind had already convinced him that major tech firms are fixated on prestige and on being first to claim famous results.

Why it matters

If it holds up, an AI-derived solution to Navier-Stokes would be only the second Millennium problem ever solved and one of the strongest demonstrations yet of machine reasoning at the frontier of mathematics. But the fallout is just as significant. The episode highlights how the competitive incentives of AI labs clash with research mathematics, where the provenance of ideas often matters more than the final result, and where new techniques frequently outlast the problems they were built to crack. It also leaves an unresolved question that affects every researcher using commercial AI tools: whether data generated through those tools can later benefit the vendor. For OpenAI, the win may prove easier to defend than the way it was pursued.