OpenAI said Tuesday its internal AI model produced a Lean-verified proof that the Navier-Stokes equations can “blow up,” a result tied to one of the seven Millennium Prize Problems carrying a $1 million award from the Clay Mathematics Institute. The company said the work used roughly 10,000 coordinating AI agents over 88 hours and involved a next-generation model described as significantly more capable than GPT-6 Astra.
Hours earlier, NYU mathematician Tristan Buckmaster alleged that he and Anthropic researcher Levent Alpöge had already solved a closely related version of the problem by August 22 after nearly a year of AI-assisted work. Buckmaster claimed OpenAI’s Sébastien Bubeck learned of their project on September 3 and, in a call three days later, presented options including a coordinated publication or leaving Alpöge off the paper because of his rival-lab affiliation. According to Buckmaster, 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.”
Bubeck disputed that account, publishing text messages he said showed an offer to coordinate the release with Alpöge and sharing OpenAI’s prompts. “I never ever asked for Levent to be removed from authorship of his own work,” Bubeck wrote. OpenAI CEO Sam Altman backed him, saying Bubeck “acted with integrity and generosity throughout” and that OpenAI offered to let Buckmaster’s team publish first after learning the other group had solved only Euler, not full Navier-Stokes.
OpenAI said it never saw the pair’s unpublished work and accessed no specific user data, but its blog noted it could not rule out that “de-identified data derived from their usage of our products helped improve our models.” The Clay Institute has not recognized the proof; it requires publication in a qualifying outlet, a two-year public availability period, and broad mathematical acceptance. OpenAI said it will not seek the prize money, and Fields Medalist Terence Tao called Buckmaster and Alpöge’s underlying math “a remarkable achievement.”
