OpenAI Says It Solved a $1M Math Problem. A Rival Mathematician Says He Did It First

OpenAI announced that a next-generation internal model produced a computer-checked, Lean-verified proof indicating the Navier-Stokes equations can experience finite-time blow-up. The company said the result emerged after roughly 88 hours of computation carried out by about 10,000 coordinating copies of its models, and framed the output as addressing one of mathematics’ Millennium Prize Problems.

Hours before OpenAI’s public statement, NYU mathematician Tristan Buckmaster published a four-page account alleging a different chronology. Buckmaster said he and Anthropic researcher Levent Alpöge had been using AI models for almost a year to pursue fluid blow-up and reached a solution by August 22. He says that after telling an OpenAI mathematician about the project on September 3, he spoke by call with OpenAI researcher Sébastien Bubeck, who informed him that OpenAI had produced a 100-page proof for a forced Navier-Stokes variant and then discussed options about publication and credit.

OpenAI and Bubeck dispute Buckmaster’s version of events. Bubeck posted text messages he says demonstrate he proposed a coordinated release that included Alpöge and offered OpenAI’s prompts, and he wrote that he never asked for Alpöge to be removed from authorship. CEO Sam Altman defended Bubeck’s conduct, saying OpenAI intended collaboration and later proposed letting Buckmaster’s team publish first once it realized some differences in the problems addressed. OpenAI also stated it had not seen the pair’s work before publication and had not accessed specific user data, while acknowledging it could not completely rule out that de-identified data derived from product usage influenced model training.

Neither OpenAI’s 100-page proof nor Buckmaster and Alpöge’s most advanced version has been independently reviewed outside the teams involved; Buckmaster and Alpöge’s closest-to-prize result remains unpublished pending a final Lean check. Fields Medalist Terence Tao praised the pair’s underlying mathematics as a “remarkable achievement.” The episode follows another recent claim by Anthropic that its Claude system produced a computer-checked proof of Fermat’s Last Theorem, underscoring growing competition between AI labs in producing and publicizing machine-assisted mathematical results.