OpenAI says one of its internal AI systems produced a major mathematical result related to the Navier–Stokes equations, but the announcement has sparked a dispute over who reached the breakthrough first.
The Navier–Stokes problem, which concerns the behavior of fluids, is one of the Clay Mathematics Institute’s seven Millennium Prize Problems, each carrying a $1 million prize for a valid solution.
According to OpenAI, its system spent about 88 hours on the problem using roughly 10,000 coordinated AI agents working in parallel. The resulting proof was also checked using Lean, software designed to formally verify mathematical arguments step by step.
However, NYU mathematician Tristan Buckmaster says he and Levent Alpöge, a mathematician working at Anthropic, had already been pursuing a closely related approach for nearly a year and reached significant results by August 22.
Buckmaster said he privately discussed the project with an OpenAI mathematician on September 3. Days later, OpenAI researcher Sébastien Bubeck told him that an internal OpenAI model had independently produced a roughly 100-page proof involving a similar area of fluid dynamics.
Buckmaster later accused OpenAI of handling the situation unfairly and claimed Bubeck pressured him over how and when the competing research should be published. Bubeck disputed that account, saying he acted in good faith and shared messages that he said showed OpenAI had proposed coordinating the releases.
OpenAI CEO Sam Altman also defended Bubeck, saying he acted with integrity. OpenAI said it had not seen Buckmaster and Alpöge’s research before publication and had not accessed their specific user data, while acknowledging it could not completely rule out whether de-identified product usage data may have contributed to model improvements.
The competing claims have not yet settled the mathematical question. Buckmaster and Alpöge’s strongest result is still awaiting a final Lean verification, while OpenAI’s reported 100-page proof has not yet been independently reviewed outside the company.
Fields Medal-winning mathematician Terence Tao described Buckmaster and Alpöge’s underlying work as a remarkable mathematical achievement, but for now, the question of who ultimately deserves credit—and whether the full $1 million Millennium Prize problem has actually been solved—remains unresolved.