OpenAI said its internal AI model solved the Navier-Stokes Millennium Prize Problem by proving the equations can blow up, producing infinite speed; the problem is one of seven Millennium Prize Problems designated by the Clay Mathematics Institute and carries a $1 million prize. OpenAI said the result required about 88 hours of computation and the coordination of roughly 10,000 AI agents. Rival mathematicians Tristan Buckmaster and Levent Alpöge say they spent nearly a year working with AI on a similar blow-up solution and reported arriving at a solution by August 22.
OpenAI said an internal AI model produced a formal proof addressing the Navier-Stokes Millennium Prize Problem that demonstrates the equations can blow up, reaching infinite speed. The company said the model generated a roughly 100-page proof for the forced Navier-Stokes case and presented that material as a full formal argument establishing blow-up within that setting. OpenAI noted the Navier-Stokes problem is one of seven Millennium Prize Problems and carries a $1 million prize from the Clay Mathematics Institute.
OpenAI said the computational run lasted about 88 hours and involved roughly 10,000 coordinating AI agents working in a coordinated campaign to search for and construct the argument. The company said those agents were organized to handle different parts of the computation across the run. OpenAI said the resulting argument was checked step-by-step using the Lean proof assistant for formal verification.
Tristan Buckmaster and Levent Alpöge spent nearly a year using AI models to pursue proofs that would demonstrate fluid blow-up in the Navier-Stokes equations. Their work culminated in what they say was a solution reached by August 22. Buckmaster says he informed a mathematician at OpenAI about the project on September 3. That notification occurred amid circulating rumors that Anthropic had solved a major related problem, which contributed to heightened attention around the timing.
Their account outlines a chronology of AI-assisted research followed by subsequent contact with an OpenAI mathematician. Buckmaster and Alpöge present those dates and interactions as central to their claim of priority. The sequence underlies the dispute over authorship and credit described in reports about the matter.
OpenAI offered Tristan Buckmaster two publication options, Buckmaster says: publish the day after his team or allow Buckmaster to publish alone with Levent Alpöge omitted because Alpöge works at a rival lab. Buckmaster published his papers with Levent Alpöge credited there, while OpenAI did not credit either researcher. That sequence of offers and publication choices is described by Buckmaster as central to the authorship dispute.
OpenAI and Sam Altman deny Buckmaster’s characterization of those interactions. Sébastien Bubeck later posted texts that proposed a coordinated release with Alpöge and offered OpenAI prompts. Bubeck stated, “I never ever asked for Levent to be removed from authorship of his own work.” Buckmaster expressed concern about authorship removal with the questions, “Why would you ruin your career?” and the remark, “I hope it’s clear from the message that we came in with the best possible intentions.”
The exchanges over publication options, authorship, and credit form the core of the dispute. Parties involved have issued denials and public messages about the events.
The dispute over the Navier-Stokes proof remains ongoing, centered on competing claims about who should receive credit for the purported solution and disagreements over authorship decisions and publication choices. Parties involved have issued differing accounts and denials, and the disagreement over credit and authorship continues to be the principal unresolved element of the controversy.
