OpenAI claims Navier-Stokes proof as NYU mathematician alleges it built on his work

NYU mathematics professor Tristan Buckmaster announced three proofs on Tuesday, including a preliminary finding on the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems that each carry a $1 million bounty from the Clay Mathematics Institute. The work was done with Anthropic mathematician Levent Alpöge using both Codex and Claude models. Shortly after Buckmaster's statement, OpenAI published what it describes as a full proof of the problem, which has stood for around 90 years. OpenAI says the proof was discovered by an unreleased next-generation model that has worked on a range of unsolved problems over the past week. The week-long effort consumed 300 billion output tokens, which TechCrunch values at $22.5 million of compute at current Astra rates. Buckmaster's statement alleges that a parallel OpenAI effort built on his team's work before it became public. "There is another part of this story," he wrote, "and one that, honestly, I very much wish I did not have to be concerned with." The Verge reports that OpenAI's claim, first covered by The New York Times and Wired, is being challenged by the researchers who solved the related problem. The dispute matters because it concerns credit for a result that would be among the most significant attributed to an AI system, and because the mathematical community has yet to verify either claim.