OpenAI announced on Tuesday that its latest internal AI model, deployed through a swarm of roughly 10,000 autonomous bots, produced a solution to the Navier–Stokes existence and smoothness problem in just 88 hours. The puzzle, a cornerstone of fluid dynamics and one of the Clay Mathematics Institute’s Millennium Prize problems, has resisted proof for nine decades.
The company said the bots exchanged nearly three million messages and generated 130 billion output tokens while working on the problem, a computational effort that would cost roughly $10 million under OpenAI’s pricing. The solution reportedly resolves two of the four statements required for the Millennium Prize, which offers a $1 million reward.
OpenAI’s claim has yet to be independently verified or accepted by the Clay Mathematics Institute. The firm emphasised that it does not seek the prize and that its internal model remains a proprietary tool. It also noted that it had not accessed any user data from external researchers during its work on the problem.
Controversy erupted when New York University mathematician Tristan Buckmaster alleged that information from his own research had been passed to OpenAI before the company began its work. Buckmaster, who has been collaborating with Anthropic’s Levent Alpöge, said he had not seen OpenAI’s full proof but felt compelled to publicise what he was told.
OpenAI praised the concurrent efforts of Buckmaster and Alpöge as “remarkable” but insisted its proofs differ significantly from theirs. The company remains open to further scrutiny and welcomes independent verification of its findings.
