OpenAI says AI solved part of 90-year-old Navier–Stokes problem in 88 hours

OpenAI says its internal artificial intelligence model, working with about 10,000 agents, found a solution to part of the Navier–Stokes problem, one of the hardest mathematical questions left unresolved for roughly 90 years.

The company said the agents completed the work on 5 September, about 88 hours after the task began. They exchanged nearly 3 million messages and used 130 billion output tokens.

The result has not been independently verified or accepted by the Clay Mathematics Institute, which administers the Millennium Prize. OpenAI said it is not seeking the $1m award.

OpenAI’s claimed result

The company said its solution covers two of the four statements required by the prize’s Navier–Stokes existence and smoothness problem. The equations describe fluid movement, while the problem is connected to turbulence, a phenomenon that remains poorly understood.

OpenAI began training the new model at the end of August. On 1 September, it said it had heard rumours that two Millennium Prize problems had been solved and then assigned thousands of agents to work on remaining problems.

Computing scale and estimated cost

OpenAI estimated that the effort would have cost about $10m using the prices for its most advanced models. The new model remains an internal tool because the company considers it significantly more capable than its latest public release.

Dispute over concurrent research

Tristan Buckmaster, a mathematics professor at New York University, said he and Levent Alpöge of Anthropic had also been working on the problem using OpenAI’s Codex. Buckmaster said he learned on 3 September that information about their progress may have reached OpenAI.

He alleged that OpenAI began work on the Navier–Stokes equations after receiving information about their research. Buckmaster said he had not read OpenAI’s full proof but went public with concerns about the company’s timing and methods.

OpenAI congratulated Buckmaster and Alpöge on their concurrent work and said it had not seen their material before it was released publicly. The company also said it had not accessed user data, while acknowledging that it could not rule out de-identified data from product use indirectly helping improve its models. OpenAI said the proofs and the precise results were significantly different.