OpenAI says 10,000 agents solved Navier-Stokes in 88 hours; two researchers object

OpenAI said on Tuesday, 8 September, that an unreleased model, running as a swarm of about 10,000 coordinating agents, produced a solution to part of the Navier-Stokes existence and smoothness problem in 88 hours. The agents started on 1 September and finished on Saturday, 5 September, the company said. It published a Lean formalisation alongside a technical paper.

Navier-Stokes equations describe how liquids and gases move. One of the seven Millennium Prize Problems set by the Clay Mathematics Institute asks whether smooth three-dimensional solutions can stay smooth for all time, or whether they can blow up. The prize is $1 million. OpenAI researcher Ven Chandrasekaran told a briefing that the proof shows there exist fluids that start out normal and, under the equations, reach infinite speed in finite time. That is a blow-up result, not a statement that every flow explodes.

BBC reporting put the compute bill at roughly $10 million if priced at OpenAI's own rates for its most advanced models. The company said the group that produced the resolution ran on the order of 10,000 concurrent agents. It also said the solution resolved two of the four statements the Millennium Prize text demands. That last clause matters. A partial answer is not the same as Clay's cheque.

The timing is the other half of the story. On 7 September, New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge posted work on a related problem: blow-up for the Euler equations, which describe fluids with no viscosity. They said they used a mix of large language models, including Anthropic's Claude and OpenAI's Codex and Astra, and that the effort had run for months.

OpenAI said it began its own push on 1 September after hearing a rumor of progress, later learning the rumor pointed at Buckmaster and Alpöge. In its Tuesday note the company said it did not see their work until they released it, and that no specific user data was accessed. It added a caveat: while unlikely, it could not rule out that de-identified data from their use of OpenAI products helped improve the models. It said it offered the two researchers a concurrent release and visibility into prompts and the proof.

Buckmaster has said OpenAI rushed the problem after learning of their progress. Forbes reported that he also alleged an attempt to sideline the Anthropic researcher on credit. OpenAI researcher Sebastien Bubeck told a briefing the firm started after rumors that Anthropic had made headway. Nature's Davide Castelvecchi framed the claim as the first time a major open problem in mathematics had been solved by computer, according to OpenAI. Mathematicians will now read the Lean file line by line.

That reading is the real test. Formal proofs in Lean can be checked by a computer, which cuts one kind of error. They do not automatically settle priority, nor do they settle whether the theorem matches Clay's exact statement. Two of four Millennium clauses is a score that invites argument about what counts as solved.

The episode also shows how research now leaks through product logs. Buckmaster and Alpöge fed drafts into tools that OpenAI operates. OpenAI says it did not peek. It also cannot swear that training signals from that usage did not touch the models. That is a new kind of credit dispute. It is not plagiarism in the old sense. It is a question about whether a lab can race a customer on a problem the customer has been typing into the lab's own software.

For readers who already saw the headline about 88 hours, the useful remainder is this: the proof is partial against Clay's list; a competing pair posted a no-viscosity result a day earlier; OpenAI's own statement leaves a crack about de-identified product data; and the Lean artifact, not the press note, is what the field will accept or reject.