OpenAI says an internal model found a solution to the Navier-Stokes equation, the roughly 200-year-old description of how liquids and gases move that sits on the Clay list of Millennium Problems, each carrying a $1 million prize. According to the company, more than 1,000 agents worked the problem for over 50 hours before the system produced a result, and by Sunday morning the team had a final version fully formalised in Lean. The claim arrived with a dispute already attached: a New York University mathematician says OpenAI learned of his unpublished work with an Anthropic researcher and only then aimed serious resources at the same problem.
The OpenAI account, given at a press briefing by Sébastien Bubeck, the company's mathematician and AI researcher, runs like this. On August 28 OpenAI began training a new model with expanded mathematical ability. After rumours that Anthropic was closing in on Navier-Stokes, the company decided to put additional resources on it. The agents ran, the system found something, and Bubeck's first assumption was that it had to be wrong. It was not, he says, and the Lean formalisation followed.
The compute bill was, by OpenAI's own description, far larger than anything it had previously spent on mathematics. Mark Chen, who runs research at the company, put the figure at millions of dollars. Set that against the $1 million the Clay prize attaches to the problem and the economics of the exercise become clear enough: nobody did this for the prize.
The objection came from Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic. On Monday the two published documents describing significant advances in territory adjacent to Navier-Stokes, work they did with the help of several AI models, including Claude and Codex. Buckmaster also put out a statement saying he had learned the week before that OpenAI had obtained information about their work and had begun directing substantial resources at the problem.
He says he asked OpenAI's leadership directly whether the company had gone into the pair's Codex logs. He was told the model had not looked at user data. On the separate question of whether that data was used for training, he says, the company did not answer. Buckmaster then says OpenAI floated several ways the situation could play out. One of them had him publishing a paper stating that Navier-Stokes had been solved by an OpenAI internal model, without Alpöge's name in it.
Buckmaster, Alpöge and Anthropic did not immediately respond to WIRED's request for comment.
OpenAI's denial at the briefing was specific. Bubeck and other executives rejected the suggestion that the company had examined the pair's Codex prompts for its own use, and Bubeck said that neither OpenAI's researchers nor its agents had seen the mathematicians' materials before they were published, which happened the previous night. He said OpenAI had not used their prompt or their proof to construct prompts for its own models, and had not used them to steer the agents. He also acknowledged the priority of the Alpöge and Buckmaster work on the unforced Euler equation and congratulated them on it. Ven Chandrasekaran, a mathematician at the company, added that the pair's solution differs substantially in character from what OpenAI's model produced.
Read the two accounts side by side and they are less contradictory than they look, because they answer different questions. Buckmaster's allegation is about training data and about timing. OpenAI's denials are about reading: nobody looked, nothing was seen before publication, no prompt was copied. Whether user prompts entered the training corpus is, on Buckmaster's telling, the one thing the company declined to address, and it is not covered by any of the denials as reported. Neither is the alleged offer to publish a solution announcement with one author's name removed — the most serious item in the statement, and the one OpenAI's public response walks past.
The part nobody is fighting over is the part I would look at hardest. By OpenAI's own account, the trigger for escalation was a rumour that a competitor was close. That is not a proof and not a prompt, but it is a direction, and when you have 1,000 agents and millions of dollars of compute, direction is most of what you are buying. Knowing which famously hard problem is currently falling is worth a great deal even if you never see a line of someone else's work. OpenAI has denied the theft. It has not denied the tip-off, because the tip-off is in its own timeline.
There is also a gap in the claim itself that the announcement has not closed. OpenAI says it continues to clarify details. Its own mathematician draws a line between the pair's result and the model's; the credit Bubeck extends is for the unforced Euler equation; the work Buckmaster and Alpöge published is described as adjacent to Navier-Stokes rather than a solution to it. Precisely which statement the model proved, and how it relates to the Millennium Problem as Clay states it, is the question that decides whether this is a landmark or a strong result with a landmark's press cycle.
As agents take over more of the search for proofs, the contested object stops being the proof and becomes the log. This dispute is not really about fluid dynamics. It is about whether a company that hosts a rival's working notes can be asked to prove a negative, and about what "did not look at user data" means when the looking is done by a system nobody can interrogate afterwards.