OpenAI solves 90-year-old Navier-Stokes maths problem with 10,000 AI agents; NYU professor who spent a year on the same problem using OpenAI’s own AI says: “I asked again, about training, and I did…”
OpenAI says an unreleased AI model has solved the Navier-Stokes existence and smoothness problem, a fluid dynamics question that has resisted mathematicians for roughly 90 years and carries a $1 million prize from the Clay Mathematics Institute. The company set about 10,000 AI agents on the task. They returned a proof in 88 hours.Tuesday’s announcement should have been a clean win for the ChatGPT maker. It landed instead a few hours after Tristan Buckmaster, a mathematics professor at New York University, published his own findings on a closely related problem and accused OpenAI of racing down a research path it had picked up from his unpublished work. Buckmaster and his collaborator had spent months feeding their drafts into Codex, OpenAI’s own coding tool.
The equations run our aircraft and weather models, yet nobody could prove they always hold
The Navier-Stokes equations describe how liquids and gases move, and engineers rely on them for wing design, weather forecasting and blood flow simulation. What nobody could settle is whether they break down: whether a fluid that starts out smooth can be pushed to infinite speed in a finite time, a state mathematicians call a singularity. OpenAI’s proof says it can. The solution describes a vortex that spirals inward and stretches out while speeding up, with its energy staying finite throughout.
Ten thousand agents and 130 billion tokens turned a 90-year question into a four-day job
OpenAI began training the internal model on August 28 and calls it significantly more capable than GPT-6 Astra. On September 1 it heard rumours that two Millennium Prize problems had been resolved and pointed its agents at the rest. The group working on Navier-Stokes exchanged about 2.7 million messages and used roughly 130 billion output tokens before arriving at the proof on September 5. Verification in the Lean proof language took another 17 hours. Estimates of the compute bill for the wider effort run from about $10 million to $22.5 million. OpenAI says it will not claim the prize money.
Buckmaster’s case is that no model finds this specific route in four days
He had been working with Levent Alpöge, a mathematician employed by Anthropic in a personal capacity, using both Codex and Claude. On August 15 the pair proved that the Euler equations, the frictionless cousin of Navier-Stokes, do blow up. Their approach rests on a technique called forcing, opened up by Diego Córdoba and Luis Martínez-Zoroa, which Buckmaster says almost nobody else was pursuing. He posted the results at 11:58 pm on Monday with a statement describing his calls with OpenAI researcher Sébastien Bubeck. “I asked again, about training, and I did not get an answer,” he wrote of his questions about the Codex sessions. He alleges he was offered sole authorship on a paper that left Alpöge’s name off, and that when he threatened to go public the response was: “Why would you ruin your career?”
OpenAI denies seeing the work but leaves the training data door open
The company’s post says “no specific user data was accessed in order to solve this problem” and that neither its researchers nor its agents saw the pair’s work before publication. It also concedes it cannot rule out that de-identified data from their use of its products improved its models. Bubeck denies asking for Alpöge’s name to be dropped, and Sam Altman says the two approaches look different now that both are visible.The Clay Mathematics Institute has not verified anything yet, and some mathematicians point out that the version OpenAI cracked leans on a term most of them leave out of the problem entirely. So the clean win is still unclaimed twice over. What is settled is the warning underneath it, aimed at every researcher currently doing unpublished work inside a frontier lab’s tools. Terence Tao, who has cautioned about what this does to the field, put the wider cost plainly: “It’s like having machines that can lift weights for you at the gym.“
