OpenAI says it has resolved part of the Navier–Stokes existence and smoothness problem — an open question in mathematics for 90 years — in 88 hours, by setting roughly 10,000 AI agents to work on it, the Daily Mirror reported, carrying BBC copy.
The Navier–Stokes equations describe how fluids move, and the unresolved problem sits at the heart of turbulence, which remains poorly understood. OpenAI called the result a “milestone.”
What was actually claimed
The claim is narrower than the headline suggests, and OpenAI is explicit about the limits:
- The work resolved two of the four statements the Millennium Prize requires for a full proof.
- It has not been independently verified or accepted by the Clay Mathematics Institute, which administers the prize.
- OpenAI said it does not intend to claim the $1 million prize: “Our goal in releasing this result is to report on the substantial progress of our AI models.”
The model used is internal and unreleased, which OpenAI describes as “significantly more capable” than its most recent public model. Training began at the end of August. On 1 September the company said it had “heard rumors that two Millennium Prize problems had been resolved,” and put the agents to work on remaining problems. It reached its Navier–Stokes result by 5 September and announced it on 8 September.
The cost
The agents exchanged nearly 3 million messages and consumed 130 billion output tokens on Navier–Stokes alone. At OpenAI’s own published pricing for its most advanced models, that is roughly $10 million (£7.3 million) of output.
That is about ten times the value of the prize the work was not submitted for — a detail that says more about where the economics of this kind of result currently sit than the 88-hour figure does. The elapsed time is short; the resources behind it are not.
A dispute over what reached whom
Tristan Buckmaster, a mathematics professor at New York University, said he and Levent Alpöge, a mathematician at OpenAI competitor Anthropic, had also been working towards a solution — using OpenAI’s own Codex tool.
Buckmaster said that on 3 September he learned “information about our progress had been passed to OpenAI,” and that the company did not begin work on Navier–Stokes until after that point. He published emails exchanged with OpenAI and questioned its timing and methods. His statement came hours before OpenAI published its own result.
He said he had not yet read OpenAI’s full proof but went public with “what I was told, when, and what was proposed to me… because the alternative is to let a sequence of announcements say something I know to be false.”
OpenAI congratulated the “concurrent work” as “remarkable,” said it had not seen “any of their work through any means until they released it publicly,” and said no user data was accessed. It added that while unlikely, it could not rule out that de-identified usage data had helped improve its models.
The two accounts are not directly reconcilable on the point that matters. OpenAI’s own timeline has it starting after hearing unattributed “rumors” on 1 September that Millennium problems had been resolved; Buckmaster’s has specific information about his progress reaching the company. Both descriptions can be true of the same event depending on what was passed and how it was characterised — which is precisely what is in dispute, and neither side has published the answer.
Not reported
The report does not say who passed the information, in what form, or whether Codex usage was the route. It does not say whether the Clay Mathematics Institute has begun reviewing the proof, how long verification usually takes, or which two Millennium problems were the subject of the 1 September rumours. Anthropic had not commented in the account.
