Independent mathematicians and the Clay Mathematics Institute must now examine technical arguments before OpenAI’s claim is accepted or any prize is considered. The company says a new internal model, coordinated by roughly 10,000 concurrent AI agents, produced proofs for two of the four formal Navier‑Stokes statements within 88 hours, a development OpenAI calls a milestone but which remains unverified.
OpenAI says it began training the new model at the end of August. After reports on 1 September about progress on Millennium Prize problems, the company deployed thousands of agent processes to focus on the Navier‑Stokes challenge. By 5 September, OpenAI says, its system reached what it describes as solutions for parts of the problem central to the mathematics of fluid motion and turbulence. During the run the agents exchanged nearly 3 million messages and produced 130 billion output tokens. OpenAI calculated that the output alone would cost roughly $10m, using its own pricing for advanced model responses.
The company says the work addresses two of the four formal statements required by the Navier‑Stokes Millennium Prize, a prize worth $1m to an accepted winner, and that it does not intend to claim the award for this result. The claim has not been accepted by the Clay Mathematics Institute and prompted immediate dispute from researchers pursuing related lines of inquiry.
Tristan Buckmaster, a mathematics professor at New York University, said he and Levent Alpöge of Anthropic had been exploring similar ideas using OpenAI’s Codex tool. Buckmaster told reporters he learned on 3 September that information about their progress had been passed to OpenAI and published excerpts of emails and questions about the company’s timing and methods. He said he had not yet read OpenAI’s full proof and released a statement intended to correct the public record, adding "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 responded by congratulating the "concurrent work" of Buckmaster and Alpöge, calling it "remarkable", and denying it had seen their work before it was made public. The company also said no user data was accessed in its Navier‑Stokes effort but acknowledged "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models." OpenAI added that its proofs differ significantly from the other work.
What follows is formal scrutiny: independent experts and the Clay Mathematics Institute must vet the technical details before the community accepts the result or any prize is awarded. The episode highlights how quickly large-scale internal models can produce advanced mathematical output and raises fresh questions about information sharing between academic teams and AI developers as the field moves faster than traditional peer review processes.
