Tech and AI

An OpenAI system claims Navier-Stokes in 88 hours, and the mathematician it raced goes public

By Staff Writer  |  9 September 2026

The company says about 10,000 agents running on an unreleased model resolved a Millennium Prize problem in under four days. Hours earlier a New York professor published an account of the week in which, he says, the effort began only after word of his own work reached the company.

OpenAI published its claim on Tuesday 8 September 2026: a written proof and a Lean formalisation that a smooth fluid at rest, under a smooth applied force and with finite energy throughout, can develop a singularity in finite time. That is statement C, and also D, of the problem as the Clay Mathematics Institute posed it in 2000, one of seven Millennium Prize Problems carrying a one million dollar award. The company does not intend to claim the prize.

The company says it has been training a new internal model since 28 August, one it describes as far more capable than GPT-6 Astra, and that on Tuesday 1 September it heard rumours that two Millennium Prize problems had been resolved. Groups of coordinating agents were set on every open Millennium problem; the Navier-Stokes group involved on the order of 10,000 concurrent agents and arrived at its resolution on Saturday 5 September, about 88 hours after launch. Lean verification took a further 17 hours. On this problem alone the agents exchanged 2.7 million messages and used about 130 billion output tokens.

The other announcement

The same day, before the company's post, Tristan Buckmaster, a professor of mathematics at New York University, released three results with Levent Alpoge, a mathematician employed by Anthropic, in what he describes as a purely personal collaboration: finite-time blow-up with smooth forcing for the incompressible porous media equation, for Boussinesq, and for three-dimensional incompressible Euler. He credits the underlying programme to Diego Cordoba and Luis Martinez-Zoroa.

His statement sets out a timeline. On Thursday 3 September, having been told that information about their progress had been passed to OpenAI, he wrote to a mathematician there. On Sunday 6 September, in two calls which Sebastien Bubeck joined, he says he was told an internal model had proved forced blow-up for Navier-Stokes by the same route he and Alpoge had chosen, which almost nobody else was working on. He says it emerged that a whole team had worked on it, that the first prompt had been sent in the previous few days, and that he was offered two arrangements, one of which would have had him alone write up the company's result. He declined both.

I have not seen OpenAI's proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything. I am stating what I was told, when, and what was proposed to me. I am stating it because the alternative is to let a sequence of announcements say something I know to be false.

Tristan Buckmaster, professor of mathematics at New York University

He reports that when he said he would go public, the reply was "Why would you ruin your career?" and, when he pushed back, "If you don't want me to be nice, then I don't have to be nice." He attributes both remarks to Mr Bubeck. He says the pair had put all their drafts into the company's coding tool and that his question about whether the model had been trained on those sessions went unanswered.

The company's reply

The company's post has a section on concurrent work. It says its effort began on 1 September after a rumour it later realised related to the pair, that on 6 September it approached them to offer a concurrent release and a joint announcement recognising their priority, and that it then learned their result was the forced Euler problem, whose priority it recognises. It says the researchers and the agents did not see any of their work through any means until it was public and that no specific user data was accessed, though it cannot rule out that de-identified data from their use of its products helped improve its models. At a press briefing on Tuesday Mr Bubeck denied the company had used the pair's work.

a spectacular culmination of the arc we have seen over the past 12 months

Sebastien Bubeck, OpenAI researcher, on the Navier-Stokes result

The result has not been independently verified and the institute that runs the prize has not accepted it. What neither side disputes is the shape of the week: a year of work by two mathematicians using models, a rumour, then a result from a system nobody outside the company has seen. Professor Buckmaster's reading is that a mathematician and a model can now do all of this in a month, and that the community needs an unhurried discussion about what that means for how it trains, credits and referees.