OpenAI says 10,000 agents solved Navier–Stokes in 88 hours. The mathematicians it raced say the rumour started the clock

OpenAI said on Tuesday that roughly 10,000 coordinating agents, running an unreleased model it calls "significantly more capable than GPT‑6 Astra", produced a proof that the three-dimensional Navier–Stokes equations can blow up in finite time. The agents got there on Saturday, September 5, about 88 hours after launch. Lean verification took another 17 hours. The Navier–Stokes effort alone burned 2.7 million messages and about 130 billion output tokens, and the company says it will not claim the Clay Institute's $1 million.

OpenAI@OpenAI

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.

The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.

The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.

Hours before that post went up, Tristan Buckmaster, a mathematics professor at NYU, published four pages describing the same week from the other side. He and Levent Alpöge, a mathematician who works at Anthropic, had spent close to a year pushing a program of Diego Córdoba and Luis Martínez-Zoroa toward smooth-forcing blowup, leaning hard on Claude and Codex and paying for it out of Buckmaster's own research grant. On August 15 they had blowup for Boussinesq and for 3D incompressible Euler. Lean signed off on August 22. They released those papers on Sunday night, sooner than they wanted to, in a state Buckmaster describes without flinching.

The Euler writeup, in particular, can only be described as AI slop. I am sorry for this. The reasons are below, and they involve our being pressured by outside factors.

Two timelines that agree on every date

Here is the odd thing about this dispute. The two accounts differ in tone and in almost nothing that can be checked.

OpenAI's own post says its effort began on September 1, "after hearing a rumor which we later realized was related to Levent Alpöge ... and Tristan Buckmaster." Buckmaster says that on September 3, with the rumour circulating and word that it had reached OpenAI, he emailed a mathematician there to explain the work was personal and unaffiliated. The reply came the same day, offering compute and saying "it would be useful to avoid competing here." Calls followed on Sunday the 6th, with Sébastien Bubeck joining. Alpöge was not on them.

What Buckmaster says he was told on those calls is the heart of it. Asked when the first prompt had been sent, he says the answer eventually was "in the past few days, after information about our work had reached OpenAI." Then the question that matters more:

I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.

OpenAI's written answer is narrower than a denial. "No specific user data was accessed in order to solve this problem," the post says. "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."

The authorship offer

Buckmaster says two proposals were put to him: post Euler first and OpenAI posts Navier–Stokes the next day, or he alone writes up the Navier–Stokes result crediting OpenAI's model, with Alpöge left off because he works at Anthropic. He declined both and said he would go public. He reports Bubeck asking "Why would you ruin your career?" and then, "If you don't want me to be nice, then I don't have to be nice."

Bubeck's account, posted Tuesday, is that he "never ever asked for Levent to be removed from authorship of his own work," that the offer was for Buckmaster to lead a rewrite of OpenAI's proof, and that he "deeply apologize[s] for this extremely poor choice of words," which he says he retracted on the spot. His reason for keeping Alpöge out was that "it would be inappropriate for an Anthropic employee to author OpenAI's work." He also volunteers something Buckmaster could not have known: OpenAI's team "collectively had no research-level expertise in fluid dynamics."

Sebastien Bubeck@SebastienBubeck

I would like to clarify a few things:

1) The screenshot is my reaching out to Levent to coordinate our releases. I hope it’s clear from the message that we came in with the best possible intentions.

2) I never ever asked for Levent to be removed from authorship of his own work (as indicated by my text). I was surprised to learn during the call with Tristan that they had only solved Euler and not Navier-Stokes; after learning this we brainstormed possible paths forward. One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work. Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic. Another option I wanted to propose (but got cut short) is to offer access to our internal model so that they could try to finish their proof and bridge the gap between Euler and NS. Again I did not know how to navigate giving access to internal OpenAI IP to an Anthropic employee.

3) To reiterate it plainly: as my text clearly indicates, and as I said during our call, OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler. In the call I was immediately met with a litany of slander, including direct threats that if we were to announce Navier-Stokes he would immediately go to the press with a barrage of unfounded accusations. I refuted all these accusations but he replied “there is nothing you can do, I simply do not trust you”. I was confused why one would turn an incredible source for celebration (of their achievements!) into such bickering, which is when I said that I did not understand why one would risk their career [over unfounded accusations]. Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve. I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)

4) Overall, on a personal level, it was incredibly difficult to have these conversations. Levent refused to attend any of the meetings despite my repeated asking. As Sholto Douglas said, there will need to be coordination between Anthropic and OpenAI in the future; I felt I was doing a proxy negotiation with Anthropic while the Anthropic employee refused to directly participate.

Sam Altman backed him ("Seb--and everyone else--acted with integrity and generosity throughout") and, in the same post, conceded the origin without being asked: "It is true that we tried this because there were rumors on the internet last week that Anthropic's models had solved a millennium problem and we were curious if ours could do it too."

What has actually been proved

Not the same thing, on both sides' account, which matters for the priority question. OpenAI proved statement C (and D) of the Clay formulation: blowup under a smooth external force, finite energy throughout, on R³ and T³. Buckmaster and Alpöge have released forced Euler, Boussinesq and porous-media blowup, with a hypo-dissipative Navier–Stokes result waiting on its Lean check. OpenAI's agents also produced an unforced Euler disproof ("nearly 100 agents ... for approximately 50 hours"), which is the more mainstream target and the one the pair had not reached.

Terence Tao called the Buckmaster–Alpöge work "a remarkable achievement" and added, dryly, that he would "not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task." Nobody outside OpenAI has read its 100-page proof. A Lean certificate says the formal statement follows from the axioms. It says nothing about who had the idea.

Our read

Was this a scoop? By OpenAI's own sentence, yes: the run started because of a rumour about someone else's result, and Altman says so plainly. That is not misconduct. It is how the company chose to spend what Simon Willison estimates, at Astra list prices, to be on the order of $15 million in output tokens across all the problems it attempted. Companies are allowed to spend money racing.

The question that will outlast the priority fight is the one OpenAI declined to settle: whether a year of two mathematicians' Codex drafts sits inside the training set of the model that beat them. "Cannot rule out" is probably the honest answer. It is also a bad one for every researcher who has ever typed an unpublished idea into a coding agent, which by now is most of them. We'd expect at least one of the major labs to offer a research tier with a contractual no-training, no-derived-data guarantee before the end of 2026, and we'd expect OpenAI to be pushed into going first, because this is now its example.

What got lost this week is the norm that you tell colleagues what you're working on. Tao wrote on Tuesday that "the incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community." Buckmaster's September 3 email was written under the old norm. It is hard to see who writes that email next time.