Did OpenAI really solve a 90-year-old math problem?

What OpenAI announced on September 8

On September 1, OpenAI hears that two Millennium Prize problems have just been cracked. The company tells the story itself: "Inspired by these rumors", it turns its agents loose on every problem still open, then narrows everything down to one.

Seven days later, it says it has solved Navier-Stokes. Those are the equations that describe how fluids move: water in a pipe, air over a wing, the weather, blood in your arteries. They date back to the 19th century, and nobody argues about them.

What was open is something else. In 1934, Jean Leray proved that the equations admit solutions, without establishing that those solutions always stay smooth. The question fits on one line: can a fluid that starts out well behaved, following the equations, reach infinite speed in finite time? More than ninety years with no answer. In 2000, the Clay Institute made it one of its seven Millennium Prize problems, with $1 million attached.

The numbers are public because OpenAI published them. On the order of 10,000 agents running in parallel. The solution landed on September 5, 88 hours after the first agents went out, plus 17 hours of formal verification. Across all the problems attacked, 4.9 million messages exchanged between agents. The Guardian puts the bill at $15 million.

So does it hold up?

As of today, yes. For two reasons, and neither of them comes from the twenty-five mathematicians we will get to below.

The first is the verification in Lean, a formal proof language where every step is checked by machine: nobody has to take the author's word for anything. The catch is that Lean only checks the statement you hand it. OpenAI's statement is public, and it matches Clay's official formulation, external force included.

The second is the silence of the specialists. Since September 8, no mathematician has publicly challenged the proof. The Société mathématique de France, which published in French, calls it "a major breakthrough" in the society's own English wording. Luis Martínez-Zoroa, who has worked on the problem, told Nature: "I think it is a truly remarkable result."

What the proof establishes, exactly

It does not say that any fluid left to itself eventually runs away. It builds one specific case: a fluid at rest, under a smooth external force, whose speed becomes infinite in finite time. That is one of the four formulations the Clay Institute accepts, and the official statement explicitly allows for that force. The case with no force applied is still open.

The institute will not rule on anything until there is a peer-reviewed publication and two years of scrutiny by the community. OpenAI says it has no intention of claiming the million.

What the twenty-five say, and what they don't

On September 11, a short text appeared on a website created for the occasion. It carries the signatures of 25 Fields medalists, from Pierre Deligne (1978) to Yu Deng (2026). Five are French: Artur Avila, Hugo Duminil-Copin, Pierre-Louis Lions, Cédric Villani, Wendelin Werner. Roughly the equivalent of 25 Nobel laureates signing the same page.

Careful what you have them saying. They don't validate the proof: they never mention it, and they name no company. Not contesting is not endorsing. Their argument is about something else.

Their text is titled "A Severe Misalignment of AI in Mathematics." The word misalignment comes from AI safety, where it describes a model drifting away from what it was asked to do. The signatories move it somewhere else: what's misaligned, they write, are the goals of the AI companies and those of the mathematical community.

Solving versus understanding

That's their subject, and they settle it in one sentence: "solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight." The result was never the point. It was how you measured that someone had understood.

Hence the grievance, and it's a precise one: these solutions often get announced in a rush, "leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others." Hence, the text goes on, "severe attribution and plagiarism questions."

And they write in as many words that AI offers the possibility of "enhancing and accelerating genuine mathematical study and understanding." These are not scholars frightened by a tool.

A mathematician apologizes for his own paper

Tristan Buckmaster, a mathematician at NYU, was working with Levent Alpöge on part of the same problem. They published on September 7, the day before the announcement. Buckmaster posted a signed four-page statement on his university page, relayed by the Société mathématique de France since September 15.

The first thing he does there is exactly what the twenty-five are asking for: he attributes. The starting idea belongs to Diego Córdoba and Luis Martínez-Zoroa, in Madrid, who have been on this track for years. He adds that in his view Martínez-Zoroa deserves a Fields Medal.

Then he apologizes. He isn't happy with the writing quality of his own papers: he would have wanted weeks to make the AI-generated proofs readable. The one on the Euler equations, he adds, "can only be described as AI slop." Then comes a sentence you rarely read under a researcher's signature: "I am sorry for this."

So their complaint isn't a guess about what a machine might do. It's a description of what just happened to someone, and that someone confirms it.

OpenAI's answer, and its date

OpenAI has responded twice. On its September 8 page, it writes that neither its researchers nor its agents saw the two mathematicians' work before publication. On September 17, a spokesperson gave Nature a tighter wording: after investigation, "no user inputs past July 3rd could have influenced this system in any way."

Buckmaster told Nature he had been using OpenAI's tools on this problem for a year, with three ChatGPT accounts, only one of which was left open to training. So the denial comes with a date, and the work in question predates it by several months. None of that proves anything, and Buckmaster refuses to go there: he writes that he is accusing nobody and is only reporting what he was told.

Why other professions should be watching

Nature took a position on September 16, asking AI companies for explicit consent: conversations would feed training only if the user agrees to it. Until then, anyone thinking out loud with a chatbot has no idea where those words end up.

The text of the twenty-five doesn't stop at mathematics, and says so itself. It declares itself applicable to other scientific and creative professions, and it asks a question that isn't specialized at all: as AI changes the way work gets done, how do we make sure we don't lose sight of what that work was meant to achieve in the first place?

Which leaves what Buckmaster told the Guardian, and it describes precisely the chain of transmission the twenty-five are afraid of seeing break: "The big story now in mathematics is that nobody wants to share anything. Mathematics is different today than it was only a few days ago. We have to decide what to do about that."