25 Fields Medalists against AI companies - famous problems are not a benchmark

It started with a rumor that turned out to be false. Word went around that two Millennium Prize Problems had been solved, so OpenAI checked whether its own system could do the same. The company put roughly 10,000 agents to work in parallel on the Navier-Stokes equations, and 88 hours later, on Saturday, September 5, it had a proof that a flow with a smooth velocity field can produce a singularity in finite time. Formalization took another 17 hours. The announcement went out on September 8, and the company's post on X was viewed more than 73 million times. The rumor, meanwhile, had been about something else: Levent Alpöge and Tristan Buckmaster were working on the forced Euler equations, which are not one of the Millennium Prize Problems.

Three days later a declaration signed by 25 Fields medalists appeared on Terence Tao's blog. The medal was first awarded in 1936, and since 1950 it has been given every four years, to no more than four people at a time and only to mathematicians under forty. Sixty-eight people have received it in all. Twenty-five of them signed, more than a third of the total. Among them are Pierre Deligne, who received his medal in 1978, and Yu Deng, who collected his seven weeks earlier, in July in Philadelphia.

The charge is a single sentence, put plainly: "the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community." The line that explains the rest goes like this: solving problems is only a tool that serves understanding, and an indirect measure of how much we already understand. Forgetting that in a world of AI could turn the tool into an obstacle to the goal. Hugo Duminil-Copin, one of the signatories, put it vividly to The Economist: being dropped on top of Mount Everest is an entirely different thing from climbing it.

It is easy to miss what the document does not do. The declaration names no company. It demands no ban, no moratorium, no regulation. It does not claim the proofs produced by models are wrong. It states outright that AI can accelerate real mathematical research. It makes no specific demand either, and ends by saying the matter needs urgent attention. One commenter on Hacker News put it well: he shares the authors' concern but does not understand what behavior they expect. Tao was the one who named the target, attaching to his post a link to an article in The Economist headlined "Top mathematicians are outraged by OpenAI's methods."

The backdrop is sharper than the document. On the night before OpenAI's announcement, the mathematician Tristan Buckmaster of New York University published a four-page statement. In it he wrote that his co-author had received signals that word of their progress had reached the company. Their drafts had been processed by Codex, a tool that works on the user's files. In its September 8 statement OpenAI said it could not rule out that de-identified data collected during use of its products had helped improve the models. Two days later, after its own investigation, the company said that Buckmaster's queries could not have influenced the system in any way, including through training.

Authorship is a separate matter. Buckmaster says he was offered the chance to put his name on a corrected version of OpenAI's proof if he removed Levent Alpöge, who works at Anthropic, from the list of co-authors. Sébastien Bubeck of OpenAI replied that he had never demanded Alpöge's removal from their own paper on the Euler equations. He did acknowledge that when a rewrite of OpenAI's proof was discussed, he said it would be simpler if Alpöge were not an employee of a competitor. The declaration speaks of solutions announced in haste that raise serious questions about authorship and possible plagiarism. No names appear.

Buckmaster himself wanted to talk about something entirely different from the dispute. He had planned to say, when announcing his work, that the results are not the important part, and that what matters is that a mathematician and a language model now do in a month what used to take years. He called it a moment on the scale of Kasparov against Deep Blue.

The rest of the facts explain the anger better than the declaration does. OpenAI's paper runs to 166 pages, and for all that length it contains few of the explanations mathematicians usually offer when sharing a discovery. The author is listed as the company itself. The formalization was published, so a machine has checked the proof, but the community has not yet reviewed it. The Clay Institute still lists the problem as open, because its rules require three things: publication in a peer-reviewed journal of worldwide repute, the passage of two years since that publication, and general acceptance in the mathematical community. That last condition is the one that stings. Fortune estimates the compute cost at anywhere from $2 million to $22 million, with the higher figure covering everything the company ran that week. The prize is $1 million, and OpenAI has said it will not claim it.

The pushback against the declaration is just as loud. Nassim Nicholas Taleb asked whether this is simply bad for today's mathematicians, who are losing their privilege, rather than bad for mathematics itself. On Hacker News, where the thread drew more than 800 points, the chess comparison keeps coming back: in the 1990s people said computers would kill the game, and today chess is more popular than ever. David Madore of Télécom Paris wrote even before the declaration was published that medalists do not represent the nearly 100 percent of mathematicians who have no medal. After it appeared he said the same thing again: he supports the content, but sees no reason why medalists in particular should speak for the whole community.

The signatories are not arguing on X, because they are simply not there. Tao announced the declaration on Mastodon and on his own blog, Cédric Villani deleted his X account in January 2025, and Peter Scholze never had one. OpenAI says nothing about the declaration itself. The day before, the company withdrew from sponsoring the Mathathon at Caltech, a 40-hour contest for a hundred teams, but it did so in response to a separate letter from mathematicians there.

The declaration can be signed after identity verification through ORCID or with a university email address. By Saturday morning there were more than 2,400 signatures, and the number was climbing by the hour. They come from institutions around the world, including departments across the United States and Europe.

The most practical conclusion reaches beyond mathematics. Andrew Sutherland of MIT put it this way: mathematicians may be to many other professions what the canary was to miners. The authors of the declaration say the same thing, only more carefully. When the way you work changes, it is easy to lose sight of what that work was for.

Benchmark - a standardized test in which models get the same set of tasks so their results can be compared numerically. Millennium Prize Problems - seven problems named in 2000 by the Clay Mathematics Institute as the most important unsolved problems in mathematics, with a $1 million prize for each. Codex - OpenAI's coding tool, which works on the user's files. Formalization - writing a proof in a language in which a computer checks every step, such as Lean.