25 Fields Medalists Warned on AI. Math Will Be Fine

On September 11, twenty-five Fields Medalists put their names to a document called A Severe Misalignment of AI in Mathematics. The signatories include Terence Tao, Peter Scholze, Maryna Viazovska, Pierre Deligne, and Yu Deng, who received his medal in Philadelphia seven weeks earlier. Their argument is that the race by AI labs to knock over famous problems as benchmarks is damaging the discipline: solutions announced in a rush, no time for a proper writeup, prior work uncited, and a flood of verified-but-unabsorbed results that they warn could "destroy fertile ground instead of breathing life into new ideas."

It is a serious document signed by serious people, and it deserves a serious answer. Here is ours: on the specific question of whether AI is good or bad for mathematics as a body of knowledge, the evidence of the last four months points the other way. The declaration's strongest claims are not about mathematics. They are about mathematicians' careers, and those are two different arguments wearing the same coat.

What the declaration is responding to

The timing is not subtle. Three days before the statement appeared, on September 8, mathematicians at OpenAI announced that 10,000 autonomous agents running on an unreleased model had found a singularity in the three-dimensional Navier-Stokes equations, apparently resolving one of the six remaining Clay Millennium Prize Problems. Twelve hours before that, Tristan Buckmaster of NYU and Levent Alpöge of Anthropic reported resolving several closely related problems with help from a range of AI models.

Before that came the Erdős run. On May 20, an internal OpenAI model produced a counterexample to Erdős's 1946 unit-distance conjecture — the first historically significant proof to come from a machine. On August 1, a model called Astra was credited with ten further advances, three of them on Erdős problems catalogued at erdosproblems.com. Quanta's account of that run is the best single explanation of why the Erdős problems in particular fell first.

So the declaration is not an abstract worry about a future technology. It is a response to a specific eight-week stretch in which the thing mathematicians said could not happen happened four or five times.

The signature list is a generational document

We matched the twenty-five signatories against every Fields Medal ever awarded — 68 laureates since 1936 — using death dates from Wikidata's laureate records, to see who actually signed and who did not. Forty-seven laureates are alive. Twenty-five of them signed, which is 53%.

The interesting number is what happens when you split that by cohort.

Fields Medal years	Living laureates	Signed	Share
1954–1974	6	0	0%
1978–2002	18	7	39%
2006–2022	19	17	89%
2026	4	1	25%
All living laureates	47	25	53%

Among laureates awarded between 2006 and 2022, seventeen of nineteen signed. One of the two who did not is Grigori Perelman, who has declined every honor and essentially every communication since 2006; discount him and the rate is seventeen of eighteen, or 94%. Every living laureate from the 2010, 2014 and 2022 classes signed. Go one generation up, to the 1978–2002 cohorts, and the rate collapses to seven of eighteen. Not one living laureate from the 1954–1974 classes signed at all.

Share of living Fields Medal laureates signing the declaration, by cohort. Source: signatory list at mathandai.org as of September 11, 2026, matched against all 68 laureates and their death dates in Wikidata (Q28835). Denominator is living laureates only.

That distribution tells you what the document is. The people who signed at near-unanimity are the generation currently running research groups, supervising doctoral students, sitting on hiring committees and writing the letters that determine who gets a permanent job. The generation above them, largely past the business of building careers for other people, mostly did not sign. Read the declaration again with that in mind and its center of gravity is unmistakable: students, attribution, the years of training that produce a mathematician. Those are labor concerns. They are real, and they are not the same thing as a claim that mathematics is being degraded.

The optimistic case, in three parts

First: formal verification answers the "true/false flood" objection rather than causing it. The reason the Navier-Stokes claim was taken seriously within hours instead of debated for a year is that it was checked in Lean. For most of mathematical history, the only way to establish that a long proof was correct was to hand it to human referees for months. Machine-checkable proof turns correctness into infrastructure. That is the opposite of a flood of unverifiable assertions — it is the first time in the field's history that the truth of a result can be separated cleanly from the sociology of who believes it. The declaration's fear of mass-produced true/false statements is precisely the fear that verification makes cheap to dispel.

Second: attribution worked. Both the OpenAI result and the Buckmaster–Alpöge result leaned heavily on a strategy developed by Diego Córdoba of Madrid's Institute for Mathematical Sciences and Luis Martínez-Zoroa of CUNEF University, who had abandoned the approach everyone else was using. Charles Fefferman, who wrote the Clay Institute's official statement of the problem, named those two as the heroes of the episode. Buckmaster went further in his own announcement, writing that Martínez-Zoroa "deserves a Fields Medal." When an AI system closed a Millennium Prize Problem, the mathematical community's reaction was to publicly campaign for a human to get the field's highest honor. That is the attribution norm functioning under maximum stress, not failing.

Third: the human transmission chain got faster, not shorter. The declaration's most substantive worry is that AI-conceived ideas will never be integrated into the mathematical canon because no human will do the work of developing them. Look at what actually happened to the unit-distance counterexample: human mathematicians substantially improved on the machine's result within weeks, and within days researchers had carried the underlying techniques — imported from a branch of mathematics nobody had previously applied to the problem — into other open problems. Talks, discussion, simplification, generalization. The cycle the declaration describes as endangered ran at compressed speed, with humans doing every step of it.

The strongest objection, and why it has already been survived

There is one version of the declaration's argument that does bite, and it is worth stating in its sharpest form. Verification is not comprehension. A proof can be machine-checked, correct beyond dispute, and still illegible — thousands of case distinctions, no human-graspable idea, nothing a graduate student could learn a technique from. If AI produces a generation of results that are certainly true and completely opaque, mathematics accumulates facts while losing the thing it was actually for. That is a real epistemic worry and no amount of Lean solves it.

But mathematics has run this experiment twice already and come out intact. The four color theorem was settled in 1976 by an argument that no human could check by hand, and the resulting controversy over whether it constituted a proof at all lasted years; it was formally verified in Coq in 2005 and is now uncontroversial textbook material. Kepler's conjecture went the same way: Thomas Hales announced a proof in 1998, referees spent years and declined to certify it completely, and Hales responded by spending a decade leading the Flyspeck project to formal verification, finished in 2014. In both cases the field's response to an opaque proof was not to reject it but to build the tooling that made it legible, and the tooling outlasted the individual result. The opacity was temporary; the infrastructure was permanent. There is no reason to expect the third round to go differently, and considerably more machine assistance available for doing the work.

Where the declaration is right

The parts of it that hold up are the ones about people. A doctoral problem chosen to develop a student's skills over three years is worth much less if a model closes it in an afternoon, and nobody has a good answer yet for how to structure a mathematics PhD in that world. Rushed announcements that skip the literature review really do erase credit, and the pressure to announce first is a product of corporate PR calendars rather than mathematical necessity. A field whose hiring and funding signals are calibrated to "solved a hard problem" will mis-sort a generation if that signal degrades. These are genuine institutional problems, and the 89% signature rate among the cohort that runs the institutions is exactly what you would expect.

None of that is an argument that mathematics is getting worse. It is an argument that the profession's incentive structures were built for a slower world. The honest version of the declaration is a demand that AI labs adopt publication norms — wait for the writeup, cite the prior work, name the humans whose strategy you used — and that is a reasonable ask that costs the labs almost nothing.

The century-old conjectures are falling, the proofs are checkable by machine, and the humans who built the ideas underneath them are being nominated for medals. Mathematics is having the best year in its recent history and its leading practitioners have chosen to describe it as a crisis, because what is actually in danger is not the subject but the career ladder attached to it. Those are worth defending. They should be defended under their own name.

Cover image generated with AI for Stanford Tech Review. Chart by Stanford Tech Review from the sources noted above.