Mathematician Frank Calegari has published a blunt assessment of what artificial intelligence has done to his field, arguing on Terence Tao's influential blog that the release of more than 700 research papers by OpenAI on October 6 was "a watershed in the history of mathematics." The post, titled "Mathematics has changed. Let's act like it," went up on Saturday and quickly reached the front page of Hacker News, where it drew hundreds of comments. The essay's core message is as much a challenge to mathematicians as to AI companies — for ongoing coverage of that collision, see our AI research news.
"AI is now undeniably capable of making groundbreaking contributions across many areas of mathematics," Calegari writes. "So why are some mathematicians so unhappy?" His answer is not what you might expect from one of the field's most prominent skeptics of AI-generated research.
A Blunt Verdict on the Papers Themselves
Calegari's criticism of the OpenAI release is scathing on questions of craft and community norms. The papers, he writes, are "atrociously written and violate our community expectations of attribution. Some of them are even wrong." The complaint is not that AI cannot do mathematics — he grants that it can — but that it is doing mathematics without respecting the standards that make mathematical literature usable.
His remedy is pointedly practical. Mathematicians "have much more control over how we hire mathematicians, publish papers, and train students than over the behavior of trillion-dollar companies," he argues, and that is where the field's energy should go.
'Everything Has Been Claimed to Be Proved'
The most striking passage in the essay is personal. Calegari observes that not a single one of the major open problems he has publicly mentioned throughout his career — in talks, lectures, articles, or grant proposals — "was left untouched by the announcement. Everything has been claimed to be proved."
"I expected to see a few of them in the list," he writes. "But not all of them. Not all at once. Not with such nonchalance." For a working mathematician, the experience of watching every problem you have touched get swept up in a corporate press cycle is disorienting in a way that abstract arguments about AI risk are not.
The Periodic Table Is Not Chemistry
Calegari pushes back hard on the idea that claiming the field's famous landmarks means the field is finished. The OpenAI papers, he notes, made "barely a dent" on the general problems of functoriality and reciprocity in the Langlands program — one of the deepest structures in modern number theory.
But even if the release had solved every problem in the Langlands program, he writes, imagining that would have "solved number theory" would be "as naive as saying that the construction of the periodic table solved chemistry." It is an argument mathematicians need to make to the public, he suggests: central problems are merely the most visible peaks, and the mountain range extends far beyond them.
A Warning From the History of Group Theory
The essay's historical anchor is the classification of finite simple groups — a saga Calegari knows from the inside. In 1972, Daniel Gorenstein announced a program toward the classification. After about a decade of frantic activity, the classification was announced complete in 1983 — prematurely, as it turned out, with the case of quasithin groups not finished until Aschbacher and Smith completed it roughly two decades later.
The classification was "in many ways a huge success," Calegari writes, "but it was also a failure" — the announcement that the famous problem was gone cooled interest in the subject, and mathematicians turned their attention elsewhere. Yet rich questions remained, including what he identifies as John Conway's favorite: why does the Monster group exist? For some fields, Calegari suggests, the OpenAI dump may feel exactly the way the classification felt to group theorists.
What Calegari Wants Mathematicians to Do
The essay closes with a program rather than a lament. The field needs efforts like the Gorenstein-Lyons-Solomon revised treatment of the classification — the patient, multi-volume work of making a claimed result actually solid. And it needs to resist pronouncing the subject "done," because with the new tools available, mathematics is "ripe for further investigation."
The old paths missed by what Calegari calls the "galactic bypass" of AI-assisted proofs still exist, he argues, and mathematicians should seek them out — and, crucially, "we need to reward that behavior when it comes to offering people jobs." The essay carries a footnote from Tao noting the post was initially written in a different file format and converted using AI, a small irony that underscores how thoroughly the tools have penetrated the field's daily work.
Part of a Much Bigger Reckoning
The essay lands amid a year of escalating friction between mathematicians and AI labs. AI Buzz Wire has previously reported on mathematicians demanding proof that OpenAI's models weren't trained on their private discussions, on 25 Fields medallists including Terence Tao declaring a "severe misalignment" between AI and mathematics, on the Institute for Advanced Study's concerns over 377 AI-derived math results, and on Tao's own warnings that AI is non-renewably mining the world's stock of good open problems.
What makes the new essay notable is the shift in posture. The dominant note in previous responses was alarm; Calegari's is adaptation. The technology, in his telling, is not going away, the extraordinary claims are not going away, and the only variable the field controls is its own response — how it publishes, how it trains, and whom it hires.
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