University of Chicago mathematician Frank Calegari published a guest post on Terence Tao's blog on November 1 under the title "Mathematics has changed. Let's act like it." Tao added only a short note explaining that it is a guest piece, that the original was in a different format and was converted with the help of AI, and that everything else is Calegari's.
The essay starts from the more than 700 research papers OpenAI released on October 6. Calegari sees them as a milestone, but he also criticizes the batch as poorly written, careless about authorship conventions, and partly wrong in its conclusions. He cites a remark from statistical physicist Hugo Duminil-Copin, roughly to the effect that the major open problems he had publicly discussed were all now announced as proved:
"Everything has been claimed to be proved."
Calegari says he is disappointed in how AI companies have behaved, but argues that the more practical move is to focus on what the mathematical community controls: whom it hires, what it publishes and how it teaches students.
Six proposals, most aimed at how work is evaluated
First, evaluate all work as if it may involve AI. In his words, "Evaluate all work as if it is AI-assisted." Reviewers should ask authors to explain the mathematical significance of the work, what questions it opens up, and how it connects to the field. He believes the stigma attached to AI-assisted papers will fade sooner or later.
Second, make interviews central to hiring. Postdocs and graduate students should be interviewed too. He gives the example of candidates whose application materials look excellent, but whose understanding turns out to be thin once you talk with them.
Third, press journals to raise their standards, and walk away from those that refuse. He argues that journals stopped guaranteeing correctness long ago and now serve mainly as a stamp of quality, and that many papers on arXiv do not need to be published at all. He also mentions platforms such as hexagonmath, which record AI proofs verified in Lean.
Fourth, broaden graduate education without giving up technical training. Students need to understand how subfields connect, even if they later forget the technical details. He also reminds readers that many PhDs will not stay in academia.
Fifth, give better seminar talks. A talk should begin with the background, the sticking points and the hopes, and put the new results last.
Sixth, claim AI's results collectively. Those results rest on thousands of years of human mathematics, so they should be claimed in the name of humanity, and the credit need not be handed to Silicon Valley.
The classification of finite simple groups as a precedent
The historical case Calegari points to is the classification of finite simple groups. Gorenstein launched the program in 1972 and declared it complete in 1983, though the quasithin case took roughly another twenty years before Aschbacher and Smith filled it in. The classification succeeded, and enthusiasm for the area cooled afterward. He sees that as one possible future, but it also leaves behind the kind of question Conway asked: why the Monster group exists at all.
His other analogy is the periodic table. Even if AI settled the core problems of the Langlands program, that would not mean "number theory is solved," just as the periodic table did not "solve chemistry." In his account, choosing problems and understanding structure will carry more weight:
"Choosing worthwhile problems may end up mattering more than producing proofs."
The debate has been running for months
Set against recent discussion, the thread is fairly clear. Tao has previously said that good problems are being mined in a non-renewable way, and has warned of a crisis of proof overabundance, with the emphasis on judgment. Days ago, Fields medalist Yu Deng criticized AI companies, aiming his objection at the fact that chains of thought are not made public. Calegari's essay goes a step further and starts talking about concrete institutions: hiring procedures, journal policy and graduate curricula.
His proposals also leave several questions open. Interviews can reveal how deep someone's understanding goes, but the essay does not elaborate on how to control for interview bias. On abandoning journals that will not change, he offers no alternative standard for evaluating the CVs of younger scholars. And as for OpenAI's batch, the essay does not go through which conclusions hold and which are wrong.
He acknowledges that part of mathematical culture will disappear, and that feeling sad about it is natural. His message to senior colleagues is fairly blunt: if you worry about being scooped by AI, your goals are not big enough.
Sources: Terence Tao's blog (What's new) guest post; CocoLoop; the judgments and analogies in the article are Calegari's personal views.