Mathematics Has Changed. Let's Act Like It

On October 6, OpenAI released over 700 research papers covering groundbreaking contributions across many areas of mathematics. The response from the math community has been a mix of awe, denial, and existential dread. Now Frank Calegari, a professor at the University of Chicago, has written a guest post on Terence Tao's blog that cuts through the noise. His argument is simple: the game has changed, and mathematicians need to change with it [1].

The post, titled "Mathematics has changed. Let's act like it," is not a eulogy for mathematics. It is a battle plan.

The shock

Calegari quotes Hugo Duminil-Copin, a Fields Medalist who wrote that not a single one of the major open problems he has publicly mentioned throughout his career was left untouched by the OpenAI announcement. Everything had been claimed to be proved [2].

For a working mathematician, that is not a gradual shift. That is a wall falling on you. Calegari compares it to what happened in group theory after the classification of finite simple groups was announced in 1983: the big problem was "solved," and the field cooled. But he pushes back on the analogy. The classification did not end group theory. It opened new questions. John Conway's favorite question was never "what are the finite simple groups?" but "why does the Monster group exist?" That is the kind of question that becomes more interesting, not less, after the classification is done [3].

Choosing problems over proofs

The core of Calegari's argument is that the math community's reward structure is broken, and AI is about to break it further. Right now, mathematicians are rewarded for proving hard theorems. But if an AI can produce a proof on demand, the value of a proof shrinks. What grows in value is choosing which problems are worth asking in the first place.

He writes: "To me, someone who chooses a worthwhile problem, obtains a proof completely using AI, understands it thoroughly, and uses it to develop interesting further questions or directions has made a substantial mathematical contribution." That is a radical statement in a field that has spent centuries equating contribution with novel proof techniques [4].

He also takes aim at the rush of AI-assisted papers hitting the arXiv. The Leiden Declaration, which was meant to ensure responsible use of AI in mathematics, is being "honored more in name than in spirit." Senior mathematicians with tenure, he says, should stop worrying about being scooped by AI and start doing something more ambitious than cranking out the next incremental result [5].

Concrete proposals

This is where the post gets interesting, because Calegari does not stop at philosophy. He proposes specific changes:

Evaluate all work as if it is AI-assisted. Stop treating AI use as a stigma or a disclosure footnote. Instead, ask authors why the mathematics is interesting, what questions it raises, and how it connects to the broader subject. This shifts the evaluation from "did you prove it?" to "does it matter?"

Make hiring about personal interactions. Lazy committees have long pointed at a JAMS paper or an Annals paper to justify a hire. Calegari wants interviews to become standard for postdocs and even graduate student positions. He wants candidates who can articulate a vision for where mathematics should go, not just list publications [6].

Demand more from journals. A significant proportion of arXiv papers should not be published anywhere. Journals should demand better writing, better exposition, and genuine ideas. If editorial boards cannot adjust, abandon the journals. Let papers stand on their own merits [7].

Reform graduate education. The traditional thesis, where a student solves a variation on an old problem to demonstrate technical skill, is obsolete if AI can produce the same result on demand. Graduate training needs to emphasize breadth, communication, and the ability to ask new questions [8].

The bigger picture

What makes this post worth reading is not just the proposals. It is the framing. Calegari is not arguing that mathematics is dead. He is arguing that the part of mathematics that was about being the first to climb a specific wall is over, and that mathematicians need to become explorers who choose which walls are worth climbing in the first place.

He quotes Christian Szegedy: "That specific kind of heroism will matter less, and other skills will matter more: choosing which terrain is worth exploring, steering fleets of airplanes, and explaining what they find to the rest of the world" [9].

The post has 319 points and 356 comments on Hacker News, which tells you something. This is not just a math community conversation. It is a conversation about what happens to a profession when the thing it has optimized for suddenly becomes cheap. Programmers are having it. Writers are having it. Mathematicians are having it. Calegari's answer, roughly, is: stop optimizing for the thing that is now cheap, and start optimizing for the thing that is still expensive, which is knowing what matters [10].

That is good advice for everyone, not just mathematicians.