Frank Calegari's AI Mathematics Proposal: Papers, Hiring and Proofs

Frank Calegari published a proposal on November 1 for changing how mathematics evaluates research as AI produces more of it. The University of Chicago professor argues for more emphasis on demonstrated understanding in hiring and higher expectations for papers. His essay is a guest post on Terence Tao's blog, not an announcement of new university rules.

What Calegari proposes

In Mathematics has changed. Let's act like it, Calegari recommends evaluating work as potentially AI-assisted, relying more on personal interactions in hiring and asking journals to demand better exposition. He also wants broader graduate education while retaining deep technical training.

He explicitly distinguishes understanding mathematics from explaining it fluently. His proposals should not be read as replacing mathematical ability with presentation skills. Nor does the essay establish that the mathematical claims it discusses have all been verified.

The distinction matters for anyone trying to judge AI-assisted work. A polished output can be useful without showing who understands the decisions behind it. An interview can reveal some of that understanding, but it also needs a fair way to separate technical competence from confidence or communication style.

OpenAI's math repository still needs result-by-result scrutiny

OpenAI's public math repository describes its manuscripts as research material at different stages of verification. Some have Lean formalizations, and others do not. OpenAI explicitly warns that unformalized results could contain issues and preserves revisions rather than treating the collection as a set of finished academic papers.

Lean is a proof assistant that checks formal mathematical arguments. A checked formal proof can provide evidence about a precisely stated result. It does not, by itself, tell a hiring committee what a particular candidate contributed, whether a paper explains its ideas well or which research question deserves attention next.

Those are separate decisions. Combining them into a single judgment such as “AI solved this” makes it harder to see what has actually been established and what still needs work.

There is already a practical response to the publication problem: the independent oai-math-revised project accepts improvements to explanations, citations and arguments. Its contribution history can make otherwise scattered review work visible. That project predates Calegari's essay and is not a new launch here.

What would make a different evaluation system useful?

For a research team, one practical experiment would be to ask authors to explain a specific decision, identify a fragile assumption and respond to a changed condition. That would produce different evidence from asking for another polished summary. It could also help distinguish someone who can use a result from someone who has only reproduced its presentation.

There are tradeoffs. Deeper assessment takes time, and an interview alone is a weak substitute for a careful record of work. A credible process would need both: inspectable contributions and a chance to demonstrate understanding. Otherwise, replacing publication counts could simply introduce a different unreliable shortcut.

The useful test is whether evaluation rewards work that another researcher can check and build on. Generating more papers does not automatically make that work easier to find.

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