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What It Means to Be a Mathematician When AI Does the Math
A new generation of AI proof systems is making the theorem cheap. The harder question is what the years of work that used to produce a proof were actually for.
A new generation of AI proof systems is making the theorem cheap. The harder question is what the years of work that used to produce a proof were actually for.
When the mathematician Jeremy Avigad watches a proof system finish a derivation in seconds, he does not feel relieved. The Carnegie Mellon logician has spent years on individual proofs, and the understanding he cultivated along the way is not the kind of thing a model can hand back. The result is no longer scarce. The question is what the long path was for.
That question is now the live one inside mathematics. It is not, despite the headlines, a question about jobs. It is a question about identity: what was the mathematician actually for, when the theorems can increasingly be produced by machines?
The asymmetry at the heart of the field sharpens it. Applied mathematics, the kind of work an Edinburgh PhD student in the mid-2000s might have spent a year simulating, say, special light-wave interactions in liquid crystals, is now plausibly completable in days or hours with AI assistance, according to a recent IEEE Spectrum editorial on the question. Pure mathematics, where the bottleneck is a single idea, often resists for years. AI has compressed one half of the field without touching the other, and the two halves have never shared a calendar.
The research frontier, on the evidence of recent arXiv submissions, is racing to close the gap. "Towards Autonomous Mathematics Research" describes a system that loops a language model through its own conjectures, attempts, and revisions, an agent that does not just verify but proposes. "Eigenweights for arithmetic Hirzebruch Proportionality" is doing something stranger, weighting Hodge-theoretic data inside arithmetic geometry, the kind of deep abstract territory where humans are still firmly in the lead.
An IEEE Spectrum editorial framing the same debate places the fault line in human terms. Applied math reorganizes first because its products are now reproducible. Numerical analysis, optimization, simulation work that once anchored a dissertation is being reclassified as a workflow. Conceptual math reorganizes slowest, because the bottleneck is a person sitting with a problem long enough to be changed by it.
Both halves of the field are true at the same time, and the discipline has not yet built a vocabulary for the gap. Mathematicians who are most disoriented are not the ones using AI tools. They are the ones who built their sense of self around problems that may not be the ones AI touches first. The honest version of the story is that some mathematics is now trivially automatable while the deepest proofs still resist, and these are not the same mathematicians.
Training pipelines will absorb this regardless of how individual researchers feel. Hiring committees are quietly asking whether the next assistant professor should be fluent in proof-search agents and Lean, and conversant with the failure modes of the autonomous systems on arXiv. The applied side will get the new tools first. The conceptual side will decide what the tools are for.
What to watch next is whether mathematics departments begin to separate, in print, the work AI now does from the work that justifies a human apprenticeship. The first programs to do that out loud will signal what "doing math" is about to mean.