Two Fields Medalists Ask What Happens to Mathematics When AI Writes the Proofs

The trigger was a single release: a commercial AI company publishing more than 700 frontier-level mathematical proofs generated by its internal model, all at once. The first reaction everywhere — China's feeds included — was that AI had come for the mathematicians. The considered answer arrived this week, when the SAIR Foundation released a podcast putting two Fields Medalists a generation apart in one conversation: Terence Tao of UCLA, the discipline's most cited living voice, and Deng Yu of the University of Chicago, newly awarded the medal, whose work centers on partial differential equations and probability.

Their argument reframes the threat. Mathematics, they said, is leaving an age of "proof scarcity" for one of "proof abundance" (证明丰裕). For most of its history, a proof existed in the meaningful sense only when someone could understand it; publication carried the guarantee of comprehension. Machine generation breaks that identity — a proof can now be logically valid and still never be read by anyone. The bottleneck moves from proving to digesting, what the conversation called "proof indigestion" (证明消化不良): machines now produce reasoning faster than the profession can check, absorb and teach it, and a result nobody can absorb stays inert as knowledge, however valid it may be.

Tao's illustration was a thought experiment that had already earned him mockery online: suppose an AI designs a cancer drug from an unknown molecule, and it passes clinical trials — would we take a drug that works but that no one understands? A listener who played the episode over dinner mounted a defense: medicine routinely uses drugs whose active mechanism has never been isolated. But the analogy, as that listener reconstructed it, is not really about medicine. It is about mathematics as a discipline where every symbol must have its reason — where the chain of reasoning, not just the endpoint, is the product, and where handing the chain to machines changes what mathematicians are for.

What the two proposed in place of doom was machinery. The conversation announced work on an "open math models" plan — keeping the models that generate mathematics inspectable and public rather than sealed inside a company's servers. Line-by-line transcripts of the episode were circulating on Weibo within hours, one reader's typed-up version annotating the speakers' opening exchanges, with corrections arriving in the comments in public view — the profession doing in real time exactly what the two laureates said it must.

The episode matters beyond the field. In China's running argument about AI, "AI will replace X" is the default headline, applied in turn to translators, drivers and animators. Here, the two people least likely to be replaced by a theorem-prover argued that the risk is subtler: not the end of the mathematician, but a widening gap between what machines can produce and what humans can absorb — and a reminder that a proof, like a drug, is only as good as someone's understanding of it.