Terence Tao isn’t asking whether AI can do mathematics. He’s asking what mathematics is for once it can. In a new essay for the 2026 International Congress of Mathematicians, the UCLA mathematician argues the field is sleepwalking into its most serious identity crisis since Gödel’s incompleteness theorems forced a reckoning with mathematical foundations a century ago. Back then, the threat was logical paradox. Now, Tao says, the stress test has moved to something murkier: ‘the largely implicit framework of mathematical values and practices.’ What counts as a contribution? What does it mean to understand something? Can a machine be said to have done the work?
The evidence that this isn’t abstract hand-wringing comes from the First-Proof Project’s second round, where ten unpublished research problems were fed to four AI systems under controlled conditions. Seven of the ten got at least one passing grade from at least one system—solutions judged essentially flawless or needing only minor revisions—at costs ranging from tens to hundreds of dollars per problem. That’s not a demo. That’s a production line.
Tao’s working hypothesis is blunt: AI tools will ‘reasonably soon’ handle a meaningful fraction of research-level tasks with reasonable quality and cost. The consequence isn’t more math. It’s proof abundance—a flood of results nobody has time to read, verify, or learn from. He notes the Erdős problem database already contains dozens of AI-generated submissions no human expert has volunteered to check. And the problem runs deeper than volume. Tao observes that human proofs carry useful friction: the carefully built lemma, the notation shift, the paragraph obviously rewritten five times. AI-polished proofs erase those signals, producing text that’s ‘easy to read and hard to learn from.’
His proposed guardrail is simple and severe: if authors can’t give a clear, expert-level talk defending their result, it shouldn’t be published—even if formally verified. That’s a direct challenge to the verification-first optimism that’s been building since formal proof assistants started getting serious attention. Timothy Gowers and Peter Sarnak recently credited LLMs with real mathematical ability but drew the line at genuinely new ideas. Tao goes further: the bottleneck isn’t machine capability. It’s human judgment about what mathematics is supposed to be for. The Leiden Declaration, backed by the International Mathematical Union, offers institutional cover. But institutions move slowly, and the incentives—benchmarkable wins, quotable results, industry money—are already pulling the other way. Goodhart’s law, Tao reminds us, doesn’t care about peer review.
