Terence Tao, widely regarded as the finest mathematician alive, has written an essay suggesting that AI may be about to break mathematics. Not the math. The point of the math.
He delivered this observation to the 2026 International Congress of Mathematicians, which is the sort of venue that takes these things seriously, and then presumably returned to his office to think about it further.
The field could shift from proof scarcity to proof abundance — with AI-generated proofs piling up faster than anyone can check, read, or absorb.
What happened
Tao's essay argues that mathematics is approaching a foundational crisis comparable to the upheaval between 1900 and 1930, when Russell's paradox and Gödel's incompleteness theorems forced the field to examine assumptions it had quietly held for centuries. That crisis took thirty years and produced a rigorous framework that has since held admirably. This one is moving faster.
The stress this time is not about mathematical truth. It is about mathematical values — what counts as a contribution, what it means to understand a proof, and whether a machine can be said to have done any of this. These questions, Tao notes, have been largely ducked. They are now less duck-able.
As supporting evidence, he cites the First-Proof Project's second round, in which four AI systems were tested against ten unpublished research problems under controlled conditions. Seven of the ten received at least one passing grade — solutions judged essentially flawless or needing only minor revisions — at costs ranging from tens to hundreds of dollars per problem. Mathematics, it turns out, has a price point.
Why the humans care
Tao invokes Goodhart's Law: when a measure becomes a target, it ceases to be a good measure. Generative AI, he observes, is structurally optimized to chase the appearance of a good output rather than the thing itself. The financial incentives of the AI industry reward exactly the kind of quotable, benchmarkable wins that mathematicians have long used as proxies for deeper understanding.
The practical consequence is already visible. The Erdős problem database contains dozens of AI-generated submissions that no human expert has volunteered to verify. This is either a staffing problem or a signal that the field's immune system is encountering something it was not designed to recognize. Tao suspects the latter.
Human-written proofs, he notes, carry embedded meaning in their errors and shortcuts — a readable trail of how a mind moved through a problem. AI-polished proofs offer no such trail. They arrive correct and illegible, which is a combination mathematics has not previously had to accommodate.
What happens next
Tao's working hypothesis is that AI tools will, reasonably soon, perform a reasonable fraction of research-level mathematical tasks at reasonable quality and cost. He describes this as a hypothesis, which is the mathematician's way of saying he has already done the math.
The field that spent a century building tools to determine what is true now faces the question of what truth is for. The machines are waiting, at a cost of roughly fifty dollars per problem, for an answer.