Mathematics in the age of AI: Terence Tao’s view from ICM 2026

On 24 July 2026 Terence Tao, professor at the University of California, Los Angeles and Fields medallist, delivered the lecture “Mathematics in the age of AI” at ICM 2026 in Philadelphia (Pennsylvania Convention Center). The slides, published on his official site, set out the historical context of the “crisis of foundations” (1900‑1930) and propose a new crisis — this time not about axioms, but about the values and practices of the mathematical community. Tao frames a “Community Response Question” that is not a traditional mathematical problem but a metamathematical, political, ethical and cultural one, keeping the “AI Capability Conjecture” (how capable the tools actually are) separate from the question of what the discipline wants and values.

Tao observes that the plentiful data cited for and against the various forms of the conjecture was not gathered under controlled scientific conditions, and that public evidence comes with selection bias, non-scientific incentives and undisclosed costs. The one exception he names is the independent First Proof project (1stproof.org), whose second batch of ten problems was tested under controlled conditions on 28 May 2026 against four AI “harnesses”: seven of the ten were solved at publication quality by at least one team, with expert referees judging correctness and exposition. The results are documented in arXiv preprint 2606.18119 and on the page of Harvard’s Center of Mathematical Sciences and Applications. It remains a sample of ten problems, not generalisable to mathematical research as a whole; nor is it verified which commercial systems the four tested harnesses correspond to.

A focal point of the talk is the breakdown of mathematical production into five stages: generation, verification, exposition, publication and canonisation. According to Tao, AI systems and auto‑formalisation assistants (Rocq, HOL, Lean) have already sped up the first two stages, while the last three remain dominated by human work. Tao also points to the AI proofs on erdosproblems.com, where solutions are not checked by human reviewers — a concrete symptom of the reliability problem. He is critical of automatic exposition too, arguing that “natural friction” — the difficulties a human author runs into — gives the reader useful signals, while a proof polished too smooth by AI can strip those clues away. As Tao puts it, “In short, we will transition from an era of proof scarcity to an era of proof abundance”.

Tao invokes the Leiden Declaration on Artificial Intelligence and Mathematics (2 June 2026) and suggests a rule of thumb: if the authors cannot convincingly give a clear, expert-level talk on their own results — correct and properly attributed — then the result should not be published. He concludes that the analysis of problem solving should extend to teaching, mentoring, hiring and funding, with AI use in training kept tightly limited. A final note: the public document of the lecture is the slide deck; there is no official transcript of the spoken talk.