Mathematics in the Age of AI: Terence Tao's Public Lecture at ICM 2026

Terence Tao delivered a public lecture titled "Mathematics in the Age of AI" on July 24, 2026, at the International Congress of Mathematicians. He draws a parallel to the early 20th-century foundational crisis caused by Russell's paradox and Gödel's incompleteness theorems, suggesting that AI now poses a similar challenge. Tao formulates an "AI Capability Hypothesis" with weak and strong forms, but chooses to focus on the orthogonal question of goals and values. He adopts a working hypothesis that a reasonably strong version of the AI capability hypothesis is true: AI tools will soon be able to perform a reasonable share of research-level math tasks with reasonable success, quality, control, and cost. Under this assumption, he argues that the community must examine its true goals—solving problems, building theories, educating, creating aesthetic works—and warns that optimizing for AI-generated solutions risks diverging these goals. He cites results from the First Proof challenge (firstproof.org), where seven out of ten research-level problems were solved by AI teams at costs of $10–$1000 per problem on May 28, 2026. Tao notes that AI-generated proofs on sites like Erdős Problems raise verification concerns, as human experts often lack the time or qualification to validate them.