Mathematics in the Age of AI

Tao gives a useful template for any expert community facing AI: stop arguing only about capability, and make the values, review stages, and human bottlenecks explicit.

Logged at IST: 2026-08-19 14:33 IST

What it is: Terence Tao's essay, based on a public lecture at ICM 2026, on how mathematics should respond if AI tools become capable of research-level mathematical work.

Gist: Tao deliberately does not make the paper about whether that capability will arrive. He conditions on a reasonably strong version of the AI-capability hypothesis and asks the orthogonal question: what are the actual goals, objectives, and values of mathematical research, including the implicit ones the community optimizes for in practice?

The key move is to treat problem-solving as a case study. "Solve as many unsolved problems as possible" is too crude. It becomes a pipeline: generate proofs, verify them, communicate them clearly, have the community digest and accept them, and finally incorporate them into the definitive theory of the field. AI may accelerate proof generation and verification, but that can create proof abundance and "proof indigestion" if exposition, refereeing, attribution, publication, and canonicalization do not scale with it.

Tao's practical recommendations lean on the Leiden Declaration: disclose tool use, support the needs of reviewing, keep authorship and responsibility human, and put real effort into attribution. His own rule of thumb is especially sharp: if the authors cannot convincingly give a clear expert-level talk on their result, correct and properly attributed, the result should not be published. A proof no human can properly explain should be viewed as incomplete, even if formally verified.

Newsletter angle: Strong general framing for AI in expert work. The scarce resource shifts from producing outputs to digesting, validating, explaining, attributing, and canonicalizing them. That applies well beyond mathematics.