Tao's ICM 2026 essay sets ground rules for AI in mathematics

Terence Tao has posted an essay for the 2026 International Congress of Mathematicians that skips the usual debate over whether AI can do research-level math and instead asks what mathematicians should insist on if it can. The arxiv preprint, based on a public lecture at ICM 2026, runs twelve pages and takes problem-solving as its case study.

Tao walks the reader up a ladder of goals. The simplest version, 'Solve as many unsolved problems as possible,' becomes, by the end, 'Solve unsolved problems, verify them to be correct, ensure they are clearly communicated, and have them digested, accepted, and incorporated into the definitive theory.' Generation, verification, digestion: each stage carries a different kind of pressure.

For evidence that the pressure is real, Tao points to the First Proof project, a controlled evaluation of AI systems on novel problems. 'Of the ten problems, seven received at least one passing grade... from at least one system, with compute costs on the order of tens to hundreds of dollars per problem,' the paper reports. What worries him more is what happens next. 'AI-generated proofs will accumulate faster than they can be verified,' he writes, and 'verified AI-generated proofs will accumulate faster than they can be given a readable write-up.' He calls these impedance mismatches and stacks four of them along the pipeline, ending with published proofs too numerous for the community to work into definitive form.

The recommendations are process-first. Authors should 'transparently disclose the use of automated tools, including large language models.' Credit stays human: 'Artificial intelligence may obscure, but does not replace, the collective human labor.' His hardest line is on comprehension. If authors cannot give a clear, expert-level talk on their own AI-assisted result, 'then the result should not be published.' Two of the researchers on our AI Weekly radar had already circulated the paper.