Terence Tao Urges AI Model Companies to Slow Down on Mathematics

The remarks mark a turn for a mathematician who, in March 2026, told an IPAM conference that AI was "ready for primetime" in mathematics and theoretical physics and could spare researchers large amounts of wasted effort. In an interview with MIT Technology Review the same month, he described mathematics as undergoing a Copernican revolution. In an earlier conversation with QbitAI, he said that even middle school students would eventually be able to contribute to frontier research by combining AI with the Lean proof assistant.

At the center of his current argument is what he calls proof indigestion. A proof, he says, normally passes through five stages: a proposed solution, mechanical verification in a formal language such as Lean, exposition that translates the derivation into language people can read, peer review that turns the result into a shared consensus, and finally absorption into textbooks that teach the next generation. AI has compressed the first two stages while the last three have barely advanced, he said, leaving proofs that nobody has presented, published or explained.

Tao compared unsolved problems to lighthouses. Most ships do not sail to a lighthouse, he said, but it illuminates the surrounding waters and land; the value of a hard problem lies in the tools, frameworks and insights built while working on it, not in the answer itself, since proofs of major conjectures cannot cure cancer or crack nuclear fusion.

Two longer-term risks follow, according to Tao. New problems and research directions often emerge from gaps noticed while writing textbooks or from chance discoveries made during slow exploration, and a model that jumps straight to the final answer removes those opportunities. He also warned of data contamination: models are strong at mathematics today because they consumed centuries of polished textbook material, and no one knows what happens when future models train on a literature filled with AI-generated proofs no human understands. He drew an analogy to cloning mice, where repeatedly cloning from cloned cells accumulates shortened telomeres, lost epigenetic marks and somatic mutations, so that later generations develop abnormalities or fail to survive. Releasing proofs this way, he said, is irresponsible.

Tao has also signed an open letter with 25 Fields Medalists, among them Peter Scholze, Deng Yu and Pierre Deligne, criticizing OpenAI and other model companies for treating mathematics as a benchmark to be scored, a practice the signatories said is misaligned with what mathematics is for. He has written several blog posts on the subject.

Other leading mathematicians have reacted more strongly. Cedric Villani, another Fields Medalist, said he was shaken by OpenAI's reported solution of a Millennium Prize problem and described it as a catastrophe without precedent in mathematics, according to QbitAI. Three months earlier, the same report noted, he had dismissed large language models as statistical parroting machines with no intelligence, citing their failure on a simple car-wash question.

OpenAI responded to the criticism by announcing an independent advisory group based at the Institute for Advanced Study in Princeton, called the Advisory Group on Mathematics and AI. The company said the group would advise on the review and dissemination of emerging results, help assess their importance and coordinate how they are communicated. Its statement also said the group would not advise on internal mathematical progress, QbitAI reported.

Comments on the dispute, as described by the outlet, were largely unsympathetic to the mathematicians, with readers joking about the situation and asking where Tao had been when painters, writers and programmers were displaced.

Editor's Summary

Terence Tao, previously among the most prominent advocates of AI in mathematics, now says model companies are releasing proofs faster than the field can verify, explain or teach them, and warns that a literature of machine-generated proofs could degrade future training data. OpenAI answered the criticism from Tao and 25 Fields Medalists with an advisory group housed at Princeton's Institute for Advanced Study, which it said will not advise on internal mathematical progress. The exchange leaves unresolved whether AI-driven proof generation will be absorbed by the mathematical community or continue to outrun it.