Terence Tao is a Fields Medal winner known for deep and wide-ranging contributions to analysis, number theory, and related areas. His long record of original work and clear thinking about the practice of mathematics makes his views on this subject worth careful attention.
Tao has written an essay based on a public lecture delivered at the 2026 International Congress of Mathematicians. He considers how the mathematical community should respond if artificial intelligence (AI) systems become able to carry out many research-level tasks. He does not argue about whether those systems will succeed. He assumes they mostly will, and asks instead what the real goals and values of mathematical research are. Mathematics once relied on informal foundations until crises forced the community to state its rules of truth more clearly. A similar clarification is now needed for the unwritten aims of the subject, such as what counts as a true contribution and what deserves recognition.
Tao notes that the traditional goals of mathematics, including solving problems, building theory, training new researchers, and creating lasting understanding, have usually supported one another. AI is especially skilled at chasing measurable targets, which can pull these goals apart. This risk follows Goodhart’s law, the idea that a measure stops working well once it becomes a target.
Examining the process of solving problems
As a concrete case Tao looks at problem solving. Simply producing many solutions is not enough, because many are wrong. Solutions must also be checked for correctness, often with the help of proof assistants, which are computer programs that verify formal proofs. Even a correct proof is of limited value if no one can understand or explain it. The fuller goal therefore includes clear writing, careful reading by the community, acceptance through review, and eventual refinement into the standard form used in textbooks and teaching. Under the assumption of powerful AI the field may face an excess of proofs rather than a shortage. Institutions built for scarcity may then need adjustment. Tao points to practical steps such as open disclosure of tool use, greater weight on explanation and review, and continued human responsibility for results. Making the community’s values explicit, he concludes, will leave mathematics stronger.