Terence Tao warns of a new mathematical crisis: Proofs will become too complex for anyone to digest

According to Dynamic Beating Monitor, Chinese mathematician Terence Tao stated in his speech at the International Congress of Mathematicians (ICM) that mathematics is facing a fundamental crisis regarding values and research methods. ICM is held every four years, and the Fields Medal is also awarded during the opening ceremony of the conference.

He first established a premise: AI will soon be able to complete a significant proportion of research-level mathematical tasks at a reasonable cost. In the latest First Proof test, four sets of AI systems were presented with 10 new research problems, and at least one system produced publishable quality solutions for 7 of them. The cost of computing power per problem ranged from $10 to $1000.

Tao believes that mathematics will transition from a state of "proof scarcity" to "proof abundance." The proofs generated by AI will accumulate waiting for verification; the verified results will then need to be elucidated, peer-reviewed, digested, and eventually incorporated into textbooks and established theories within the field.

The truly scarce ability will no longer be merely the first to solve a problem, but rather to assess the significance of the result, explain the proof clearly, and transform it into knowledge that is collectively understood by humans. If an author is unable to articulate their accomplishments clearly and accurately, even if the proof is generated by AI and passes verification, it should not be published.