Terence Tao delivers Caltech talk 'Math 2.0': mathematics is moving from proof scarcity to proof abundance

Terence Tao publicly delivered his Caltech lecture "Math 2.0." According to him, the lecture began planning over a year ago, initially titled "Machine-Assisted Proof," originally scheduled for May of this year, and later postponed to October; due to a series of recent events, the lecture content also changed greatly. However, the Caltech event webpage still retains the original title and abstract.

This detail itself serves as the entry point for understanding the entire lecture: the title changed from "Machine-Assisted Proof" to "Math 2.0," pointing not to a single technological advance but to an overall shift in how mathematical research operates. The lecture's landing point is also not "how many problems AI can solve," but how the mathematical community should use this capability.

Tao called traditional mathematical research "Math 1.0," believing it was built on a core premise: mathematical proofs are scarce. Finding an answer to an unsolved problem and rigorously proving its correctness is usually very difficult and quite rare, requiring deep professional knowledge and a great deal of time and energy. Many existing institutions, traditions, incentive mechanisms, and research goals in the mathematical community were established around this assumption.

In his view, the reason mathematics is particularly susceptible to this round of AI impact is that it simultaneously possesses three conditions: objective verifiability, high digitization, and large amounts of high-quality data. Once proofs are written in formal languages such as Lean, computers can even mechanically check their correctness; mathematical proofs do not need a physical carrier, nor do they depend on real-world data input or real-world experimental verification.

From this he judged that, as frontier AI laboratories invest heavily in mathematical capabilities, mathematical research is entering an era of "proof abundance": as long as there is sufficient compute and access to frontier AI models, it may be possible to obtain answers to many previously very difficult open problems in a relatively short time, and the questioner need not even possess the professional knowledge to solve the problem.