Terence Tao Gives Caltech Lecture "Math 2.0" on Machine-Assisted Proofs

Terence Tao has published a recording of his lecture "Math 2.0," delivered at the California Institute of Technology. He began working on the talk more than a year ago, when he called it "Machine Assisted Proof." The lecture was scheduled for May but moved to October. According to Tao, the reason was a number of recent events. The available excerpt does not say which ones. The Chinese outlet Jiqizhixin put the central idea in its headline: the time when proofs were scarce is coming to an end.

What we know about the lecture

The change of title is telling in itself. A year ago the topic sounded instrumental: a computer helps check and find proofs. By autumn 2026 the author had settled on "Math 2.0," which points to a change in the practice of mathematics itself. Tao does not explain this in a single sentence; he points to a chain of events over recent months. The full text and slides are best viewed at the primary source, because the retelling breaks off just where the substantive part begins.

Key details from the available excerpt:

• format: public lecture at Caltech, recording published on 11 October 2026;
• working title during planning: "Machine Assisted Proof";
• final title: "Math 2.0";
• timing: originally May 2026, in practice October;
• preparation time: more than a year.

Where the thesis about the end of scarcity comes from

The idea that proofs are ceasing to be a rare commodity did not appear out of nowhere. Tao has spent the past several years working publicly at the intersection of mathematics and machines. In late 2023 he led the formalization in Lean of the proof of the PFR conjecture (the polynomial Freiman–Ruzsa conjecture).

The project assembled a distributed team and took several weeks. In 2024, Google DeepMind's AlphaProof model solved International Mathematical Olympiad problems at a silver-medal level. In 2025, Tao took part in testing AlphaEvolve on dozens of open problems in analysis and combinatorics.

All of this is prior context, not the content of the new lecture, but it shows a trajectory. First, checking proofs passes to the machine; then part of the search passes to it as well.

In classical mathematics, the scarcity of proofs determined everything. A theorem was considered valuable partly because it took years of human effort, and a referee's verification also cost time. If generation and verification get cheaper, the economics of the discipline change too. Value shifts from the proof itself to posing questions, choosing directions, and understanding why a result matters.

Where the line falls

The Jiqizhixin headline is blunt, whereas Tao usually adds more caveats. Formalization in Lean demands enormous effort, and language models can make confident mistakes. Automated search works well where a result can be checked mechanically. So it is reasonable to expect that "Math 2.0" will describe not a replacement of mathematicians but a new division of labor. That is a guess, not a summary of the lecture: the available text contains no such conclusion.

How to use this in practice

For researchers and engineers following the topic, three steps are useful. First, watch the full recording of the lecture and check any secondary retellings against it, including this one. Second, learn Lean and the Mathlib library: the projects Tao talks about are built on this infrastructure. Third, for teams building AI for science, verifiability is the guiding principle. Models whose outputs can be checked automatically gain a noticeable advantage over those that produce plausible-sounding text.

For now, the lecture is published, and its main thesis remains a matter for reading and discussion. If Tao is right, the coming years will show it in a shift in what journals and conferences consider a result worth publishing.