Terence Tao’s Caltech lecture ‘Math 2.0’

Tao’s Caltech public lecture had been booked more than a year earlier under the title “Machine Assisted Proof”. It slipped from May to October and, in his words, “with recent events the talk changed significantly”. He gave it on Friday evening, 9 October, three days after OpenAI posted 722 AI-written manuscripts on GitHub, and posted the slides the next morning. The short blog post sums it up as three parts: the historical “Math 1.0”, “the current state induced by the excessive emphasis on automated solving of open problems by AI”, and a “Math 2.0” in which AI tools “sustain both the internal mathematical community, and the role that mathematical understanding plays in advancing and aligning the applications of mathematics to the real world”.

The slides give the argument in steps. Mathematics was built around proof scarcity. Proofs are objectively checkable (even by Lean), fully digital and backed by a huge digitized literature, which makes them ideal for machine learning. Frontier labs therefore invested heavily in maths, and the field is now in an era of proof abundance. Many hard open problems can be solved “in relatively short amounts of time” given compute and frontier models, often by users with no special expertise. Tao separates this from the public impression. A slide titled “Reporting bias” mocks the feeling that every problem on social media is being solved by AI, and he insists most frontier problems remain open “even with massive computational expenditure”, asking for reports that include compute used and failed attempts.

His central claim is about alignment within mathematics. Solving open problems was always a proxy for longer-term goals, mainly human understanding that can then be carried safely into messier applied problems. The proxy worked under scarcity and “has become misaligned in the era of proof abundance”. Open problems are “lighthouses”, and reaching them early with automated tools can “sterilize the surrounding field”. A diagram shows AI short-circuiting the cycle from pure problems to understanding to aligned applied solutions. A medical thought experiment (a Lean-confirmed, trial-passing cancer cocktail that nobody understands) makes the point that verification is not the same as understanding.

The constructive half lists “Math 2.0” uses of AI: open exposition problems instead of open research problems (the revised Caltech event, renamed “Old Problems, New Proofs”, Nov 13–15), the Integrated Explicit Analytic Number Theory Network, large formal libraries such as Mathlib, ablation studies (re-proving a theorem without a key input), mapping the “neighborhood of a theorem”, interactive syntheses of whole theories, and open, interpretable maths models. On the last he adds: “Some open math models to be released very soon - stay tuned!” He also points to large-scale “experimental mathematics” (the Equational Theories Project, the IGP24 Inverse Galois challenge). He ends: “The primary bottleneck to achieving ‘Math 2.0’ is not technology, or even institutional culture. It is imagination.”

Tao is the mathematician most often cited on AI and maths, and this is his fullest public statement after OpenAI’s release. It turns his 6 October Mastodon post into a framework that other commentators already use, “proof scarcity” giving way to “proof abundance”. It is neither a boycott call nor a celebration. He accepts the capability jump and calls further problem-solving races harmful, and he makes specific proposals that institutions can adopt. The “open math models” remark suggests a non-lab, open-source tool release is coming (no date or details given).