Terence Tao, a Fields Medallist and one of the most prominent living mathematicians, argues that his field was built around a scarce resource and that AI has made it plentiful. The argument comes from a slide deck titled “Math 2.0,” dated October 2026 and given at Caltech according to its filename. It is slides from a talk, not a paper, so this reports only what the slides say.
Tao calls traditional mathematics “Math 1.0” and says it ran on an assumption of proof scarcity. Solving an open problem and showing the solution correct was hard and rare, and often took significant human expertise. In his account, the field’s institutions, traditions, incentives and declared goals were all organised around that fact. He calls mathematics “largely stable” for nearly a century and “particularly susceptible” to AI disruption.
The slides give three reasons. Proofs can be checked objectively, and mechanically if written in a proof assistant language such as Lean. They digitize well, needing no physical experiment. And the research literature is largely online. Tao says frontier labs therefore put mathematical problem-solving ahead of applications missing one or more of those traits, and that the result is “an era of proof abundance.” With enough compute and frontier access, he writes, many open problems once thought hard fall quickly, and more and more often the person prompting needs no special expertise.
He hedges that claim hard. AI performance is “extremely jagged,” astounding in places and inadequate in others, inside mathematics and out. Despite what press releases and social media suggest, he says, most problems at the frontier stay unsolved even when huge compute is spent. One slide labels the gap reporting bias: failed attempts go unreported. He asks for assessments that report resource consumption and negative results, and names First Proof as one such effort.
On how the field should respond, he does take a position. Solving problems, he says, only stands in for deeper long-run goals, a stand-in that fit under scarcity and drifts under abundance. Pushing blindly on problem-solving alone is now, in his words, “actively harmful” to the field’s health. That judges a target, not AI itself. Open problems, he says, work as “lighthouses” that guide exploration, and reaching them prematurely by automated tools can “sterilize” the surrounding field.
A thought experiment makes the worry concrete. An AI is asked for a cancer cure that passes a stage 3 trial, supplies a Lean certificate, and succeeds, while nobody knows how it was found. Tao asks whether it could still be misaligned by gaming a flaw in the trial, and whether a patient would want at least one human expert to understand the mechanism.
The proposal is the most useful part. Math 2.0 means expanding the frontier while decentering problem solving, and Tao lists what that looks like. “Open exposition problems” ask for clear, motivated explanations of results whose existing proofs are opaque, with the revised Caltech Mathathon named as an experiment. A student-run event on November 13 to 15 uses open-source AI tools to improve unsatisfactory proofs. The Integrated Explicit Analytic Number Theory Network, an early attempt, is a living “spreadsheet” of linked papers. Other items: formal libraries like Mathlib, AI that surfaces new principles and methods instead of only new proofs, “ablation studies” that re-prove a theorem without a key input, and open-source math models, some due “very soon.”
He also describes a new experimental mathematics built on “population surveys” in place of “case studies.” The Equational Theories Project (2024 to 2025) crowdsourced human and automated arguments to resolve more than 22 million statements in universal algebra. The Inverse Galois Problem challenge’s first stage located degree 24 polynomials for all 25,000 Galois groups of that degree; a second stage aims for degree 31. The primary bottleneck, he says, is “imagination.”
Mathematics is the test case because its output can be checked by machine. That makes it the first field where cheap generated output arrives with a cheap verdict attached, which exposes how much of the surrounding structure was priced on scarcity. Tao’s slides name institutions and incentives in general terms. Credit, publication, hiring and prestige are our reading of what sits under that heading, and each assumed a finished result was costly. Most of our readers work where nothing like Lean exists. Output there will get just as cheap, with no inexpensive way to sort the sound from the plausible, so the scarce asset becomes the person who can judge, and credit and pay will follow that person.
Tao’s own diagram marks aligned applied work as what “requires subjective judgement.” If your team’s reviews or retainers still reward volume of finished work, the first audit this quarter is who among you can actually verify it.
Terence Tao, slides from the talk “Math 2.0,” given at Caltech, dated October 2026.
