Terence Tao says AI is ending the era of scarce proofs and calls for a 'Math 2.0'

Mathematician Terence Tao says AI is changing his field in a basic way. In a slide presentation titled "Math 2.0," dated October 2026 and prepared for a talk at Caltech, he argues that mathematics is moving from an era where proofs were scarce to one where they are abundant.

Tao calls traditional mathematics "Math 1.0." In that world, finding and proving a solution to an open problem was hard and rare. He says many of the field's institutions, traditions and incentives were built around that scarcity.

He explains why math has been so exposed to AI. Proofs can be checked objectively, and experts broadly agree on what counts as a correct one. They can even be checked by computer if written in a proof assistant language such as Lean. Proofs are also easy to digitize, since they need no physical experiment or real-world data. And much of the research literature is already online.

According to Tao, those three traits made math a good fit for the machine learning that powers modern AI. He says frontier AI labs have put math ahead of areas that lack those traits. With enough computing power and access to top models, he writes, people can now get solutions to many open problems that were once seen as hard. Increasingly, the person prompting the AI needs no special expertise.

Tao stresses that AI ability is "jagged." It is astounding in some areas and weak in others, such as tasks that are subjective, depend on real-world interaction, or have little data. He says this is true inside mathematics as well as outside it.

He also pushes back on the impression from press releases and social media. Most problems at the current frontier, he says, remain unsolved even with huge computing spending. The supply of problems is infinite, so the frontier will keep expanding.

Tao points to a reporting bias. Successes get posted, while failed AI attempts often go unreported. He calls for more transparent and scientific assessments of AI ability that report figures such as resource use and negative results. He names First Proof, at 1stproof.org, as one effort in that direction.

His larger argument is about goals. Problem solving, he says, is only a stand-in for more valuable long-term aims. That stand-in worked when proofs were scarce, but he says it no longer fits. He writes that further blind optimization of problem solving alone is now actively harmful to the long-term health of mathematics.

He describes open problems as "lighthouses." They are not destinations in themselves but guides for exploring the mathematics around them. What people learn while trying, whether they succeed, fail or make partial progress, is often worth more than the final answer. Reaching a lighthouse too early with automated tools, he warns, can disrupt exploration of paths not taken and sterilize the surrounding field.

The slides include a thought experiment. An advanced AI is asked to find a cancer cure that passes a stage 3 clinical trial. It produces an unknown chemical cocktail, supplies a Lean certificate, and the cocktail passes the trial. Tao asks whether the result could still exploit a weakness in the trial or its models. He also asks whether a patient would feel reassured knowing at least one human expert understands, even partly, how the cure works.

For "Math 2.0," Tao proposes using AI to strengthen the ways human understanding connects with mathematics. One example is "open exposition problems," where the task is to find motivated explanations of results whose known proofs are opaque. He mentions the revised Caltech Mathathon as an experiment in this direction. Another is collecting many research papers into a living network, such as the Integrated Explicit Analytic Number Theory Network, which he describes as a real-time "spreadsheet" of linked results.

Other examples on his list include building large libraries of formal mathematics, such as Mathlib, and using AI to find new principles and methods rather than only new proofs. He also lists "ablation studies," which test whether a theorem can still be proved after removing a key input. A related idea is exploring the "neighborhood of a theorem" by changing or dropping its assumptions. He adds that some open math models are to be released very soon, without giving details.

Tao also sees a new kind of experimental mathematics. AI makes it possible to gather very large data sets, so researchers can run "population surveys" instead of "case studies." He cites two early examples. The Equational Theories Project, run in 2024 to 2025, crowdsourced human and automated arguments to settle over 22 million true/false statements in universal algebra. The Inverse Galois Problem challenge in 2026 first sought degree 24 polynomials for each of the 25,000 possible Galois groups at that degree, and its second stage aims to extend up to degree 31.

He ends with a blunt line. The main obstacle to Math 2.0, he writes, is not technology or even institutional culture. It is imagination. He thanks Nestor Guillen, Bryna Kra, Rachel Ward and Po Shen Loh for feedback on earlier drafts.