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Terence Tao - How the world's top mathematician uses AI

2026-03-20 - 84 min - source - Read full transcript
Dwarkesh Patel (host)Terence Tao

Key insights

AI has driven the cost of generating scientific ideas to near zero, but this does not create abundance by itself - verification and evaluation are the new bottleneck.
Tao compares it to how the internet drove communication costs to zero without automatically producing good communication. Peer review systems built for a world of scarce ideas are now overwhelmed: journals report being flooded with AI-generated submissions, and there is no scaled mechanism to sort signal from slop when thousands of candidate theories can be generated per problem.
ai-idea-generation-glut
The Kepler-Brahe story shows verification loops for correct theories can take decades, and a correct theory can initially make worse predictions than an incorrect one.
Copernicus's heliocentric model with circular orbits was actually less accurate than Ptolemy's geocentric model, which had a millennium of ad hoc refinements. It took Kepler, using Brahe's decades of naked-eye observational data, to fix the circular-orbit error and make heliocentrism more accurate. Tao uses this to caution against assuming AI can compress scientific validation timelines just because it generates more candidate ideas faster.
history-of-science-analogies
In systematic testing, AI models solve open math problems (like Erdos problems) at only a 1-2% success rate per attempt - the appearance of frequent breakthroughs is survivorship bias.
About 50 of roughly 1,100 open Erdos problems have fallen to AI assistance, which sounds impressive when only the wins are publicized. But large-scale sweeps show a 1-2% hit rate per problem; models 'buy scale' and the successes get broadcast while failures don't. Tao expects the same pattern with more prestigious problems: occasional lucky solves generating outsized publicity relative to the underlying reliability.
ai-mathematical-proof
AI-assisted math currently succeeds mainly where existing techniques already solve 80% of a problem and the AI supplies a missing, underused method from the literature - not where genuinely new mathematics is required.
Tao notes that almost all the solved Erdos problems had essentially no literature attempting them; the AI's contribution was combining one obscure known technique with another known result, not inventing anything new. He calls this 'the median level of what AI can accomplish' - useful, but not yet capable of filling holes where no existing technique applies.
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AI models don't accumulate understanding across a research session the way a human collaborator does - they can jump toward a solution but can't build cumulatively from partial progress.
Tao uses a climbing-wall analogy: AI tools jump higher than any human but either succeed outright or fail, without the intermediate 'reach a handhold, hold it, pull others up' process human collaborators use. A new AI session starts from scratch with no memory of the last one's partial progress; at best, a session's work becomes an infinitesimal fraction of the next model's training data.
human-ai-complementarity
AI has made Tao's papers richer and broader, but not necessarily deeper - it speeds up auxiliary tasks, not the hardest reasoning.
Tao estimates papers written with today's AI tooling would take five times longer without it, because AI now handles literature search, generating plots and numerics, and reformatting. But the core, hardest part of solving a problem still happens with pen and paper at roughly the same pace as before; if he simply rewrote an old paper without adding the new AI-enabled extras, the time savings would be minimal.
human-ai-complementarity
Humans and AI are complementary along a breadth/depth axis, and science needs to be redesigned around AI's new breadth capability rather than forcing it into human-style depth-first work.
Humans excel at sustained depth on a small number of hard problems because that is the only mode available to a single mind; AI can apply broad, moderately competent effort across huge numbers of problems simultaneously. Tao argues the field should invest more in mapping very broad problem classes with AI first, then directing human depth at the resulting islands of difficulty.
human-ai-complementarity
Math currently lacks a way to formally assess research strategy and plausibility, the way Lean formally verifies proofs - Tao wants a semi-formal language for mathematical strategy, though it doesn't exist yet.
Lean automates checking whether a completed proof is valid, but offers nothing for judging whether a conjecture, strategy, or direction is worth pursuing before it's proven. Tao points to the prime number theorem and the statistical/pseudo-random model of primes as an example of the kind of non-rigorous but highly persuasive reasoning mathematicians rely on, and says no formal framework yet exists to make that reasoning auditable or trainable the way Lean makes proofs auditable.
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Formalizing a proof in Lean lets mathematicians inspect individual lemmas in isolation, which Tao expects to spawn a new discipline of refactoring and interpreting giant AI-generated proofs.
Because each Lean step is identified precisely, a mathematician can tell which lemmas are standard boilerplate and which are the actual novel insight enabling the result. Tao is not worried about an incomprehensible AI-generated proof of something like the Riemann hypothesis, pointing to the Erdos problem website's pattern of AI-generated proofs being subsequently summarized and refactored by other AIs and humans.
ai-mathematical-proof
Tao deliberately protects unstructured time and 'serendipity' in his schedule, arguing that optimizing everything (including via AI) risks eliminating the inefficient encounters that produce real ideas.
He cites the pre-internet experience of browsing physical library shelves and finding unexpected adjacent articles, versus instant AI/search retrieval that gives exactly what was asked for and nothing more. He also describes running out of inspiration after several distraction-free months at the Institute for Advanced Study, concluding he needs 'a certain level of distraction' and worries that COVID-era all-scheduled remote meetings, and now AI efficiency, are compounding a broader loss of serendipity in academia.
tao-personal-practice
Tao's advice for people starting a math career in the AI era: still get traditional credentials, but stay open to genuinely new, non-traditional routes into frontier research that didn't exist before.
He notes that AI tools and Lean now make it plausible for a high-schooler to contribute a real result to frontier math research, something that used to require a math PhD. He frames this as an unpredictable era where some skills become obsolete while others are retained, and recommends an adaptable mindset over betting heavily on any single specialization.
tao-personal-practice

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Summary

Dwarkesh Patel and Terence Tao spend the episode testing an extended analogy: was Johannes Kepler, cycling through decades of wrong hypotheses about planetary orbits before hitting on his three laws, effectively "a high-temperature LLM"? The framing lets them work through what AI actually changes about scientific discovery. Tao's central claim is that AI has driven the cost of generating ideas to near zero, much as the internet did for communication, but that this does not by itself create scientific abundance. The bottleneck has simply moved: from generating hypotheses to verifying and evaluating them at a scale current peer-review institutions were never built for. Journals are already reporting being flooded with AI-generated submissions, and Tao argues there is no working mechanism yet to sort genuine progress from plausible-looking slop when thousands of candidate theories can be produced per problem.

Much of the conversation runs through history-of-science case studies - Kepler and Brahe, Copernicus versus Ptolemy, Darwin versus Newton's reception, the discovery of "the bit" at Bell Labs - to probe how correct new theories get recognized and adopted, often slowly, often while looking worse than the incorrect theories they replace. Tao repeatedly returns to the idea that assessing whether a discovery constitutes real progress is inherently contextual: it depends on future developments, culture, and communication skill (Darwin's plain English versus Newton's guarded Latin), not just on internal correctness. This is why he doubts scientific-idea-assessment can simply be reinforcement-learned the way narrow, verifiable problems can.

On math specifically, Tao gives a granular account of where current AI tools actually help: roughly 50 of about 1,100 open Erdos problems have fallen to AI assistance, but systematic sweeps show a 1-2% success rate per attempt rather than a reliable capability - the visible wins are survivorship bias at scale. The AI solves that have worked follow a consistent pattern: problems where existing literature already gets 80% of the way and the missing piece is one obscure known technique the AI can locate and apply, not problems requiring genuinely new mathematics. He distinguishes "artificial cleverness" from intelligence: AI can jump toward solutions and fail cheaply and repeatedly, but it can't build cumulatively from partial progress across a session the way two human collaborators refining an idea together can, and each new session starts from zero.

Tao is concrete about his own productivity: AI-assisted papers would take roughly five times longer to produce without today's tools, mostly because AI now handles literature search, generates plots and numerics, and reformats his writing. But the actual hardest reasoning - the core of solving a difficult problem - still happens with pen and paper at about the same pace as before. His verdict is that AI has made his papers "richer and broader, but not necessarily deeper." Looking forward, he expects humans and AI to remain complementary along a breadth/depth axis for a long time rather than AI simply replacing human mathematicians, and predicts an emerging discipline built around Lean-formalized proofs: taking giant AI-generated proofs and refactoring, ablating, and interpreting them for human understanding, since Lean lets any individual step be inspected in isolation to see whether it's novel or boilerplate.

The episode closes on Tao's own working habits and advice. He describes himself as a "fox" (Isaiah Berlin's framework) who learns new subfields through obsessive curiosity, collaboration, and a long-running blog he started specifically so he wouldn't forget techniques he'd learned. He argues deliberately for protecting unstructured time and serendipity - citing his own experience browsing physical library shelves versus instant AI retrieval, and running out of inspiration after months of distraction-free research at the Institute for Advanced Study - and worries that both remote-work scheduling culture and AI efficiency are compounding a broader loss of the inefficient, unplanned encounters that actually generate ideas. His closing advice to someone starting a math career: still pursue traditional credentials, but stay open to genuinely new non-traditional routes into frontier research, since AI and Lean now make it plausible for people well outside the traditional PhD pipeline to make real contributions.

Notable Quotes

"I think AI has driven the cost of idea generation down to almost zero, in a very similar way to how the internet drove the cost of communication down to almost zero." - Terence Tao

"The take I want to try on you is that Kepler was a high-temperature LLM." - Dwarkesh Patel

"It's made the papers richer and broader, but not necessarily deeper." - Terence Tao

"I guess I do believe that hybrid human plus AIs will dominate mathematics for a lot longer." - Terence Tao

"We're not optimizing our own optimization." - Terence Tao