Grant Sanderson – AI and the future of math

The episode opens with its premise stated as a fact rather than a forecast: mathematics is where superintelligence will show up first, so the shape of AI progress there is the best available preview of its shape everywhere else. Dwarkesh frames the conversation around four questions — what conceptual breakthroughs in mathematics actually consist of and whether the models can produce them, whether AI on net raises or lowers human understanding of the field, how large the overhang is from systematically connecting ideas already in the literature, and what advice to give students entering fields AI is transforming fastest.

The guest is Grant Sanderson of 3Blue1Brown, now building a project documenting AI's progress in mathematics. His reason for caring is the same as Dwarkesh's: whatever is happening in this field, in whichever direction, generalises.

The episode then reaches back three years to a question Dwarkesh asked in their first interview. If we get models that win gold at the International Mathematical Olympiad, isn't that simply AGI? Given how hard those problems are, wouldn't such a system be able to do anything a human can?

Sanderson's answer then — that it would be one more benchmark, like all the others, with no aha moment attached — has aged well. Dwarkesh wants two things now: the heuristic behind why that was right, and a bound on how long the narrowness can last. If a model solves a Millennium Prize Problem, can there still be a great deal of human work in the economy it cannot automate?

Sanderson's answer begins with an epistemic caveat: the question is hard to answer without knowing what the solution looks like in advance. The IMO felt like a creativity test because the problem designers deliberately aim for things you cannot drill. The dirty secret is that for a great many of them you can.

And the spikiness is fractal. Zoom into mathematics and the subfields separate sharply. Geometry, since 2024, is cold-solved in nineteen seconds — it is a brute-force solver, and students have a brute-force approach available to them too.

Combinatorics is the wild card: more playful, more puzzle-like, and the models struggle. The IMO has four categories and six problems, so the distribution of questions is a lottery. That year had two combinatorics problems; with more geometry instead, the model would have had gold in 2024.

Sanderson then names the assumption buried in the original question. Asking whether a Millennium Prize solver also does white-collar work presumes that the rate limiter between here and there is the same rate limiter as for white-collar competence. That is the thing to test, and the rest of the conversation is the test.

The models are extraordinary at deep knowledge of one domain, and then another, and then another. What is bizarre is a system with that breadth that does not find the lightning bolts connecting the fields — and there are now sparks of it happening.

Sanderson's illustration is the Montgomery–Dyson story at the Institute for Advanced Study. A number theorist studying the statistical correlation between pairs of zeros of the Riemann zeta function writes down a formula — something like one over sine squared. Freeman Dyson, a physicist, recognises it: that expression appears in the eigenvalues of random Hermitian matrices, which appear in the study of nuclear energy levels.

Whether random matrix theory has real fruit for the zeta function is still partly open. But the bridging is the point. If the solution to the Riemann hypothesis looked like pushing that kind of connection further, it would be exactly the character of problem LLMs should be good at: they are experts in quantum physics and in analytic number theory, and they should see the similarity without needing two people to happen to have lunch together. That is nothing like editing, where the difficulty was never that the editor knows everything and simply needs to find the connecting insight.

The alternative shape of solution is Fermat's Last Theorem. The question is stated in a line — integer solutions to x^n + y^n = z^n for n greater than two — and it looks like it ought to admit an elementary number-theoretic approach. As far as anyone can tell, it does not.

The actual proof required two mountains of machinery, one built around elliptic curves and one around modular forms, each resting on centuries of work, and both had to exist before the right question connecting them could even be posed.

If the Riemann hypothesis requires building a new mountain, that is a different skill — the ability to invent the right new ideas, to crystallise a theory that tells you how a subject should be thought about. That is not what you need from a video editor. But a system capable of building the correct new mountain is at such a level of intelligence that it would be surprising if it did not permeate the rest of the economy. At the very least it would be transformative in a way that IMO gold was not.

Dwarkesh concedes the goalpost move outright. When he interviewed Dario Amodei two or three years ago he asked why models could not use their vast knowledge to connect ideas and produce a discovery — the kind of inference a moderately intelligent person could make, noticing that one drug causes migraines and another does something else and perhaps the same compound treats both.

Mathematics, from outside, looked like the field where that had just happened: finding the counterexample to the unit distance conjecture was exactly that shape. So: goalposts moved. The productive question is what the next benchmark is, now that the models have done the thing we should have expected them to do.

Two candidates. The first is generating interesting problems in the first place — Riemann did not inherit the zeta function, he built it because he suspected its zeros were connected to the density of primes. Understanding why an object is worth constructing, and why this particular question about it is worth answering, is the next frontier. The second is inventing new kinds of objects or conceptualisations that create or unify fields.

Sanderson points to a Polylog video on the unit distance conjecture, and to a line quoted in it that maps exactly onto Dwarkesh's two candidates: good mathematicians prove theorems, great mathematicians come up with conjectures, and the greatest mathematicians come up with definitions. That is the ladder — theorem generator, then conjecture generator, then definition generator, which is the premium tier.

The problem is that this does not fit the form of a benchmark. A benchmark is a goalpost: the ball is through or it is not, and you can say yes, this is done. Part of that is what makes RLVR possible; part of it is simply knowing you have not moved the goalposts while grading. OpenAI can put out a headline on disproving the unit distance conjecture because it is a clean, discrete thing that happened. A headline saying the next model came up with a really good conjecture — "we promise everyone thinks it's good" — does not land the same way.

That does not make it the wrong thing to think about. Sanderson doubts it will ever take benchmark form, because a benchmark requires quantifying how good a conjecture is. What it will look like instead is a tone shift in how mathematicians talk about what the tool is useful for.

That tone shift is already the subject of his own project — a series, still months from release, built from interviews with many mathematicians begun over a year ago. Between mid-2025 and 2026 the way they describe AI has changed, and the interval is short in the real world and geological in AI time.

So the measurement is subjective and behavioural: mathematicians saying that they are not merely using it to solve problems, but that when they step back to decide what their research field should even be, a conversation with a particular model was genuinely useful. Not a headline about another benchmark knocked down.

Dwarkesh draws the structural conclusion: the things you cannot benchmark are, at least in the current paradigm, the things you cannot easily train for, because there is no fundamental difference between a benchmark and a training environment.

Sanderson warns against his own argument. It is very easy to construct a deep-sounding reason why AI cannot do some thing, and then discover you were simply thinking about it wrong and it can do it shortly afterwards. He is going to offer a couple of such reasons anyway — Dwarkesh notes that he will — and his own hedge is that while there probably are ways to train these abilities in the relatively near term, they will have to differ from current RLVR.