Mathematicians Become Curators; the Value Is Not in the Proof
AI can solve problems, explain them, and prove theorems; the mathematician's value shifts toward judging which path is worth taking — and toward being a curator people trust.
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The argument · timestamps estimated from transcript position
An IMO gold medal is not AGI; AI capability comes in spikes
Grant revisits the debate from three years ago over whether an IMO gold medal would amount to AGI, and thinks the answer given at the time was right. A geometry problem can be cracked by a brute-force solver in 19 seconds, while combinatorics problems still defeat AI; the reason AI did not take gold in 2024 was that it ran into a combinatorics problem. The real distinction is not whether it can do the problems, but that AI capability is ‘spiky’ — breakthrough-level in certain areas, still blank across most of the rest.
— Grant SandersonWhether a Riemann proof is lightning or mountain-building decides its explanatory cost
Grant splits the possible future proofs of the Riemann hypothesis into two kinds. One is the ‘lightning’ sort, which connects two fields in an unexpected way (the Montgomery-Dyson story) and which a human can follow easily. The other is the ‘mountain-building’ sort, which erects an entirely new theoretical framework, the way the proof of Fermat's Last Theorem did; that kind demands more intelligence, and it spills over into the rest of the economy. Which of the two it turns out to be determines how much explanatory cost an AI proof imposes on humans.
— Grant SandersonCreating definitions, not proving theorems, is mathematics' highest act of creation
Grant says good mathematicians prove theorems, great mathematicians pose conjectures, and the greatest mathematicians create definitions. From Lagrange's intuition through Abel's proof, to Galois pinning the abstract concepts down, and on to Jordan organising it all into modern group theory, a single ‘definition-generating’ breakthrough took more than a hundred years to be fully validated. Verification mechanisms like RLVR have a hard time capturing a move like proposing a new definition.
— Grant SandersonWhether an AI proof can be understood depends on which type it is
Grant thinks whether humans can digest an AI proof depends on whether it is ‘lightning’ or ‘mountain-building’: a connection like the one in Erdős problem 1196 is easy to understand, while an abc-conjecture-style proof could read like alien mathematics. He cites Timothy Chow's ‘unsolved exposition problem’: a proof is not an explanation — though AI may turn out to do the explaining just as well.
— Grant SandersonMathematicians turn into curators, and people trust curators they have relationships with
Grant predicts the mathematician's role shifts toward curation: AI can solve problems and can explain them, but in an ‘almost unbounded space of ideas’ someone still has to decide which ideas are worth spending time on. The motive here is social — people trust choices made by someone they have a relationship with. Even if AI is the better curator, humans will still prefer a curator they have a relationship with.
— Grant SandersonGrindability, not just verifiability, explains where AI improves fastest
Dwarkesh argues that AI's fast progress in mathematics and programming is not only because the results are verifiable, but because the tasks are grindable: you can run the model over a large number of rollouts in parallel and then do credit assignment deterministically. Computer use is verifiable too, but websites have anti-scraping defences, so it is hard to parallelise; mathematics and code can be containerised, whereas the real world is hard to replicate. That is why AI learns code and mathematics far faster than it learns real operation.
— Dwarkesh PatelLLM explanations are Wikipedia: every sentence correct, most useful at the references
Grant says LLM explanations right now are a lot like Wikipedia: every sentence is right, which is itself remarkable, but the most useful thing on the page is usually the references at the bottom. Good exposition allows you to introduce something slightly wrong for a moment and then correct it, and a crowdsourced environment edits exactly that out. So he often asks an LLM ‘whom should I read’ rather than asking for the explanation directly, treating the LLM as a souped-up Google for locating human-made resources.
— Grant SandersonThe economic value of AI mathematics will also arrive in spikes
Grant thinks AI mathematics will contribute to the economy in a ‘spiky’ way as well: a breakthrough in algebraic number theory may unlock nothing, while work related to PDEs could be applied directly. He gives the example of a research group that used simulation to optimise aircraft design and saved Boeing billions of dollars. He predicts that within five years there will be improvements in economic value directly attributable to AI mathematics, but he stops short of spelling the rest out.
— Grant SandersonIn their own words · checked verbatim
good mathematicians prove theorems, great mathematicians come up with conjectures, and the greatest mathematicians come up with definitions.
Grant Sanderson9:00
There is a difference between proof and explanation.
Grant Sanderson14:58
You build a man a fire, and he’s warm for one night. But set a man on fire, and he’s warm for the rest of his life.
Grant Sanderson38:08
It’s not even a field of math so much as it is a research ethos.
Grant Sanderson40:56
LLM explanations feel to me at the moment a lot like Wikipedia, which is to say, amazing. Imagine a world before Wikipedia, how long it would take to find and suss everything. But nevertheless, what’s the most useful part of a Wikipedia page? It’s often just the references at the bottom.
Grant Sanderson1:02:15
It can’t be slop in the way that code can be slop and still produce the outcome you want.
Dwarkesh Patel1:07:07
It’s a little too placating. This is ultimately that sycophantic behavior where it’s very, “Oh, what an insightful question.” You want to strip that down.
Grant Sanderson1:07:20
I actually think teaching is one of the most stable post-AGI jobs that there is, because it’s so relational.
Grant Sanderson1:13:00
Figures
| Time to solve the IMO geometry problem | 19 seconds | 3:10 |
| Galois's age at death | 26 | 22:30 |
| Erdős problem number | 1196 | 30:00 |
| Key factors behind AI's progress in mathematics | verifiability + grindability | 53:48 |
| Lean's role in AI's progress in mathematics | overrated, but still holds potential | 53:48 |
| How DeepMind solved the IMO problems | Lean in the first year, natural language in the second | 53:48 |
| The other reason AI writes badly | no theory of mind | 1:07:07 |
| Amount Boeing saved | billions of dollars | 1:21:00 |
Glossary
- grindability
- A task that can be containerised and attempted in parallel at volume, so that credit assignment can be resolved deterministically.
- theory of mind
- The ability to sense and predict another person's cognitive state; writing requires it and AI lacks it.
- RLVR
- Training a model on reward signals that can be verified automatically; suited to mathematics, code and other tasks with objective answers.
- Langlands Program
- A research spirit of hunting for deep connections between different areas of mathematics, rather than one specific open problem.
How to listen
Founders and engineers trying to locate the edge of AI capability, especially anyone who cares whether mathematics and code fall to AI earlier than the real world does.
The opening recap of the IMO gold medal is skippable; do not miss the two-kinds-of-Riemann-proof split or the Galois passage.