The Mathematician's Future Is Curator, and the Value Isn't in the Proof
AI can solve problems, explain, and prove theorems; the mathematician's value shifts to judging which path is worth taking — and becoming the curator people trust.
The video won't play here. Listen to the audio instead:
The argument · timestamps estimated from transcript position
The limits of an IMO gold medal
Grant revisits the discussion from three years ago about whether an IMO gold medal equals AGI, and thinks the answer then was correct. Geometry problems can be brute-forced by a solver in 19 seconds, while combinatorics problems still stump AI; the reason AI didn't get gold in 2024 is that it ran into combinatorics problems. The real difference isn't "can it do the problems" but that AI capability is "spiky" — breakthrough-level in some areas, still blank in most others.
— Grant SandersonTwo ways to solve the Riemann Hypothesis
Grant splits a possible future proof of the Riemann Hypothesis into two kinds: one is "lightning-style," connecting two fields in an unexpected way (the Montgomery-Dyson story), which people can easily understand; the other is "mountain-building," constructing an entirely new theoretical framework (like Fermat's Last Theorem), which requires higher intelligence and spills over into other parts of the economy. This distinction determines how much explanatory cost an AI proof actually imposes on humans.
— Grant SandersonDefinitions are the highest-order creation
Grant says good mathematicians prove theorems, great mathematicians propose conjectures, and the greatest mathematicians create definitions. From Lagrange's intuition and Abel's proof, to Galois fixing abstract concepts in place, to Jordan organizing it into modern group theory, a "definition-generating" breakthrough took over a hundred years to be fully validated. Verification mechanisms like RLVR struggle to capture the act of "proposing a new definition."
— Grant SandersonWhether an AI proof is understandable depends on its type
Grant thinks whether an AI proof can be digested by humans depends on whether it's "lightning-style" or "mountain-building": connections like Erdős problem 1196 are easy to understand, while an abc-conjecture-style proof might look like alien mathematics. He cites Timothy Chow's "unsettled explanation problem": a proof is not the same as an explanation, and AI in the future may likewise be able to do explanation very well.
— Grant SandersonThe mathematician's future is like a curator
Grant predicts the mathematician's role will shift toward curator: AI can solve problems and explain, but in a "nearly infinite space of ideas," someone still needs to decide which ideas are worth investing time in. This motivation is social — people trust choices made by those they have a relationship with. Even if AI is better at curation, humans will still prefer curators they have a relationship with.
— Grant SandersonGrindability matters more than verifiability
Dwarkesh proposes: AI progresses fast in math and programming not just because results are verifiable, but because the tasks are "grindable" — you can run the model in parallel across a huge number of rollouts, then do credit assignment deterministically. Computer use is also verifiable, but websites have anti-scraping measures, making parallelism hard; math and code can be containerized, while the real world is hard to replicate. This explains why AI learns code and math far faster than real operations.
— Dwarkesh PatelLLM explanations are like Wikipedia
Grant says LLM explanations currently resemble Wikipedia: every sentence is correct, and that's remarkable, but the most useful thing on a page is often the references at the bottom. A good explanation allows temporarily introducing something slightly wrong and then correcting it, yet a crowdsourced environment edits those out. So he himself often asks the LLM "who should I read" rather than directly asking for an explanation, treating the LLM as an enhanced Google to locate human-created resources.
— Grant SandersonThe value of AI math is spiky
Grant thinks AI math's contribution to the economy is also "spiky": a breakthrough in algebraic number theory may not unlock anything, while PDE-related research may apply directly. He gives the example of a research group using simulation to optimize aircraft design, saving Boeing billions of dollars. He predicts that within five years there will be economic-value improvements directly attributable to AI math, but doesn't want to finish the thought.
— 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 an IMO geometry problem | 19 seconds | 3:10 |
| Age at which Galois died | 26 | 22:30 |
| Erdős problem number | 1196 | 30:00 |
| Key factors in AI's progress in math | Verifiability + grindability | 53:48 |
| Lean's role in AI math progress | Overrated, but still has potential | 53:48 |
| DeepMind's approach to IMO problems | Lean in the first year, natural language in the second | 53:48 |
| Another reason AI writes poorly | Lack of theory of mind | 1:07:07 |
| Amount Boeing saved | Billions of dollars | 1:21:00 |
Glossary
- grindability
- A task can be containerized and attempted in parallel at scale, thereby solving credit assignment deterministically.
- theory of mind
- The ability to perceive and predict others' cognitive states; writing needs it and AI lacks it.
- RLVR
- Training models with automatically verifiable reward signals, suited to tasks with objective answers like math and code.
- Langlands Program
- The research spirit of seeking deep connections between different areas of mathematics, rather than some specific problem awaiting proof.
How to listen
Founders and engineers trying to judge the boundary of AI capability, especially those wondering whether math/code get taken over by AI earlier than the real world.
The opening IMO gold-medal retrospective can be skipped; don't miss the Riemann two-category distinction and the Galois section.