I suppose it will fall to AI as well to compose the mathematical equivalent of The Ballad of John Henry. Who will be the human champion, the last great hero who can deliver proofs "from the book" that a machine cannot outperform?
I suppose it will fall to AI as well to compose the mathematical equivalent of The Ballad of John Henry. Who will be the human champion, the last great hero who can deliver proofs "from the book" that a machine cannot outperform?
This is an unhealthy view of mathematics. It's mathematics as envisioned by football fans.
The most valuable things in mathematics are not beautiful proofs. We need more useful definitions. Actually coming up with useful definitions (and building good conjectures out of them - not even theorems, conjectures) is something LLMs have not yet tried to conquer.
"Gonna Die With My Hand-Written Proof in My Brain" - Recorded in 2027 and compiled in the Anthology of American Folk Mathematics (2052)
It's probably not quite that dramatic yet, though it seems possible it will get there, maybe even soon.
There's no structural reason to expect acceleration any more or less than an asymptotic behavior (if even that, acceleration is probably the bigger ask). Different problems yield to a new solvent, maybe that's also more, but it could go either way and we definitionally don't know yet because we don't understand the convexity of AI capability, we cannot directly access it interiority, we don't know if it's sandbagging (other than that it does sometimes, it can). It's an emergent phenomemon that might actively resist measurement. Or it might be as predictable as a clock in a few years.
No one knows, or if they do, they aren't talking. The loud people don't know anything.