> In either case I believe people who can put AI to the most value are the mathematicians themselves
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
"Given infinite thinking time a finite number of humans will solve all theorems"
I also love the angle that this was not intelligence just brute force. As if the mathematicians didn't reeaaally want to solve this they were just too lazy to give it a good try.
What does AI have to actually do before you realize these things are actually smart?
There certainly are such proofs. Even for simple decidable theories we have very large lower bounds on decision complexity (like double exponential), which implies large lower bounds on the function from "length of theorem statement" to "length of shortest proof".
For undecidable theories, there is no computable function bounding this blowup from theorem length to proof length (otherwise, the theory would be decidable.)
bwfan123 · · focus · HN ↗
The net output of math will increase, and mathematicians have more work now to unravel all this, and make it useful. AI plays the role of a monkey in the infinite monkey theorem [1]. We now need an LLM corollary - Something like: A finite number of LLM agents will almost surely find all theorems given an infinite token budget.
[1] <a href="https://en.wikipedia.org/wiki/Infinite_monkey_theorem" rel="nofollow">https://en.wikipedia.org/wiki/Infinite_monkey_theorem
johnsmith1840 · · focus · HN ↗
"Given infinite thinking time a finite number of humans will solve all theorems"
I also love the angle that this was not intelligence just brute force. As if the mathematicians didn't reeaaally want to solve this they were just too lazy to give it a good try.
What does AI have to actually do before you realize these things are actually smart?
glimshe · · focus · HN ↗
pfdietz · · focus · HN ↗
For undecidable theories, there is no computable function bounding this blowup from theorem length to proof length (otherwise, the theory would be decidable.)