Hacker News Reader

Comment by nomel | Hacker News Reader

Is that a requirement though? If the AI used existing understanding/methods (which I assume it did) then there's nothing really "new" there, right? Shouldn't it be possible to get understanding from how the existing methods were used? Or, even knowing it's true, cull an incredible number of paths from the problem space around it, to make finding understanding easier?

I'm not a mathematician, but I've always been able to find understandings from exploring the paths starting from either direction of the conceptual graph that exists between a "problem" and a "solution".

View on HN

Would knowing that it's true cull an incredible number of paths? Well, it's either true or it's false. So imagine setting half of the world's mathematicians on proving "true" and the other half on proving "false". Being told in advance by an oracle that "true" is the right answer at best doubles the number of mathematicians you can deploy on making an understandable proof.

There's a joke telling what purportedly happened after the famously abrasive physicist Wolfgang Pauli died and went to heaven. Pauli supposedly got to meet God, and asked God why the fine structure constant had the value 1/137.08 or whatever it is. God said "good question!" and started covering a blackboard with equations. Pauli marveled at the mathematical elegance, said "that's wonderful", etc. until God got to a certain point in the calculation, where Pauli said "that's wrong!!!".

We want explanations, not just answers like 1/137.08.

Not to any great extent.

It’s the equivalent of unrolling a loop into a series of individual linear statements. You’ll never derive monadic forms from that. It requires a far greater intelligence to think that up. As nature can’t speak our language, we have to rely on the stupidity of humans instead to help discover its beauty. So we are stuck with mathematicians.

People, mathematicians, of course care about answers. But they deeply care about how those answers were derived and they’ll duel if they find a given thing looks ugly. People have invented entire fields because shit didn’t look right or left gaps in reasoning or understanding. Take quaternions. Take calculus.

AIs aren’t super intelligent and these grifters and charlatans need to be laughed out of the room.

It is unfortunate to see what happened to terry tao but not at all surprising. He endorsed the snake early on thinking the snake was a friend. It was only a question of time before it would turn on him to bite him.

What is the reason that we won't eventually be able to ask AI to simplify the lean proof, or make it more readable to humans? Or to read the swarm communication logs and summarize the process by which they arrived at the solution?

I don't understand why there seems to be a fundamental limitation on that front.

There's no reason to think the LLM can't be prompted to improve its presentation. Still, can one internalize math simply by reading solution manuals?

Yes? Isn't that what humans do when teaching each other math? I don't see why, however any human prefers to teach/learn math, LLMs can't do that too.

I think the point of the "solution manuals" reference is that you have to do math to learn it, not just read the solution that someone else has written.

Reply on news.ycombinator.com