lol same with people.

"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?

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alansaber 2 hours ago | parent | next [-]

Machines have a much higher capacity for work than human beings. Saying that these proofs did not require equivelant intelligence, but benefitted from sheer volume, does not strike me as unreasonable.

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jimmaswell an hour ago | parent [-]

It feels goalpost-movey to downplay exploring a large search space efficiently in regards to "intelligence". If we dug into a human genius's brain and found it was somehow trying out a million ways to solve a a problem at once, no one would seriously suggest the person isn't actually intelligent.

And our brains must something like that at some physical level. You can't have a "turtles all the way down" of reasoning - the building blocks must be simpler. It must reduce to something like pathfinding and brute force at some point, weighted by factors in the system and maybe some randomness.

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alansaber 37 minutes ago | parent [-]

We have a romantic view of intelligence, perhaps stemming from intuition within the context of scientific discovery. Given enough intelligence, and enough context, a brilliant person can have a stroke of inspiration that allows them to make a major leap (a-la General Relativity or Fermats last theorem). We haven't seen THAT same capacity from a machine, but we see the more ordinary, unsexy grinding type of progress that represents 99.9% of scientific reality.

	▲	williamcotton 17 minutes ago \| parent [-]
		Is there truly anything new under the sun? Hasn't all of existence alway been here? All math, all physics? We could have merely discovered it. Intuition might be nothing more than combinations of what already exists rather than some sort of divine insight that unlocks previously unknowable mysteries.

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glimshe an hour ago | parent | prev [-]

This isn't necessarily true. There may be proofs so complex, they could exceed the limit of human cognition.

	▲	pfdietz an hour ago \| parent [-]
		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.)