Re:Some stuff I found interesting about number theory research
by daxfohl on Monday July 26, 2021 @01:11PM
(#27962041)
In a way that's what makes the question of AI math interesting. Probably AIs will be better than us at math in a couple decades. But that might not change anything because it's still up to humans to determine whether a result is interesting. And it may take us just as long to understand AI-created concepts as to build them up ourselves. Maybe math starts looking more like archaeology at that point. (Though it's arguably archaeology anyway -- the proofs are all "out there", we just have to find them).
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Re:Some stuff I found interesting about number theory research
by Y_Y on Monday July 26, 2021 @03:04PM
(#27963816)
I like this idea. People often ask if maths is "created" or "discovered". Maybe we can say that it's "excavated" and that we know it's down there somewhere, we just need to put in a few years of shoveling.
Re:Some stuff I found interesting about number theory research
by yellowcake0 on Monday July 26, 2021 @06:31PM
(#27966282)
There is no way that AI will be better than us at math in a couple of decades.
Re:Some stuff I found interesting about number theory research
by daxfohl on Monday July 26, 2021 @07:18PM
(#27966705)
Yeah I think I agree now. They'll probably be better at proving straightforward things that don't require any big new insights, but I don't think machines will ever be any good at determining what kinds of new concepts will be interesting to define and explore. Like a machine isn't going to develop calculus just for fun from base principles.
Re:Some stuff I found interesting about number theory research
by daxfohl on Monday August 02, 2021 @04:33PM
(#28042253)
Actually maybe I take that back. I mean, it took how many centuries for humans to invent calculus? Maybe AIs left to their own devices in a reinforcement-learning context could do better.
The interesting thing though, is given free reign to prove whatever they want, they may go off and develop some entirely new field of mathematics and proving really deep stuff, but we just wouldn't recognize it as interesting. Like imagine if such an AI existed 200 years ago and invented Turing machines and proved P != NP, but it wasn't all that great at solving polynomials for whatever reason. We'd have probably thought it was all rubbish and threw it away.