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wongarsu 10 days ago

Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid, mathematics is in many ways about human comprehension. You can use AI to find and proof new theorems. But if you get to the point where humans can't understand it, is it even still math?

vitally3643 9 days ago | parent | next [-]

Neural networks are already systems of linear algebra that are beyond human understanding. Most humans could probably grok a 1 or 2 dimensional slice of a network, but the latent vector space is completely beyond the human brain. We have to use tools to analyze neural networks piecemeal in exactly the same way that we analyze any other higher-dimensional construct. Few humans are truly capable of reasoning in 4+ dimensions, that doesn't make string theory "not math". Nor does a trillion-dimension vector space of an LLM make it "not programming".

Humans by themselves invented mathematical concepts beyond human understanding a long time before we invented neural networks.

Spacecosmonaut 10 days ago | parent | prev | next [-]

Perhaps P=NP. The new algorithms are handed down to us. We can apply them without fundamentally understanding why P=NP.

squidbeak 9 days ago | parent | prev | next [-]

> Much like for many the point of chess is that it's played by humans, with truly superhuman AI relegated to a training aid

It's much more than just training. Humans use the engines to prepare openings and find promising novelties. Over time these novelties unearthed by engines fill out theory. It's easy to fine elite games where neither player is out of book for dozens of moves. Modern players are full hybrids in that sense. Looking back at chess, it seems natural that Mathematics will go the same way.

jrflo 9 days ago | parent | prev | next [-]

I think there would still be a place for it if it's beyond human comprehension. For instance, really complex lemmas to solve human-tractable problems. If you can pose a question in a proof assistant language like Lean, have an AI write a Lean program that solves it, you can use that as a Lemma for some other problem. There's quite a bit of math out there that is "correct assuming conjecture X is correct", maybe AI could fill that gap and "still be math".

zelphirkalt 9 days ago | parent | prev [-]

Is it still chess, if humans cannot understand it? Because that's the point we are at in chess. Engines making moves, that humans cannot understand, but somehow they work out to be best or seemingly best. Look at the Leela Zero games, when it came out. These engines play kind of other-worldly chess.

wongarsu 9 days ago | parent [-]

Exactly. If we wanted "the best chess" we'd watch Stockfish against Leela Zero. Far better mechanically than human chess. But people are much more interested in Magnus Carlsen playing Gukesh. Both train with chess engines, but the thing that makes the chess game interesting are the human beings that understand their own moves and try to understand those of their opponent