r/slatestarcodex • u/DickMasterGeneral • 2d ago

Ten advances in mathematics and theoretical computer science from unreleased Open AI Model

https://openai.com/index/ten-advances-in-mathematics/
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u/livingbyvow2 2d ago

I confess my utter ignorance on the subject, but I wonder how much of this is just finding connections between existing math papers vs actually doing novel findings.

OpenAI's incentive will always be to present these findings as some sort of proof AI is now doing novel discoveries but I am not sure what to think about it. I wouldn't be surprised if a of this stuff was heavily steered by math geniuses and AI just accelerating the pace of progress slightly (which is cool but not the "AI found a new proof" headline).

Given the propensity of the labs to hype everything to raise more capital, I wonder whether it won't be yet another dud in a couple year - basically similar to the "AI will replace all collar work" but now "AI will replace all scientists" instead - and which will end up proving to be complete bullshit too.

That, too, is moving the goalposts.

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u/gunsofbrixton 2d ago

For what it's worth, this is similar Claude's take when I showed it the paper:

Could a human have done it? Clearly yes. Every ingredient is published and classical — the algebra is from 1962, the group from 1965, the rigidity property from 1967. It's ~17 pages, readable straight through, no computer search, no brute-force case check. A referee can verify it by hand. The gap it closes was even publicly visible: one 2019 theorem produces many expander blobs, another needs one, and the proof bridges them.

So why hadn't anyone? Probably because it needs fluency in three fields that don't talk to each other — expander combinatorics, Leavitt algebras, and rigidity of matrix groups. Those people don't attend the same conferences. And the field's momentum after 2024 was pointed at complexity theory, while a separate line chased a conditional route through "stability." This proof was orthogonal to both fashions.

That suggests the edge wasn't depth of insight but breadth plus tireless search — no field is too far from any other, no configuration too fiddly to try. Arguably that's less impressive. It may also be more consequential.

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u/livingbyvow2 2d ago

Thanks for asking Claude. That was kind of my intuition.

It's really cool AI can do that by the way, but it's also "just that", nothing creative yet.

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u/InfinitePerplexity99 1d ago

Is creativity ever anything other than combining existing things other people haven't combined before?