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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#541

Post by mb7733 »

fidotron wrote: post #473
psvv wrote: post #453

Earlier quoted context omitted.

I think the parent comment meant professional, high-level chess. The kind people get played to play, not just do for a hobby. That's absolutely on life support. I'm not sure what the equivalent would look like in the math field, but it probably involves a lot of mathematicians losing their jobs and the quality of human-produced math decreasing overall. The quality of the math in general would be fine, since in this s…

> It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding th…

> But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs.

What is the purpose of that?

Its like art being produced for AI to consume. What is gained from that?

Re: A misalignment of AI in mathematics

#542

Post by youoy »

drivebyhooting wrote: post #233

All “fields medalist” signatories - a rarefied and elitist group indeed. I wish this letter could be more egalitarian and include the view points of those who AREN’T the beneficiaries of a highly competitive winner-take-all system. Since the common narrative is that AI frees up labor to do other things (engineering -> trades), maybe we can celebrate that genius mathematicians will now spend time teaching children how…

Agree. That is also the part of the letter that does not make a lot of sense to me.

Re: A misalignment of AI in mathematics

#543

Post by bayindirh »

amelius wrote: post #525
zahlman wrote: post #517

Earlier quoted context omitted.

> Ultimately we think a fatal flaw was found in Mochizuki's proof, so it didn't lead anywhere in particular. But in our hypothetical "AI lean-verified proof of RH" situation, it would presumably generate substantially more of that community activity we saw in the Mochizuki situation. And if it's correct, that community activity would be productive (expository talks, students given problems to flesh out or generalize,…

Not if it's lean-verified.

Didn't some of the recent proofs exploited a couple of blind spots of lean, and they were invalidated?

Edit: Yup. A bug report to Lean was disguised as a "Collatz" proof in a humorous way. Links below.

- https://x.com/gro_tsen/status/2082483878480977959

- https://infosec.exchange/@0xabad1dea/117002106099986943

Re: A misalignment of AI in mathematics

#544

Post by shimman »

robotpepi wrote: post #513
david-gpu wrote: post #455

Earlier quoted context omitted.

I am very specifically addressing what I have read Terrence Tao say on AI and mathematics, as that is the subject of this submission. Are we on the same page?

I don't see any meaningful analogy with your cites of Baudelaire. First of all, Baudelaire discusses art, which is very different to science. Several new forms of art have emerged, and then slowly integrated, despite the strong opinions of some. Here, Tao's letter discusses mainly practical aspect of scientific research. It is not about what a "failed mathematician" would do, or if "LLM can only record what already e…

Of course there's a meaningful analogy. The poster wants to make Tao sound unreasonable and against "progress" while ignoring the very real concerns Tao has.

It's what fanatics do when they want to enforce their view on the world, they have to attack anyone with a reasonable viewpoint because they can't imagine a world where someone tells them they don't like what they're doing.

Re: A misalignment of AI in mathematics

#545

Post by falcor84 »

Strilanc wrote: post #469
philipwhiuk wrote: post #342

Earlier quoted context omitted.

The point of mathematics is human understanding though.

That's only one of mathematics' many purposes.

Exactly!

What got me interested in memes as a kid is precisely the fact that mathematics is true in a way that is wholy independent of our understanding of it.

Re: A misalignment of AI in mathematics

#546

Post by echoangle »

david-gpu wrote: post #141

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…

Wasn’t the criticism of photography kind of correct though? I don’t think people think of photography as an art as much as painting is an art. There aren’t a lot of photographs that a layman couldn’t in principle also take, but only a few people could replicate a good painting.

Re: A misalignment of AI in mathematics

#547

Post by darkstarsys »

jrecursive wrote: post #394
cubefox wrote: post #319

Earlier quoted context omitted.

Where is the difference?

taste

Yes. I find it really interesting to consider what the machines do and will think of as intrinsically interesting to them. Will they develop their own theories of beauty, mathematical and otherwise?

Re: A misalignment of AI in mathematics

#548

Post by throwaway27448 »

latent-person wrote: post #462
Bourget wrote: post #441

Earlier quoted context omitted.

>Nobody will sit to watch two chess programs compete, or analyze their tactics. I know nothing about chess yet I dare say that I'd doubt this. Surely chess enthusiasts would be interested in analyzing how a superior chess program came out victorious, no?

Yes you are right, some people do watch chess engines play. TCEC (Top Chess Engine Championship) [1] streams them. Popular chess YouTubers goes over engine games from time to time too. [1] https://tcec-chess.com/

That's not proof of interest so much as proof of commerce. It could easily be a money-laundering mechanism.

Mostly nobody cares about professional chess. The number of people who are actually interested in today's game and not the drama are a tiny sliver of that. This is actually great because it means we can train and evaluate both without interference from chess players, possibly even building a stable society.

Re: A misalignment of AI in mathematics

#549

Post by fidotron »

mb7733 wrote: post #541
fidotron wrote: post #473

Earlier quoted context omitted.

> It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound? But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. It's kind of surprising so many mathematicians act surprised by this given this was clearly where automated proof assistants would lead. I guess they assumed they'd always be the ones guiding th…

> But in future most proofs will be for consumption by other AI models in the pursuit of yet other proofs. What is the purpose of that? Its like art being produced for AI to consume. What is gained from that?

Well if it proves useless presumably they'd stop doing it.

But if AI is to recursively self improve understanding and evolving its own foundations, which are clearly mathematical, is essential. There is no need for humans to grasp what is going on in that loop.

Re: A misalignment of AI in mathematics

#550

Post by chrisjj »

For such great minds, they seem to be rather muddled thinkers.

E.g. of the actually three misalignments in this complaint, the jey one seems to be:

"The goals of the AI companies and the goals of the mathematical community are severely misaligned."

And that's wrong. There is no misalignment. Each is independently aligned with its respective interest. And those two interests diverge - just as you'd expect.

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