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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#361

Post by magicalist »

causalmodels wrote: post #269
omnicognate wrote: post #201

Earlier quoted context omitted.

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

I mean, let's say you spun up a swarm of agents to rewrite a large component of a well used open source library to be memory safe. You could dump it in a big PR and walk away (we all know how that would go), or you could try engaging, see if they're interested, write something up and see where it goes.

The biggest problem is, IMO, drivebys uninterested in actual results, just getting a check mark, and the equivalent of dropping a 200k line PR on people and expecting them to be interested and do the work for you. These are things many on HN are familiar with and know how to do better :)

Re: A misalignment of AI in mathematics

#363

Post by nomel »

suddenlybananas wrote: post #321
CuriouslyC wrote: post #311

Earlier quoted context omitted.

Given the witch hunts around AI creative output, nobody who has put in work to avoid the stigma is going to out themselves.

Why would they have had to put work in?

If an author let AI do 90 to 95% of the work, cleaned up the remaining 5 to 10% themselves, would you say AI or the author wrote it? Because this is roughly the split between an author and an editor, with human writing, now.

Re: A misalignment of AI in mathematics

#364

Post by nojs »

bobzowak wrote: post #310

This is really only a short-term problem where the AI companies only have the internal models that can solve these. In the “long” term, which could honestly mean months, everyone will have access to Bel/C /D -level models capable of solving these anyway.

This. Like programming, the community will shortly be forced to come to terms with a lot of new self-proclaimed mathematicians “vibe-solving” problems and dumping solutions without understanding them. It’s not really a special case for mathematics.

Re: A misalignment of AI in mathematics

#365

Post by causalmodels »

lasersox wrote: post #333
causalmodels wrote: post #269

Earlier quoted context omitted.

What do we do about the problems that don't require many millions of dollars in resources? Last weekend I spun up a small agent swarm and pointed it at a field of math I have some affinity towards. Within four hours I had settled three conjectures, one of which is rather famous (for the field, not in general). It cost me about four hundred dollars. I am at a loss about what to do with these results. On one hand I fee…

How do you know the proofs are correct?

The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private.

They're valid.

Re: A misalignment of AI in mathematics

#366

Post by alkyon »

tzumaoli wrote: post #234
tmhn2 wrote: post #200

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

Is this the scenario described in Ted Chiang's short story https://en.wikipedia.org/wiki/The_Evolution_of_Human_Science where scientists are "catching crumbs from the table" trying to decipher the results generated by superhuman intelligence?

It's still an optimistic scenario. Artificial superintelligence may develop hypermathematics of a kind that never will be accesible to human mind, enhanced or not. One can't teach geometry to ants even if you put them on a Moebius strip.

It would be more like Lem's novel where it completely disappears from the human horizon: https://en.wikipedia.org/wiki/Golem_XIV

Re: A misalignment of AI in mathematics

#367

Post by [deleted] »

318274 wrote: post #277
stabbles wrote: post #251

Earlier quoted context omitted.

The maths community is now in the antithesis phase, synthesis will take a while ;) Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available. But on the other hand, people l…

Chess is kept afloat by a couple of billionaires like Sinquefield, MBS and the guy who sponsors freestyle (Fisher random) chess. Carlsen is bored by studying engine lines. The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content. I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now.

[deleted]

Re: A misalignment of AI in mathematics

#368

Post by [deleted] »

omnicognate wrote: post #201
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…

[deleted]

Re: A misalignment of AI in mathematics

#369

Post by lbrito »

>Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others.

That's just capitalism seeping through a previously unexplored crack into academia, and attempting to do the only thing capitalism knows to do - maximize profits - with no additional concern.

Re: A misalignment of AI in mathematics

#370

Post by exhaze »

iamkeithmccoy wrote: post #340

There's a reason mathematics is generally within liberal arts programs rather than science programs. Mathematics is the art of logic. Yes, sometimes mathematics becomes incredibly useful but most mathematics is never applied. Compare that with computer science. Most of the work we do in software engineering is in service of an applicable output - software products that facilitate processes or bring in revenue. Turnin…

You are referring to Boubakhism, not mathematics.

“Mathematics is a part of physics. Physics is an experimental science, a part of natural sciences. Mathematics is the part of physics where experiments are cheap” - Vladimir Arnold

On the matter of computer science having anything to do with computers, please refer to Djikstra.

It’s about computation, not computers - an application of mathematics, predominantly thanks to Turing, Von Neumann, and Claude Shannon’s masters’ thesis; though ofc many others as well but I see them as three individuals who made the minimal structurally necessary contributions - VNA and silicon are one of many possible substrates.

Also in the service of others around us.

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