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A misalignment of AI in mathematics

mathandai.org

531–540 of 645 posts

Re: A misalignment of AI in mathematics

#531
My interpretation is they don't care about scooping mathematicians they were just trying to scoop a competitor. They had a short window in which to complicate Anthropic's priority, when Anthropic announced be able to say "ok nice but we did that too". Upon realizing they'd misunderstood, incredibly they said to this academic (who did not resolve NS) okay well just go ahead and claim the prize, so long as you're not Anthropic let's make this a good story.

If you spend $20M working out a Millennium Prize problem, in what universe would you offer that an unrelated effort should take credit? This is a branding game rather over whether software engineers are going to use codex or claude. In that light $20M (or whatever it was) might be worth it to squash even the rumor that claude code is more capable. Engineers look up to mathematics, while at the same time business and probably most engineers think the problem was to solve the problem. GPTs solved one the hardest known problems so they can solve my company's problem.

Some go further looking at these people, very on-the-nosely likened by one commenter here to ants, talking about education and responsibility and "core values" etc and just don't care. There was a major problem at the beginning of the week that is not a problem now and that is uncomplicated progress.

It's not wrong for OpenAI/Anthropic to do math for product development or even just branding but seemingly at no cost now they could work in an arena real mathematicians aren't interested in, versus just mowing the field. Everyone involved on their side should admit the purpose of these demonstrations is not to engage mathematical ideas it's about Claude/Codex. there's no shame in that. Which is better at solving random hard Diophantine systems? That would seem to tell me as much as I need to know insofar as a model's value is represented by raw mathematical power - then, take my money just as well!

Assuming the worst accusations are not true I think there are ways forward going to be acceptable for all. The labs themselves do not represent Terrance Tao as some kind of gate-keeping dinosaur in this. They're not interested, not the kind of entity that can care about theoretical mathematics. These dudes are paid 7-8 figure salaries ultimately for the product, they solve a Millennium Prize problem then pretty quickly seem to move past it.

Re: A misalignment of AI in mathematics

#532

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'm not a mathematician but it seems to me that if all it took to solve the problem was an enthusiast level understanding of the domain and a few hundred dollars of tokens then the result probably isn't that valuable. Even assuming you are the first person in the world to solve it, these kinds of LLM-friendly problems that are now easy to solve and easy to verify will almost certainly be picked off by one person or another in the near future.

It's also possible that the result is already known and you just weren't aware of it. It's easy for someone outside of a field, or even one steeped in it, to not be aware of certain solutions.

Re: A misalignment of AI in mathematics

#533

Earlier quoted context omitted.

Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity…

> AI is now capable of constructions so complex that no human or human team can unpack Can you give an example of this?

The first major computer-assisted proof, of the four-color map theorem in 1976, was an example of this. It created a lot of controversy at the time. It used proof by exhaustion, i.e. essentially analyzing every possible relevant case, something that no human could do without the assistance of, at the time, a supercomputer.

Re: A misalignment of AI in mathematics

#534
post #439

Earlier quoted context omitted.

As a laymen, I wish the same. But I also hope it doesn’t disincentivize those that dedicated themselves to the study

Math department administrators fire Terence Tao. Based on current reward models, the frontier AI labs will burn down mathematics as an impressive display of capabilities and in doing so, will make it impossible for people that get paid to do mathematics to stay employed. If your job is literally to publish papers, and OpenAI and Anthropic decide that making an infinite-paper-printing machine is the best thing to show…

I wouldn't expect them to destroy that industry, imagine global squadrons of academics and mathematicians focusing their attention on LLM's, training algorithms, scaling laws, ... they're gonna try and beat the incumbent frontier AI labs, eye for an eye, tooth for a tooth

Re: A misalignment of AI in mathematics

#535

Earlier quoted context omitted.

Where is the difference?

He sees value in mathematicians using AI to carefully study mathematics, develop an understanding of both old and new things, and help others understand the new things. He doesn't see value in scrolling through unsolved problems asking an AI to please solve them. In his view, this is a fundamental confusion about what mathematical research is for. Knocking down unsolved problems without developing the community's und…

Isn’t it more like it merges the code without a dev reviewing or understanding it?

Re: A misalignment of AI in mathematics

#537
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…

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…

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Re: A misalignment of AI in mathematics

#538

This letter is complaining that human understanding has been crucial to advancing of mathematics, and AI companies are not bothering with it. But the promise (and horror) of AI mathematics is that, if it succeeds, human understanding becomes irrelevant. That's the goal . So this letter's message will fall on deaf ears. Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10…

> Keep in mind employees at AI companies are publicly stating that they believe they're risking a >10% chance of human extinction.

Are we really going to take what they say in public seriously?

Re: A misalignment of AI in mathematics

#539
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…

> Maybe mathematics just becomes a little more like other fields--relying on labs with lots of money for compute, digging through a corpus of AI-generated proofs, etc.

I think a better comparison is: mathematics just becomes like mining bitcoins.

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