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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#591

Post by moralestapia »

esafak wrote: post #577
moralestapia wrote: post #540

There's massive cope and then there's this. I've never been a fan of Tao et. al, so I'm glad he's being wiped out. He'll do fine anyway, doing conferences, etc. Also funny they deliver that on vibecoded site, lol.

Which mathematician's take on AI do you like? Do you think mathematics should no longer be an intellectual pursuit?

I haven't heard about his take on AI (sorry about derailing a bit), but generally I like Robert Ghrist's approach to life and math.

I'll check out if he has said something about it. Interesting guy.

Re: A misalignment of AI in mathematics

#592

Post by geraneum »

seizethecheese wrote: post #471

I don’t think they make a coherent argument here? This seems to hinge on some argument that because AI doesn’t properly explain its breakthroughs, therefore the breakthroughs are less fertile for human understanding? This makes no sense. Why wouldn’t these under-explained breakthroughs be extremely fertile soil for explanations? Imagine time traveling back in time and offering Leibniz a packet of proofs from the inte…

> Would he say no?

And that’s the issue the article is trying to explain.

Re: A misalignment of AI in mathematics

#593

Post by vouaobrasil »

stabbles wrote: post #519
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…

Mathematics is more than establishing arbitrary facts (although some look like curiosities), it's also defining what interesting research directions are and establishing common language/notation. I think that will stay relevant?

People become interested in things when they become invested in it personally, because they've contributed to it. So I don't think it will stay relevant...

Re: A misalignment of AI in mathematics

#594

Post by lacunary »

saghm wrote: post #554
mb7733 wrote: post #541

Earlier quoted context omitted.

> 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?

I mean, was the point of math ever just because some humans enjoyed doing it? Even though a lot of it is theoretical, there's been all sorts of useful things that have come out of it as well due to an improved understanding of the universe through new ways of thinking about it. If it got to the point where no human could understand it and there were no ways to actually use it, I don't think anyone would bother having…

wouldn't AI solving problems in science, engineering, economics, etc be able to apply the new AI math?

Re: A misalignment of AI in mathematics

#595

Post by [deleted] »

tejstead wrote: post #490
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…

> I am at a loss about what to do with these results. I would recommend publishing them to Palomar ( https://palomar-registry.org/ ) - I have no affiliation, this is an online registry of Lean-verified proofs created by Terrence Tao. I have submitted a proof there that's also minorly important in an extremely niche field. Anyway, I feel like it's a good place to dump AI slop lean proofs because the main point of the…

[deleted]

Re: A misalignment of AI in mathematics

#596

Post by david-gpu »

shimman wrote: post #544
robotpepi wrote: post #513

Earlier quoted context omitted.

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.

I do not want to make him sound unreasonable. He is a brilliant man. But I also think that he is a bit shell shocked, much like other luminaries in the past have been when confronted with rapid technological development, so I wanted to highlight some historical similarities, imperfect as they can only be.

As for the rest of your comment, I hope you have a great day.

Re: A misalignment of AI in mathematics

#598

Post by embedding-shape »

kzz102 wrote: post #590
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…

The difference is the scale. A few incomprehensible long papers per year, sure, we will study it. A flood of AI results closing research directions left and right, that will be a problem.

> closing research directions left and right

Why would research be closed in one direction? Even if AI or human says "Tried that, didn't work" or whatever, someone (or something I suppose) might very well retry it in the future, if nothing else to reproduce it didn't work, in theory at least.

Re: A misalignment of AI in mathematics

#599

Post by gravity2060 »

First they came for the graphic designers, and I did not speak up, because I was not a graphic designer.

Then they came for the writers, and I did not speak up, because I was not a writer.

Then they came for the programmers, and I did not speak up, because I was not a programmer.

Then they came for the mathematicians, and I did not speak up, because I was not a mathematician.

And then they came for me.

By then, there was no one left to explain to the frontier labs that there is a severe misalignment problem.

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