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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#461

Post by jaccola »

nadermx wrote: post #196

Back in the day you could think of a cool idea. I don't know maybe a plane that could fly without drag. To even see if this was feasable you had to understand physics, engineering, and then from there you had to have a math person see if it was actually possible. Now, I can ask ChatGPT about this and get back a proof that shows "a passive airframe cannot sustain zero-drag motion through still, viscous air" So, I thin…

This is a pretty moronic take. You only have to understand the first thing about physics (e.g., a 14-year-old's understanding) to know that a dragless airplane is impossible.

If you are suggesting there is some new model of physics or groundbreaking technology that would allow such a dragless plane, then don’t let me discourage you! But AI won’t help at all, since it will only regurgitate conventional wisdom…

Re: A misalignment of AI in mathematics

#462

Post by latent-person »

Bourget wrote: post #441
djierardi wrote: post #393

Earlier quoted context omitted.

But computers have destroyed chess as a "sport". Nobody will sit to watch two chess programs compete, or analyze their tactics. Kinda like how now, anybody can construct a "game" over the weekend or a new song or a slop video. The value of each of these decreases to 0 as the slop overwhelms.

>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/

Re: A misalignment of AI in mathematics

#463

Post by NateEag »

onetimeusename wrote: post #428
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…

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. I don't like nuance here…

Tangent:

> From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it.

Keep in mind those ~88 hours were spread across ~10,000 simultaneous agent instances.

So, roughly 880,000 hours of compute.

Assuming a fifty-year career, and forty-hour workweeks, a human mathematician's career is about 100,000 hours of "compute".

I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already.

The perverse incentives of academia mean this has never occurred.

The perverse incentives of industry mean OpenAI intentionally scooped researchers who were getting close (granted, with AI help).

I'm not trying to dismiss the achievement - if the proof turns out to be solid, it's quite impressive (though much less so if the training data included the recent human breakthrough, which seems pretty plausible).

I'm just pointing out that "88 hours" is a very misleading way of framing this.

Re: A misalignment of AI in mathematics

#464

Post by ArcHound »

Quekid5 wrote: post #442
ArcHound wrote: post #430

Earlier quoted context omitted.

It's not that easy. Playing stockfish is like playing tennis against the wall (for untitled players at least). Even if you don't blunder anything, you'll still find yourself in a worse position without any clue as of what went wrong and why. Whereas when playing humans, they can usually explain their approach and when they noticed errors in your play.

> Playing stockfish is like playing tennis against the wall (for untitled players at least). It's the same for Magnus Carlsen. Even with Queen odds, Stockfish is literally unbeatable for the best players in the world. It's just too strong at evaluating all kinds of random tangent moves (and ensuing positional advantage) which no human player can possibly pay attention due to the time required. Stockfish vs any human…

No worries, I know stockfish is unbeatable by humans.

But sometimes, these GMs can flag it, which counts as a win (especially when it's proxied by a cheater). Sometimes they can also explain the idea that cost them the game, so they've learned something maybe.

Whereas us scrubs literally cannot do anything at all for reasons completely beyond our understanding.

Re: A misalignment of AI in mathematics

#465

Post by feoren »

Animats wrote: post #358

There's an unpopular branch of mathematics which does not have infinities - finiteism.[1] The constructive version of finitism takes the position that there is no such thing as infinity, just arbitrarily large upper bounds. You can have theorems about arbitrarily large numbers, but you never get 1 + 1/2 + 1/4 + 1/8 ... = 2 The benefit of finitism is that it escapes undecidability. The big objection to finiteism is th…

> 1 + 1/2 + 1/4 + 1/8 ... = 2

It's not necessarily clear that this statement requires infinity, if you're willing to treat "... =" as a shorthand. You might prefer something like "1 + 1/2 + 1/4 + 1/8 ... -> 2" if it's more clear, where "->" means something like "gets as close as you like without ever getting further away than that", but really the "=" sign is already overloaded in all sorts of subtly different ways anyway, so there's not really any trouble using it here. Almost any rigorous definition you can write down of exactly what that statement means would not rely on the use of infinity.

Re: A misalignment of AI in mathematics

#466

Post by youoy »

We should create a platform where people can upload AI slop proofs anonymously without taking credit for it. That way the incentives of planting a thorem flag would go down. And if someone wants to clean an AI slop proof to advance the field, they can do it without cleaning the house for free of the person that planted the flag.

Would OpenAI have uploaded their proof to such a platform? If you know the answer then you know what the problem with what happened is.

Re: A misalignment of AI in mathematics

#467

Post by azkalam »

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…

I think it could be useful to know something like P=NP, even if we don't understand why.

Re: A misalignment of AI in mathematics

#469

Post by Strilanc »

philipwhiuk wrote: post #342
Strilanc wrote: post #236

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…

The point of mathematics is human understanding though.

That's only one of mathematics' many purposes.

Re: A misalignment of AI in mathematics

#470

Post by CamperBob2 »

onetimeusename wrote: post #428
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…

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. I don't like nuance here…

I think progress is really measured by what humans are able to do and understand, not machines.

Building a machine that solves Millennium problems is pretty cool too. You wouldn't know it from reading these stories, though.

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