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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#471

Post by seizethecheese »

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 intervening years, but with the caveat that there would be no explanations. Would he say no?

Re: A misalignment of AI in mathematics

#472

Post by youoy »

causalmodels wrote: post #429
youoy wrote: post #377

Earlier quoted context omitted.

It depends. If you are trying to understand better the field, then do a good write up of the proofs so that people can learn from it. If you want to earn the respect of people because you found interesting proofs. Then do a good write up of the proofs so thst people can learn from it. If you want to plant flags and pollute peoples minds. Then please publish it anonimously, no one wants to correct LLM slop for you. Pr…

Maybe I'll end up doing the write ups pseudonymously. I have taken care to make sure the results can meaningfully contribute to field but I don't want to plant flags or really receive credit of any kind. I just think they are interesting. I like my current life and don't want to get dragged into the current fracas surrounding the use of AI in math.

If you have taken care, then share it with the community. People will be thankful and happy.

The problem is with people that may do it without contributing to the community.

Re: A misalignment of AI in mathematics

#473

Post by fidotron »

psvv wrote: post #453
mna_ wrote: post #299

Earlier quoted context omitted.

Chess is kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on.

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 them.

Re: A misalignment of AI in mathematics

#474

Post by feoren »

jrowen wrote: post #121
datakan wrote: post #65

Everyones outraged all the time. It doesn't mean anything anymore. It's that meme from years ago about the red ants and the black ants living in a box peacefully until someone shakes the box and they start trying to kill each other. They go after each other and not the one shaking the box. OpenAI/Anthropic are shaking the box.

Everyones outraged all the time. It doesn't mean anything anymore. Everything is sensationalized, every super niche happenstance is sold as earth-shattering drama, the outrage arms race is so tiresome.

Yeah, I'm so tired of people moaning about how huge swaths of Earth's ecosystem are being destroyed and rendered uninhabitable to humans, how secret police are murdering Americans in the streets, how the president is a child rapist who openly accepts bribes, how unfettered capitalism is destroying tens of millions of lives, how the United States is rapidly falling into facism, how civil rights are being systematically destroyed, consumer and environmental protections are being gutted, and entire generations are being intentionally cut out of the possibility of economic prosperity. YAWN! Give it a rest!

Man, the people who want to just get away with open corruption sure love you.

Re: A misalignment of AI in mathematics

#475

Post by magoghm »

senfiaj wrote: post #274
gwd wrote: post #243

This sounds a lot to me like people in the 90's complaining that computers were destroying chess. Thirty years later, chess is more popular than it ever was, and chess players are better than they ever have been. I wouldn't be surprised if there are now more chess books now than there ever have been. Furthermore, it turns out that a lot of chess books written before computers were just wrong about a lot of things. It…

Well, chess is a sport where humans are supposed to compete. But math, programming, science are mostly not, and AI might affect economy, careers, etc.

That's correct. As far as I know nodody builds any kind of science or technology on top of chess, but mathematics is at the base of most science and technology. It would be horrible if we prevented AI from solving mathematics problems, just because mathematicians want to solve them by themselves the "hard way".

Re: A misalignment of AI in mathematics

#476

Post by againstapples »

avsegal wrote: post #270
againstapples wrote: post #125

At this rate AI will be doing all of the mathematics within 5 years, I don’t see why a mathematician would be worried about anything other than that at this point?

Sure, but who will care? If no one understands it, it may as well have not happened. There's not much incentive to understand or internalize the results generated by AI. A human operator gives it a prompt and it produces some lean proof no one wants to (maybe can) read. Without the community of human mathematicians internalizing the proof, simplifying it, and re-communicating it to others we end up losing the main ou…

Why would we assume AI will learn to solve millennium prize problems but will struggle with the easy part of doing the explaining? I think it’s too easy to predict that models 5 years from now will have the same limitations as the they do now, I would be amazed if this was true, GPT3 was the best model available 5 years ago.

Re: A misalignment of AI in mathematics

#477

Post by onethought »

Forgeties79 wrote: post #225
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…

It’s not a parallel. No one ever claimed photography to be the same as painting or some other medium - it was a new medium that wasn’t respected. AI is being treated and pushed as a replacement for every medium.

It literally was a replacement for portraits.

Re: A misalignment of AI in mathematics

#478

Post by CamperBob2 »

genxy wrote: post #425
alkyon wrote: post #366

Earlier quoted context omitted.

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

Which is why if humanity had empathy, it would be working on how to make smarter ants, so that they can learn more advanced geometry.

What do you think we're doing?!
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