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A misalignment of AI in mathematics

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Re: A misalignment of AI in mathematics

#831

Post by joe_the_user »

david-gpu wrote: post #281
pred_ wrote: post #210

Earlier quoted context omitted.

Are you aware that Tao is among the largest proponents of using AI in mathematics? The usage itself is not the point here.

Tao doesn't go as far as Baudelaire, but there are some similarities. In particular, Tao has criticized that AI is not being used to create new interesting conjectures, and that the rush to prove old conjectures is not giving human mathematicians enough time to carefully analyze and understand the proofs and the methods used in those proofs. My answer to both is the same: nothing stops mathematicians from doing both…

But the point is your original analogy with Baudelaire now just boils down to "both of them were critical" which is quite shallow indeed.

It's especially annoying given that many people are making repeat Baudelaire's critique of photography (or Socrates critique of writing) in the context of AI and the declaration is interest because it's not that.

Re: A misalignment of AI in mathematics

#832

Post by ArcHound »

jacobolus wrote: post #626
ArcHound wrote: post #464

Earlier quoted context omitted.

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.

> Whereas us scrubs literally cannot do anything at all for reasons completely beyond our understanding Computer moves are typically much more concrete than human moves: a human will play based on pattern matching ("intuition") and can only make explicit calculation of a small fraction of possibilities, after which decisions are guided by guesswork. The computers are unbeatable in practice because they can calculate…

You put it better than I could. The lesson of "in this exact position you can kick the pieces for 7 moves to get a fork, so instead you should play a4" is not something that I can implement into my games

Re: A misalignment of AI in mathematics

#834

Post by reasonableklout »

redox99 wrote: post #811
reasonableklout wrote: post #795

Earlier quoted context omitted.

But what does the human researcher do in this future? If they are not needed to understand the result, then what's their role? Asking the right questions? But how will they know what questions to ask if they don't have a deep understanding of the domain earned by sweating the details themselves? And how long will they be needed to ask the right questions, how long until AI can do that too? > Software has always progr…

I think it will be like how a lot of people know how to code in python but have zero understanding of assembly or how a cpu works. As a researcher you'll accept there's this low level stuff that if you want you can dig into but isn't worth your time, like looking at the generated ASM isn't. You're exaggerating the LLM progress a bit but yeah progress has been crazy. Yet not much has changed right? We mostly have the…

True, surprisingly not much has changed in software despite the incredible progress. I think it's partly because much software is an "open loop" system where what you build depends on running the software on client computers, devs talking to users, etc. There are still things that only human engineers can do. I worry it is less so for poor mathematicians, where math is "closed loop", and the exchange of capital into research progress is more liquid.

I can't help but be pessimistic about AI moreso than any other technology. Why? I used to be excited to learn the next big thing because I knew it would unlock much more things to do and get paid for, and there would always be more for me. With AI, the new things come nearly too fast, are not very deep or satisfying, and it's hard to see that there will always be a place for me. And so while I leverage AI in my day-to-day, I will yell at the cloud, too.

Re: A misalignment of AI in mathematics

#835

Post by robotpepi »

david-gpu wrote: post #584
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…

> It is not about what a "failed mathematician" would do, or if "LLM can only record what already existed" This is what I was alluding to: I wrote recently about how the collection of good, fruitful open problems is now being mined in a non-renewable fashion, leading to the potential scenario of these problems becoming scarce [0] [0] https://mathstodon.xyz/@tao/117237320796901560

I still don't see the analogy, can you care to develop?

Re: A misalignment of AI in mathematics

#836

Post by joe_the_user »

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…

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.

It's more than the yardstick for individual contributions. It's also the yardstick for the contribution of ideas. And that kind of yardstick is very important.

Math has a challenge that's only occasionally acknowledged imo, that's it's possible to just go up the ladder of abstraction, formulate ideas but have those ideas actually not be useful or interesting. The ideas that math has developed, that mathematicians consider important, are those that have helped people solve hard problems.

Re: A misalignment of AI in mathematics

#837

Post by Turfie »

afiodorov wrote: post #752
pks016 wrote: post #665

I never expected this many people (on this thread) arguing semantics and what not. I know that not everyone has morality and ethics, but I didn't realize it was this bad. I'm afraid of the ripple effect of the agenda pushed by AI companies will have. In future and even now, they say AI has significantly progressed math and scientific research in general. There is truth to this, but the narrative has done more damage…

I used to be a PhD student more than a decade ago, and I published a paper containing a solution to an open problem. Yet shortly after my first publication I became increasingly disillusioned, because I started to think that within my lifetime AI would reach and eventually surpass my ability to solve such problems—and that we only had a decade or two left. So I started saying that it only made sense to focus on probl…

Fantastic! E-mail him and ask if he thought about it at all

Re: A misalignment of AI in mathematics

#838

Post by sdeframond »

cute_boi wrote: post #748
sdeframond wrote: post #162

Earlier quoted context omitted.

Say AI becomes the best at everything. Best at chess/go, best at maths, philosophy, economics, romantic advices ... and so on. Then what's the point of thinking by oneself? Of talking to one another? What's the point of being human if we dont do human things but entirely rely on AI? I believe this is more or less these mathematicians' argument.

>> Once a robot can do everything an IQ 80 human can do, only better and cheaper, there will be no reason to employ IQ 80 humans. Once a robot can do everything an IQ 120 human can do, only better and cheaper, there will be no reason to employ IQ 120 humans. Once a robot can do everything an IQ 180 human can do, only better and cheaper, there will be no reason to employ humans at all, in the unlikely scenario that th…

Who is "we" ? Because if you dont need to employ a human, then who needs your services? If nobody needs anybody, what are we?

(Edit: assuming you are human)

Re: A misalignment of AI in mathematics

#839

Post by redox99 »

reasonableklout wrote: post #834
redox99 wrote: post #811

Earlier quoted context omitted.

I think it will be like how a lot of people know how to code in python but have zero understanding of assembly or how a cpu works. As a researcher you'll accept there's this low level stuff that if you want you can dig into but isn't worth your time, like looking at the generated ASM isn't. You're exaggerating the LLM progress a bit but yeah progress has been crazy. Yet not much has changed right? We mostly have the…

True, surprisingly not much has changed in software despite the incredible progress. I think it's partly because much software is an "open loop" system where what you build depends on running the software on client computers, devs talking to users, etc. There are still things that only human engineers can do. I worry it is less so for poor mathematicians, where math is "closed loop", and the exchange of capital into…

I think in a few decades when there are more humanoid robots than humans we'll likely have skynet, so I'm pessimistic in a way lol.

But in the near future and on a personal level I think we'll need to adapt and pivot but we'll manage.

Re: A misalignment of AI in mathematics

#840

Post by omnicognate »

smj-edison wrote: post #672
pickleRick243 wrote: post #658

Earlier quoted context omitted.

sounds a bit like cope. Crouzeix's conjecture was solved exactly under these circumstances and I wouldn't describe it as "not that valuable". In any case, AI capabilities will increase dramatically over the next few years while human math capability will not. That means that there's a fixed target regarding whatever is currently considered a "serious math problem" and its difficulty level. Soon the average problem so…

> while human math capability will not. I actually partially disagree with this. What happened to all the excitement about Intelligence Augmentation (IA)? Now it's AI instead of IA. I think there's so much untapped potential for augmenting our intellect with the likes of https://dynamicland.org and https://folk.computer , as well as the work that's been going on in college math education, things like Lean, etc. I thi…

I couldn't agree more. The way everyone thunders towards "replace" instead of "improve" is depressing.
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