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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#671

Post by gpt5 »

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 think that the main thing people in this thread are missing, is that it's not about math. AI progression is very likely to affect every single thing humans can do today. Mathematicians are feeling the blow this week, especially as there was wide spread denial in that math community over the capabilities of AI over the last few years, but it's the same problem everywhere.

Re: A misalignment of AI in mathematics

#672

Post by smj-edison »

pickleRick243 wrote: post #658
rurp wrote: post #532

Earlier quoted context omitted.

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 a…

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 think the only reason human math capabilities haven't expanded that much is a failure of our imagination, not our potential.

Re: A misalignment of AI in mathematics

#673

Post by beepbooptheory »

david-gpu wrote: post #651
beepbooptheory wrote: post #610

Earlier quoted context omitted.

Are you trying to argue toward some final verdict with regard to LLMs and mathematics? I thought you were just trying to make a comparison to Baudelaire? I think maybe being clearer on this point would help. Even if you argued sufficiently for the latter (which is going to be tough already), it wouldn't really speak to the former. Or at least: that would have to be a separate argument I think. Also, how, in your word…

My opinion is that the field will adapt. AI will not spell doom for mathematics. On the contrary, it is the beginning of a new era. Math is having its Deep Fritz moment, just as computer science is going through the same. Some folks are struggling to adapt to this change. Tao actually sounds like he is doing alright compared to most, even if some of his arguments seem a bit weak, as I alluded to in other comments in…

Haha yes I imagine we all know your opinion is something like that! But isn't it much more fruitful and interesting to form an argument for it? If he is still in the context here: is there something about Baudelaire's critique you were discussing originally that has helped you arrive at this opinion? Do you think he is wrong? Or is he right, but providing the right kind of nuance that we need in order to cope with the revolutionary changes? Genuinely curious!

Re: A misalignment of AI in mathematics

#674

Post by octoberfranklin »

gpt5 wrote: post #671
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 think that the main thing people in this thread are missing, is that it's not about math. AI progression is very likely to affect every single thing humans can do today. Mathematicians are feeling the blow this week, especially as there was wide spread denial in that math community over the capabilities of AI over the last few years, but it's the same problem everywhere.

[flagged]

Re: A misalignment of AI in mathematics

#675

Post by fwlr »

deaton wrote: post #197
trillobyte wrote: post #100

OpenAI: "Our mission is to ensure that artificial general intelligence benefits all of humanity." - Except the mathematicians who we'll scoop and cause existential dread among their entire field. - Except the software developers. They'll need to become plumbers or live on UBI. - Except the people in countries that can't afford the cost of AI tokens to keep up with the rest of the world. Just keep picking off groups o…

They're building a utopia that nobody will live in.

Nick Bostrom:

   We could imagine, as an extreme case, a technologically highly advanced society, containing many complex structures, some of them far more intricate and intelligent than anything that exists on the planet today – a society which nevertheless lacks any type of being that is conscious or whose welfare has moral significance. In a sense, this would be an uninhabited society. It would be a society of economic miracles and technological awesomeness, with nobody there to benefit. A Disneyland with no children.

Re: A misalignment of AI in mathematics

#676

Post by pickleRick243 »

SJMG wrote: post #407
globular-toast wrote: post #301

Earlier quoted context omitted.

Magnus Carlsen plays fellow humans at the game because people still care about human competitions. What motivation would a mathematician have for solving already solved problems by hand? Can you imagine someone spending years working on a proof for an already-proved theorem just in case it leads to new insight?

Of course not. I'm so tired of the chess analogy. It was always a game and it was always performative. Research is fundamentally different. We are seeing the erosion of specific needs for thinking at depth. AI is the automobile for the mind. There will 100% be undesirable consequences and selective atrophy of cognitive abilities once prized. This is a loss. There's no getting the cat back in the bag at this point so…

actually I think the whole point is we're finding that the chess analogy to math is in fact quite apt. Math is just an extremely complex game. Its rules can be written down and there are win conditions. It's really not far fetched to think that through information theory, a reasonable measure of depth and beauty to a definition or conjecture can be defined. Then the game is simply to maximize the number of such artifacts produced of high depth and beauty along with proofs of the relevant conjectures.

Philosophers I'm sure can debate this back and forth but it seems probable that some things we thought were ineffable are in fact quantifiable to a degree, and now we have the technology and the machines to bring that to the logical conclusion.

Re: A misalignment of AI in mathematics

#677

Post by uvdn7 »

> But solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight. Forgetting this in the world of AI may turn the tool against the primary goal.

I will quote Richard Feynman - “the prize is in the pleasure of finding the thing out, the kick in the discovery”.

I am not saying that should be the case for everyone in every discipline. But if there is one subject that is mostly pure curiosity driven (instead of worldly impact), it is math. Robbing them the primary motivation is brutal.

If all problems can be solved by a machine, what do we have left to satisfy our curiosity, our desire to explore, and where can we find the pleasure of “figuring the thing out”.

Re: A misalignment of AI in mathematics

#678

Post by valegrete »

yieldcrv wrote: post #373
Panoramix wrote: post #357

Earlier quoted context omitted.

Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such wo…

Different person here, I read the article and they are all wrong. Hope that helps. Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they…

Mathematical breakthroughs with commercial relevance are few and far between, and often depend on dusting off old results which were, at the time of discovery, "solutions nobody asked for."

The NS counterxample is actually, by any market measure, a "problem nobody asked for" in the sense that its existence doesn't have any commercial relevance (beyond juicing OpenAI's IPO). So the only long-term value solving it could have is by virtue of whatever reusable theory/insights were generated along the way to the counterexample itself. The letter is absolutely right on that point.

It's not actually clear that those insights will come faster from reverse engineering this LLM proof vs. humans building theory to solve the problem themselves. So what you're saying may or may not even be an efficient way of operating. Also, it implicitly depends on mathematicians to do the hard work of creating problems and then deciphering LLM hieroglyphics for essentially free while the only immediately profitable component gets outsourced to a frontier lab. In what world is that model going to work?

Reading between the lines, it seems like maybe you have a personal grudge for some reason and simply think the technology will advance enough to where we won't need academics at all. But you should say that in the first place.

Re: A misalignment of AI in mathematics

#679

Post by ndriscoll »

SpicyLemonZest wrote: post #655
ndriscoll wrote: post #612

Earlier quoted context omitted.

But it does produce value. We now have an explicit solution and even a proof. Humans can then work on clarifying why it's true. Unsurprisingly, not all that different from software, where models can generate working code just fine. The details will all be there and all correct, but the architecture is currently not ideal, so a human guiding it can greatly improve the proofs. I actually found this to be the case with…

> But it does produce value. We now have an explicit solution and even a proof. Humans can then work on clarifying why it's true. Unsurprisingly, not all that different from software, where models can generate working code just fine. The details will all be there and all correct, but the architecture is currently not ideal, so a human guiding it can greatly improve the proofs. To me this analogy points in the complet…

One of the awesome things about LLMs is they make it quick and easy to make PoCs, so yes. Proving that an approach will work before spending a bunch of deep design effort is absolutely valuable. Your exact scenario is something I've literally done: give a half-completed design to a team member and asked them to vibecode a PoC to prove the approach will work and figure out some of the details, explore scaling and failure characteristics, etc. Or I do the PoC vibecoding myself too. LLMs have been a gamechanger here.

Re: A misalignment of AI in mathematics

#680

Post by pstoll »

The woman who made up the workforce of telephone switch operators would like to have a word.

Meaning - every new technology has both been perceived as a threa and often forced change in society. Agree maybe “it feels different” this time, but don’t you think everybody before us just said the same thing?

Also not clear if this is an actual called action.

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