Live data from Hacker News

A misalignment of AI in mathematics

mathandai.org

921–930 of 1001 posts

Re: A misalignment of AI in mathematics

#921

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…

I agree insofar as this may fall on deaf ears of AI folks, but that the goals are differ is exactly the point of pointing out misalignment. To talk about this may be more useful for coalescing professional societies than for conversing directly with AI advancers.

Re: A misalignment of AI in mathematics

#922
I don't feel nurtured and cared by mathematicians. I mean, it depends, it took me four years to find such professors. When I did, very recently, it felt like fresh air. A couple of good teachers among tenths of egotistical frustrated gatekeepers that humiliate students.

I do see a patient teacher on generative tools. What has keep me trying to learn math has not been mathematicians, but the support of people outside of the field.

Re: A misalignment of AI in mathematics

#923

As a consumer of mathematics, I want to attack the author’s idea of “what that work was meant to achieve in the first place”. I do a lot of programming that uses mathematics. I designed the error recovery file format “par2”. I worked as a quantitative trader. What do I want from math? To be able to search math results, understand them, and apply them. But academic mathematicians are so inwardly focused - as these aut…

I've had a similar experience.

LLMs doing math has made math far more accessible to me than it was pre-LLM.

Not just using existing math, but developing new math. (For example, I developed an alternative to NURBS surfaces for geometric kernels using LLMs.)

It's really annoying that anyone, anywhere is talking about halting math progress with AI.

Re: A misalignment of AI in mathematics

#924
post #794

Earlier quoted context omitted.

I think there's a difference between "photography will change art--we need to be ready" and "photography will change art, therefore stop photography." There is no doubt that AI has changed the practice of mathematics, just as it has changed the practice of software engineering (and will soon change almost every intellectual job). Trying to deal with change by saying, "please stop the change" is foolish, IMHO. Mathema…

> I think there's a difference between "photography will change art--we need to be ready" and "photography will change art, therefore stop photography." That wasn't the critique. The statements then were that photographs weren't actually art at all. They were the results of specialists with skills but not 'art'. Yet the photograph as a product was displacing real art in the marketplace.

AI is displacing real mathematicians.

Re: A misalignment of AI in mathematics

#925
post #851

It reminds me of Frédéric Bastiat's Candle Makers' Petition. It satirised protectionism in the 1800s: >We candlemakers are suffering from the unfair competition of a foreign rival. This for­eign manufacturer of light has such an advantage over us that he floods our domestic markets with his product. And he offers it at a fantastically low price. The moment this foreigner appears in our country, all our customers de­s…

This is a straw men argument The petition is about a much broader problem: if we’ll demotivate people from understanding math, vibe math in a rush without making it understandable - math becomes useless Basically with pic generation at least we all understand what is on a pic - some cat or something With math it is trivial to generate a lot of stuff that is half-assed and just gives a plain yes/no but doesn’t get abs…

> vibe math

Ah yes, Lean 4. Famous for how unreliable it is. Absolute slop!

Re: A misalignment of AI in mathematics

#926
post #911

I wish this were a document that clearly described how mathematicians expect AI to behave, rather than how it is misaligned. I can kind of decipher the expectation from the declaration, but it still sounds a bit like "it would be better if AI didn't meddle with mathematics", instead of "we want AI to approach problems like this and that way".

They want the AI labs to stop solving "important" math problems so that humans can do it, on the theory that when AI solves "important" math problems, it robs humans of the opportunity to gain new insights into those problems.

Total horse shit, but that's the essence of it.

Re: A misalignment of AI in mathematics

#927

As a software engineer, 6 months ago. I was better than AI in essentially every way except raw typing speed. Now AI has surpassed me in fine-grained problem-solving ability. It can write more reliable code than I can, faster than I can, provided it is given the right guidance. But one thing that I'm still much better at is identifying technical opportunities and choosing the right tradeoffs. My feeling is that fronti…

Thanks for putting it in words. I feel the same about SOTA coding models. I get visibly frustrated by this and often find myself using curse words at Astra.

You're right it's very unhuman to miss obvious opportunities you mentioned. And what's why I think these models would continue sucking as long as they don't have human level general intelligence. They may get marginally better at these tasks but I don't think we can expect them to connect dots like humans before AGI.

Re: A misalignment of AI in mathematics

#928
It sounds similar to the more thoughtful critiques of AI in programming. Treating AI as a lines of code (LOC) generator, where actual human beings end up not engaging with the domain the software is working in, and there is then little to no understanding or care to understand the resulting code, we call "slop." The term slop is definitely pejorative, but since most software is commercial, it ends up raising questions as to how much quality and domain knowledge matter if the goal is primarily marketplace success. Then we get those thorny questions of what is software for, anyway -- do we really accept the premise that "marketplace success" is the best, and perhaps only relevant, criteria?

The declaration here, as I understand it, is taking the premise that the point of mathematics _is_ the domain knowledge, and that using "solves math problems" as a benchmark is exactly the kind of shallow, domain-eroding approach to AI that in software we label "slop."

Re: A misalignment of AI in mathematics

#929

Earlier quoted context omitted.

It’s frustrating that this comment is at the top because it, along with lots of the replies it inspired, absolutely misrepresents the actual declaration. The declaration is not making any statements about not using any AI in mathematics. The entire point is to push the use of the technology in a direction which is compatible with positive pre-existing features of the math community, and to make it better known what s…

The declaration literally opens by writing that AI companies (or really anybody) saying, “Hey, let’s see if this powerful reasoning engine can solve an open problem in mathematics” is “detrimental” to the “science” of mathematics. Full stop. So I don’t think it’s being misrepresented. If it’s a science, why isn’t progress good in itself? You can’t have it both ways. The online comments I’ve read that side with the le…

Mathematics sits in a very different place w.r.t. other sciences. First of all, it's very meta. Yes, it can describe any phenomenon on our planet. On the other hand, advanced mathematics is a high mountain which is very hard to climb, and changes the climber in various and irreversible ways once the journey begins.

That's said, I'm a non-mathematician, but a computer scientist. Mathematics was always my weak part, because solving problems which doesn't mean anything doesn't motivate me, and when I'm not motivated, I fail.

Without digressing so much, I want to say that, some of the things in mathematics and mathematics adjacent sciences baffle me. Many mathematicians don't understand the proofs of others, yet they accept it since it checks out within the rules of mathematics. Moreover, many engineers don't understand the formulae they work with. I have developed a very performant Boundary Element Method evaluator, yet I don't know the reason of taking Gaussian Integrals over the surface. The only answer I got is "because the method works that way".

So, if computers can make the proofs now, and we have no curious students pecking their professors to understand how these works, the whole mathematics as a science could wither and die. Because besides it being a sport, it's the very language which can model and explain anything, but it's very hard to master and understand due to that nature.

Our professors warned us against using too much Mathematica, to make us learn things the hard way and make the knowledge permanent. Now, if we offload science to a matmul engine, it's possible that we lose the connection and never able to close the gap in some cases.

Again, it boils down to "This machine has no brain, use yours (or lose it)".

Re: A misalignment of AI in mathematics

#930
post #663

Earlier quoted context omitted.

that is incredibly depressing

I feel the opposite. Human history is depressing overall. I imagine AI will eventually lead to less scarcity and better lives overall.

I am sure it will lead to more material wealth, but I can’t help but feel pessimistic about the political economy of making millions of people redundant. What leverage will knowledge workers have in the new world?
Post reply on HN