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A misalignment of AI in mathematics

mathandai.org

331–340 of 351 posts

Re: A misalignment of AI in mathematics

#331
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

#332

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

#333
post #327

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

#334

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

#335
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

#336
I know it's incredibly presumptuous for me, a nobody, to say this to 25 Fields Medalists, but:

Perhaps you are misaligned.

Who decided the goal of math must be human insight?

First off, some mathematical truths might simply be far beyond our biological comprehension.

Second, for us non-mathematicians, the value of math isn't in understanding exactly why a result is true, it’s in how those results can be applied to actually improve our lives.

Isn't this why we have math in the first place? To solve our real problems? Over time it morphed into this pursuit of pure theoretical insight, probably out of necessity at the time, but is it still necessary?

Re: A misalignment of AI in mathematics

#337

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…

different fields have different communication cultures, that’s not inherently bad. sacrificing inward focus is expensive from the pov of the insider; i see your points but not everything can be written for a general/wide audience. after all, the audience of the author are the specialists, since only specialists spent the effort to be able to engage with the work in depth. perhaps we disagree that mathematics is not a product that mathematicians are making?

what the work was meant to achieve in the first place is what the work was achieving in the first place. it was developing mathematics. if someone wants to use it, they are free to do so, or to write a blog article how it can be used by non experts. mathematicians do that themselves sometimes, but it’s not their job. myb there should be more incentives for them to do more of such work

i keep seeing this myth that mathematics has some purpose to do this or that, but somehow its purpose is least known to mathematicians, everyone else seems to know better

Re: A misalignment of AI in mathematics

#339
post #241

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…

Academia was already crumbling for various reasons. This just hastens it. The reasons are manifold and will never be acknowledged. There will be a lot of gnashing of teeth, but it was unsustainable anyway. And historically the bloat was a very short period, a few decades only.

Re: A misalignment of AI in mathematics

#340
cc my comment from reddit :

This is true of almost any field - if we have black-box technology that only the AI can understand / fix / augment / extend, then we will lose the ability for humans to learn and understand that tech.

Its similar to outsourcing manufacturing, you lose the ability to manufacture. If you don't exercise a muscle, it atrophies. If some people dont learn to write code [ or do math or write music or books ] the hard slow way, we will lose that deep skill.

If young people don't grapple with hard problems in science, math, economics, creative writing, drawing, music making .. they will not be trained, their cognitive skills will not develop with use. We will have no doctors or engineers or musicians or lawyers in a decade or two.

We don't want to become a race of fatties who never exercise, or dummies who just scroll social media feeds without exercising their minds.

This is real.

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