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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#861

Post by milindsmart »

gammarator wrote: post #768
pickleRick243 wrote: post #662

Earlier quoted context omitted.

for many fairly strong mathematicians, the career calculus is fame and status (mild though it may be) through mathematics or anonymity but financial reward in tech or finance. Yes, clout by becoming a lifelong academic is in fact rational for some and part of their motivation. Of course they really like what they do as well, but earning the respect of the peers they know are also respected by a large swathe of societ…

I think you’re right that some of the angst here is due to a fairly insular community having its culture disturbed by commercial forces.

That fairly insular community pretty much gave up on commercial success in order to be insular. But the commercial forces were not happy being commercially successful, so they decided to disturb even their insular and commercially-unviable activities.

Re: A misalignment of AI in mathematics

#862

Post by contubernio »

NateEag wrote: post #463
onetimeusename wrote: post #428

Earlier quoted context omitted.

But the work the Mochizuki case generated can also be done by AI. AI could generate a landmark proof and then people could use it to solve or simplify intermediate problems and you could use a different AI prompt to try to disprove it if you were really skeptical. From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. I don't like nuance here…

Tangent: > From my memory I think they said it took 88 hours to solve a Millenium Problem versus the decades of time humans have put into it. Keep in mind those ~88 hours were spread across ~10,000 simultaneous agent instances. So, roughly 880,000 hours of compute. Assuming a fifty-year career, and forty-hour workweeks, a human mathematician's career is about 100,000 hours of "compute". I suspect that with six good m…

"I suspect that with six good mathematicians spending their whole careers primarily focused on it, and working together closely, Navier-Stokes might well have fallen already"

There were more than six doing that and it's essentially why it was ripe for AI to finish it off. But the finishing off was quicker than anyone expected

Re: A misalignment of AI in mathematics

#863

Post by Dylan16807 »

eru wrote: post #820
flatline wrote: post #521

Earlier quoted context omitted.

Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be. Tech companies are as much the topic of this post as AI, I think that's the immediacy.

> Does mathematics still have a practical impact without humans in the loop? There's a single answer to that question: yes, math very much has an impact without humans in the loop. Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.

We're way into diminishing returns in matrix multiplication, and being clever about ALUs and cache layout is likely to dwarf any asymptotic improvements you're going to find. Any better examples of improvements in the last decade?

The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.

Re: A misalignment of AI in mathematics

#864

Post by auggierose »

Animats wrote: post #739

This is a PR problem, not a mathematical problem. It's possibly the worst PR problem mathematics has faced since the execution of Hippasus for whistleblowing on the cover-up of the regular dodecahedron. It's still a PR problem. So what went wrong? Mathematics education. Math below grad school is all about solving stated problems. Credit is given for solving puzzles successfully. Homework is problem sets. Everybody be…

Very interesting analysis. I was just reading this announcement, and thinking, that is the most pointless thing I've ever read. What are they trying to achieve with it? Your comment explains it.

Re: A misalignment of AI in mathematics

#865

Post by Dylan16807 »

robotpepi wrote: post #847
eru wrote: post #821

Earlier quoted context omitted.

The trailing edge of AI is catching up fast. There's plenty of open source (and even more open weight) AI models and they are getting better and better. If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?

The problem with your opinions is that you tend to state certain very quesitonable ideas with 100% confidence. Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. We don't even know how much of creative work they are able to do. We cannot make decisions that could destroy decades of progress just because of h…

We don't know how good models will get, but the pattern of open weight models keeping up on a relatively short delay has been holding pretty well. And even among the proprietary models there's healthy competition. The concentration of resources is pretty well counteracted by these factors.

Re: A misalignment of AI in mathematics

#866

Post by somenameforme »

eru wrote: post #826
somenameforme wrote: post #776

Earlier quoted context omitted.

When there's a billion people playing something, money will never be an issue for those at the top. Even things like chess.com was able to sponsor a tournament with a million dollar prize pool. Also I'd argue that chess's utility is ultimately the same as pure math, particularly in esoteric fields. These things are highly unlikely to ever lead to any sort of real world breakthrough or application. The main benefit is…

> Though I think even that's probably too socially utilitarian. I think ultimately the 'real' drive is the same in both fields - it's fun and personally rewarding. That's fine, and no amount of machine excellence will keep you from enjoying recreational chess or recreational math.

Ah but it's enjoyable for billionaire and pauper alike. And the former tends to enjoy sponsoring it for the sake of seeing and promoting the bounds of human capability.
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