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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#431

Post by andai »

I note here an isomorphism with my essay from earlier this year, The deliverable is you! Programming as theory building:

A program is not the only output of programming. The other, arguably far more important output, is the programmer.

When you write the program — with your own hands — the program is proof that you have a solid mental model of the program.

When you let the computer write the program for you, the program is proof of … nothing.

https://nekolucifer.substack.com/p/the-deliverable-is-you-pr...

Re: A misalignment of AI in mathematics

#432

Post by Bourget »

robotpepi wrote: post #413
stabbles wrote: post #251

Earlier quoted context omitted.

The maths community is now in the antithesis phase, synthesis will take a while ;) Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available. But on the other hand, people l…

I really hate this overly condescending takes. First of all, what do you know about the internals of math research that allows you to speak with so much confidence. Second, you're not even addressing the issues raised by the letter! This is not about "oh they made a bunch of problems easier". There are huge economical interest behind: who owns and has access to models? are these companies interested in developing res…

If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment.

There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.

Re: A misalignment of AI in mathematics

#433

Post by anthonypasq »

matherial wrote: post #179
david-gpu wrote: post #141

Tao's critique of AI in the field of mathematics reminds me of what French art critic Charles Baudelaire said in the 19th century about photography [0]. Baudelaire argued that photography became a haven for failed painters, the sorts of hacks that could not finish proper training. Photography, as a mechanical rendering of the world, could only record what already existed; it couldn't transform reality the way a paint…

I'm really tired of these arguments (this and "it's just like calculators"). Photography decimated other forms of visual art, so the concern wasn't wrong. But AI threatens the entirety of human intellectual endeavors . I can make do without oil paintings in my home. I'm not sure I want to live in a future where we make do without brains.

you can still get oil paintings in your house. you just arent willing to pay for actual art

Re: A misalignment of AI in mathematics

#434

Post by Quekid5 »

318274 wrote: post #277
stabbles wrote: post #251

Earlier quoted context omitted.

The maths community is now in the antithesis phase, synthesis will take a while ;) Lee Sedol said in an interview that "losing to AI, in a sense, meant my entire world was collapsing. ... I could no longer enjoy the game. So I retired", and I think there will be folks in the mathematical community who would feel the same when the solutions pages to hard problems are suddenly available. But on the other hand, people l…

Chess is kept afloat by a couple of billionaires like Sinquefield, MBS and the guy who sponsors freestyle (Fisher random) chess. Carlsen is bored by studying engine lines. The popularity is boosted by YouTubers because chess is very suitable for somewhat higher class content. I'm not sure we'd want that world for math. Positions will be cut just like archaeologist positions are cut now.

Chess is a fun game. That's why it's been around for 1000+ years.

There was a renaissance during Covid and due to 'The Queen's Gambit' where it gained much more mainstream popularity, but... Chess AI was already far far (like 1000+ Elo) ahead of human players at that point.

The thing is... chess is humans playing (communicating) with humans and that's what keeps it interesting. Check out the view counts of chess AI tourneys vs. human tourneys.

Re: A misalignment of AI in mathematics

#435

Post by robotpepi »

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 complaining about the dawn of a new era of advancements seems counterproductive.

you completely misunderstood the critics. your analogy is awful. this is much closer to the industrial revolution in the uk: it brought a lot of progress, but also extreme inequality and concentration of power.

Re: A misalignment of AI in mathematics

#436

Post by ThoAppelsin »

Maths will continue as a field of natural science in understanding the results and uncovering meanings in them. It is normal that the established community is afraid of the change, because it’s their _home_ that’s changing. But it will be a better home to the new generation nonetheless, one that’s not as daunting as the higher maths has always been to many. The concerns raised here will not be a problem at all.

Re: A misalignment of AI in mathematics

#437

Post by anthonypasq »

ifethereal wrote: post #341
ThalesX wrote: post #245

Earlier quoted context omitted.

It boggles my mind. Why cure cancer? The cancer researchers will be out of a job and their kids are going to starve!

Maybe an analogy of "why not solve all medical problems at once" is closer. We absolutely want to, of course. But you extinguish an industry and the systems of training that supply it. It's hard to know if letting it go that way is right.

methinks mathematicians may have a warped perception of their own importance.

Re: A misalignment of AI in mathematics

#439

Post by genxy »

sghiassy wrote: post #424
matco11 wrote: post #401

Earlier quoted context omitted.

I get excited at the idea of a world in which advanced mathematical problems (and their solutions) become much more accessible to a much greater number of people. As a result, making mathematics much more loved at a societal level. Imagine a world where these most complex mathematical problems are not accessible to a few hundred people, but a few hundred thousands people. ...Those original few hundred gifted mathemat…

As a laymen, I wish the same. But I also hope it doesn’t disincentivize those that dedicated themselves to the study

Math department administrators fire Terence Tao.

Based on current reward models, the frontier AI labs will burn down mathematics as an impressive display of capabilities and in doing so, will make it impossible for people that get paid to do mathematics to stay employed.

If your job is literally to publish papers, and OpenAI and Anthropic decide that making an infinite-paper-printing machine is the best thing to show how effective their tech is, then as a demo, they destroy that industry.

Re: A misalignment of AI in mathematics

#440

Post by anthonypasq »

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…

dude, AI is the cheapest and most widely distributed technological revolution ever.
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