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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#141

Post by david-gpu »

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 painting could.

He also criticized the public's craze for "rushing" into it, and complained that this technical "progress" was weakening the arts.

Do you see some parallels as well?

[0] https://fr.wikisource.org/wiki/Curiosit%C3%A9s_esth%C3%A9tiq...

Re: A misalignment of AI in mathematics

#143

Post by andrepd »

oytis wrote: post #59

Looks like mathematicians (like people in many other professions) have to redefine what their work means and how to define success. Hard to agree that a tool that can find a proof is detrimental by itself, rather it voids some assumptions people relied on previously

Yes if you don't think about the matter for more than 6 seconds you would indeed conclude that, and retreat to the comfortable cliché of "it's just a tool". Meanwhile, I'm glad that there are still people who _think_ about issues and ponder the consequences and reflect on things before they become a reality.

Re: A misalignment of AI in mathematics

#145

Post by kccqzy »

vatsachak wrote: post #64
NoDodgeQuestion wrote: post #52

Earlier quoted context omitted.

You feel lean4 proof, that you 99.999% chance not understand is beautiful?

https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...

How many humans on earth have finished reading this 100+ page PDF and actually appreciate the beauty contained therein (or the lack of beauty)?

Re: A misalignment of AI in mathematics

#146

Post by fwlr »

In internet culture there’s this phrase “Hydrogen Bomb vs Coughing Baby”, meant to highlight the absurd power difference between two combatants.

In almost any scenario even tangentially involving mathematics, twenty-five Fields medallists uniting to denounce something would be a veritable Tsar Bomba.

It should give you pause that here they feel like the ailing infant.

Re: A misalignment of AI in mathematics

#147

Post by warkdarrior »

rossant wrote: post #50

> ... 25 initial signatories — all Fields Medallists — As a non-native English speaker, I initially understood this to mean that all living Fields Medallists had signed. I later realized that it meant only that all the signatories were Fields Medallists. (Apparently, there are 47 living Fields Medallists today.)

Yeah, it was a bit ambiguous. They should have picked better wording, one of the following would do to clarify.

> ... 25 initial signatories — all of them Fields Medallists —

OR

> ... 25 initial signatories — all of the living Fields Medallists —

The first one is what they meant.

Re: A misalignment of AI in mathematics

#148

Post by tmhn2 »

jrflo wrote: post #127
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

Right. It seems like reading an AI proof (although it may not be well written) will provide the same insights as reading a proof from another mathematician, assuming it's been reviewed and edited, just like any human-authored publication. If the work is inherently valuable on it's own, I feel like that's mostly what matters.

At issue is the fact that it doesn't typically work like: mathematician produces a proof in isolation, generates a PDF, and shares it with a bunch of people. There's a whole culture and community going on behind the scenes with conferences, seminars, lectures, chats in the hallway, advising students, etc. that AI-generated proofs bypass.

Re: A misalignment of AI in mathematics

#149

Post by k2xl »

I’m sympathetic to the concern, but I’m still unclear on what the concrete ask is.

If the worry is that AI companies are turning open problems into benchmarks and potentially “using up” fertile mathematical problems before humans can develop the ideas around them, what exactly should the companies do differently? Also why does discovering the answers preclude humans developing ideas from them? I don't get why solving a math problem stops anyone from doing that?

Should they (AI companies) avoid training or evaluating models on open problems? Solve them but not publish the results? Delay publication? Only release proofs after mathematicians have had time to study them? Require some attribution or review process?

The statement makes a strong case that “maximize the number of solved problems” may be the wrong objective, but it seems much less clear about what behavior they actually want from OpenAI, Anthropic, DeepMind, etc.

I’d be interested in the most concrete version of the proposal. Without that, it starts to read a little like: "Please stop getting so good at our thing!"

Re: A misalignment of AI in mathematics

#150

Post by jimkleiber »

tmhn2 wrote: post #130
jeremysalwen wrote: post #20

To me it doesn't seem like what AI has destroyed is the ability for mathematicians to develop understanding and share it with each other, but rather it's destroyed the yardstick (solving open problems) that has traditionally been used to measure how much they have contributed to that understanding. I do see how this is a problem in terms of assigning credit, but I think the cat is already out of the bag in terms of t…

The issue of credit is a relatively minor point in the declaration. It's more about bypassing the culture and processes mathematicians have developed that lead to human understanding, generating new ideas, and bringing up new generations of mathematicians. (See also his article about "non-renewable mining" of good problems.) Reducing mathematics to "let's just generate results through an isolated and automated system…

I wonder if this is a root of the complaints across fields, how AI is ruining the greater picture and process in writing, acting, drawing, filming, coding, and more.

That it makes life more ends and less means.

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