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A misalignment of AI in mathematics

mathandai.org

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Re: A misalignment of AI in mathematics

#851

Post by tim333 »

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 de­sert us and turn to him. As a re­sult, an entire domestic industry is rendered completely stagnant. And even more, since the lighting industry has countless ramifica­tions with other native industries, they, too, are injured. This foreign manufacturer who competes against us without mercy is none other than the sun itself!

>Here is our petition: Please pass a law ordering the closing of all windows, skylights, shutters, cur­tains, and blinds... https://fee.org/articles/the-candlemakers-petition/

Re: A misalignment of AI in mathematics

#852

Post by omnicognate »

tim333 wrote: 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…

Not even vaguely related to the point being made in the statement.

Re: A misalignment of AI in mathematics

#853

Post by gjulianm »

david-gpu wrote: post #279
pred_ wrote: post #208

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…

There are no similarities whatsoever, other than them having opinions on a new tech that affects their field.

> nothing stops mathematicians from doing both of those things

Actually yes, and they explain that pretty clearly in the letter. These problems have been used as "goals" not because the solutions are necessarily worth it, but because they set a clear direction whose process would probably yield very useful theories, and also more conjectures and problems. If the goals get solved by AI models that do not generate comprehension, then the direction gets less clear, it's harder to collaborate and get funding (think what would be easier, to get funding to try and solve Navier-Stokes or to try and understand an already proven Navier-Stokes?), and we get less open problems to work on.

Re: A misalignment of AI in mathematics

#855

Post by bluecalm »

Having an oracle that answers yes/no to mathematical questions is very valuable even if there aren't ever any explanation. I don't see how having an answer influences the process of making sense o it negatively. If anything it will save a lot of time - you won't spend time trying to prove something that's not true.

I get that mathematicians and other academics have their social structure and mechanism to create social hierarchies but those aren't very important to interest of general population that funds them.

If the process of making sense of the results, finding structure that humans can understand and writing explanations that allows for wider understanding is valuable it will still be valuable and there will be need for people able to provide it. If it makes higher mathematics accessible to more people then it's even better. I am hope they will not manage to sacrifice that for the sake of their little society in society.

Re: A misalignment of AI in mathematics

#856

Post by rossant »

tmhn2 wrote: post #198

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

I agree. What would stop the AI from explaining the proof in a way human mathematicians can understand, and then giving them a roadmap for spreading it through the community via textbooks, conferences, and so on?

Re: A misalignment of AI in mathematics

#857

Post by fijal »

This is quite fascinating as it looks like the esteemed professors run into a problem of runaway capitalism for the first time. Guess what? The corporations involved don't really care about your feelings or how pursuing their goals affects your life, your well being, anything at all here. Talking with them is kinda moot, this is full on adversarial as countless people around the world, say the nigerians dealing with oil spills would tell you.

Re: A misalignment of AI in mathematics

#858

Post by robotpepi »

omnicognate wrote: post #852
tim333 wrote: 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…

Not even vaguely related to the point being made in the statement.

agree. so many people missing the point. I don't think they even bothered to read the letter.

Re: A misalignment of AI in mathematics

#859

Post by breezybottom »

tmhn2 wrote: post #198

As a mathematician maybe I am a little more optimistic than this declaration. I am thinking of Mochizuki's abc conjecture: He worked in relative isolation, and dumped a huge incomprehensible proof on the community (to oversimplify a bit). That's not totally unlike what might happen if AI generates a huge, incomprehensible proof of let's say RH. Well, what is the result? In the Mochizuki case, it was a lot of skeptici…

How do you write a grant for that though? "I plan to prompt Claude until it eventually spits out an answer"?

Re: A misalignment of AI in mathematics

#860

Post by int_19h »

black_knight wrote: post #802
socketcluster wrote: post #798

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…

This mirrors my understanding when I use Claude code for mathematics. I can have deep discussions with it and it can solve my hairy problems. But whenever we go off the beaten track into design new mathematics, it struggles to make conceptual leaps and find the right definitions. Once I give it my ideas, it is back to its super-human pace and top notch intelligence. This situation suits me fine, since I am anyways mo…

> Once I give it my ideas, it is back to its super-human pace and top notch intelligence.

That's the real benefit of AI today: you can test your ideas almost as fast as you can generate them, in parallel even. If you have a crazy idea that is unlikely to work but has massive advantages if it does, you just set an agent to explore and prototype it while you focus your main attention elsewhere. And so on.

It's still GIGO, though! An AI can make a bad idea work (and will do so if you don't carefully prompt it to not be so sycophantic!) but it won't work well. Knowing when the idea is bad and should be abandoned is also the part that currently requires human judgment.

That said, given the pace at which models have been improving so far, I can't help but think that this is a transient state of affairs.

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