And here we all thought for sure that it was gonna be the "dumb" work to fall to the machines first. Human hubris really is something...
Hans Moravec likely isn't surprised by this.
A misalignment of AI in mathematics
411–420 of 642 posts
Re: A misalignment of AI in mathematics
#412Earlier quoted context omitted.
Your point is largely addressed in the article, did you try reading it? "In many fields and activities, years of training have traditionally served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas. However, building on a vast body of previous human work, AI systems are becoming increasingly capable of producing the results of such wo…
Different person here, I read the article and they are all wrong. Hope that helps. Okay, to elaborate, substantively, their point is that the people using these AI models are not doing it for the love of the game, but for marketing. And instead of them - and nobody - spending millions of dollars to solve the problem, successfully, they want every problem of their academic industry to persist because even though they…
Their claim is only indirectly related to the motivations of the people using their models. What they're saying is that doing math in this way does not produce the same value as traditional mathematical research, and the people using these AI models aren't concerned about that because their marketing objectives don't depend on whether their results produce mathematical value. If people doing valuable work are made irrelevant by people doing a larger volume of non-valuable work, that's not a positive outcome.
Re: A misalignment of AI in mathematics
#413As 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…
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 research or they just grind PR stunts without worrying about externalities in how research is actually conducted? Etc etc.
Re: A misalignment of AI in mathematics
#414Earlier quoted context omitted.
How do you know the proofs are correct?
The numerical results are trivial to check. I wrote the analytical results in Lean by hand before asking a former professor to confirm after asking him to keep this private. They're valid.
It's really tough to come to terms with it but making academic contributions in general from the outside (with or without AI tbh) is not often welcome and the whole process feels very gate-kept.
Re: A misalignment of AI in mathematics
#415I agree with many of the sentiments here. But an open letter signed exclusively by Fields Medalists that purport to define precisely what the "mathematical community" (who is inside and outside) and what their goals are raises my hackles for some reason.
It is true that the manufacturing of "true/false" statements is not the same as gaining understanding of a problem. However, for many mathematicians, true/false statements are already manufactured by others. Think of a student who is given a conjecture to investigate, with their advisor describing it as "it must be true". Most exercises in a textbook are stated such that the outcome is known before you begin. That's not really a problem -- investigating the conjecture/exercise yields its own dividends, whether or not the outcome is known. It is also the case that defining new directions involve understanding and synthesizing related problems, asking the right questions, and deciding upon the right directions, and it's not clear that AI can do that at all.
The real risk, I think, its the public's (and funding agencies') perception of the importance of "human" mathematics, but that's already a struggle. For example, it's tough to explain to the lay person why it's still important to research group theory -- the main example people cite is RSA encryption, which was invented almost 50 years ago.
Re: A misalignment of AI in mathematics
#416Earlier quoted context omitted.
I wonder if they will continue to dump proofs, though? Their point has been made, the novelty will wear off, and it maybe won't be a priority use of their resources to spend however many millions on another big proof--they will move on to the next thing to show off I'm sure. At that point, the ones generating proofs will be, I hope, mathematicians (professional and otherwise) that are more interested in the results a…
They already told the NYT that they’ve made “substantial progress” on another one of the MP Problems (most likely the Hodge Conjecture). That said, that’s probably just because of the drama miring their most recent one. After 2 I don’t see why they’d bother anymore.
>That said, that’s probably just because of the drama miring their most recent one. After 2 I don’t see why they’d bother anymore.
P/NP and the Riemann Hypothesis are part of the milllenium problems. They will 100% keep trying to crack those regardless.
Re: A misalignment of AI in mathematics
#417Maybe mathematicians should be aligned better, rather than AI? The current measure of a successful mathematician is the problems they have solved or worked on. At some point in history, the measure of a successful scholar was how well one could copy manuscripts. Once we have a tool that starts to work well for this task, it's time to define success differently. It's a classic alignment problem! ;) But seriously, thes…
Another historical analogy: this is kind of like the transition from alchemy to chemistry.
Re: A misalignment of AI in mathematics
#418Earlier quoted context omitted.
I don't think that AI would disrupt any of that. Even if AI solves a problem, you can still discuss the methods at conferences, seminars, lectures, chats in the hallway, advising students, etc.
Tao’s key point is that the way people are using AI today does disrupt that. Because people and companies are valuing the results over understanding. So we’re getting slop results rushed out that are automatically verified. Moreover in the past, discussion and idea sharing would happen naturally to overcome the friction of the process. But now when OpenAI is stuck on a particular part of NS for example, they can just…
I won’t speak for Tao. But it is not “people” who have valued the result over understanding. “People” are a bit impressed that the machines are as good or better than the priests who have been praying at the inscrutable altar of pure mathematics. But it is mathematicians—I am speaking as a mathematician—who have adopted a culture of valuing results over exposition and transparency. The field has been rife with extremely opaque papers for many years and the character of research participation has been one of exclusion and competition over proof priority at the expense of understanding and transparency. It is unbelievably ironic to listen to mathematicians complain about “AI slop” when they have built careers upon human “slop” if slop means papers crammed with technical density that prevents all but specialists from reading the work.
Re: A misalignment of AI in mathematics
#419Earlier quoted context omitted.
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.
Lots of people still make bad music that other people still manage to enjoy (a lot of it has gone multi-platinum!) even though they're not Mozart or Bach.
This would be valid if we didn’t live in under capitalism, which reduces the way we spend our time down to dollars and cents.
Re: A misalignment of AI in mathematics
#420As 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…
Even before AI we used to say if you write code that you only barely understand, then it will be to complicated to debug. (and/or maintain) Mochizuki was still one human and it required legions of other humans to unpack and untangle to confirm that it didn't lead to anywhere in particular. AI is now capable of constructions so complex that no human or human team can unpack. And its ability to increase that complexity…
> AI is now capable of constructions so complex that no human or human team can unpack
Can you give an example of this?