Is the purpose of mathematical research to understand the ‘truth’ of numbers? or be the person who find that truth? I think people who are interested in finding the truth won’t care where it came from.
A misalignment of AI in mathematics
451–460 of 637 posts
Re: A misalignment of AI in mathematics
#452> We are witnessing a general threat to intellectual work, with misalignment between the outcome of the use of AI and its initial purpose. 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 work directly, and these goals cease to align.
This is Terry Tao talking about AI's impact on Math, but this could just as well be a software engineer talking about AI's impact on software development.
Do mathematicians deserve more job security than software engineers?
Re: A misalignment of AI in mathematics
#453Earlier quoted context omitted.
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 kept afloat by chess players, not by billionaires. If all the billionaire backers stopped sponsoring tournaments, people like me would still play, still pay for chess club memberships, still pay entry fees for tournaments, and still buy chess books, and so on.
I think the parent comment meant professional, high-level chess. The kind people get played to play, not just do for a hobby. That's absolutely on life support.
I'm not sure what the equivalent would look like in the math field, but it probably involves a lot of mathematicians losing their jobs and the quality of human-produced math decreasing overall.
The quality of the math in general would be fine, since in this scenario cpus will keep producing it. The quality of cpu-cpu chess games is quite high, beyond human understanding in many cases.
Chess is a weird example because it doesn't really have any utility beyond itself. Even pure math sometimes ends up having use in the strangest places. Although if no one understands the frontier math (because no one is getting paid to), I'm not sure it even matters what the quality of the cpu math is?
It's a bit like a tree falling in a forest. If an LLM proves a theorem but no one understands it, did it make a sound?
Re: A misalignment of AI in mathematics
#454Earlier quoted context omitted.
The statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…
Are they claiming that the only value in solving these problems was for their field's personal development process? I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology. It would be insane to demand that people avoid making progress on technology that can save lives or improve general quality of life, just to protect the sanctity of your karate belt…
> I thought Navier-Stokes (and some of the other millenium prize problems) actually had implications for useful technology.
This is the core misunderstanding that the open letter is attempting to correct.
Developing a better understanding of the Navier-Stokes equations could have a number of implications for useful technology. They're fundamental to fluid dynamics, and turbulence in particular is something that many people feel we could work with more effectively if we better understood how and why it's generated. The Navier-Stokes smoothness problem is an interesting and long-standing benchmark for this understanding; we don't know why it should be so hard to answer, so we hoped that the process of developing a proof to the problem would produce more understanding. (We may still be able to extract this understanding after the fact, if OpenAI's proof is fully human-comprehensible.)
Simply knowing that there exists a finite-time blowup is not practically useful. We know that fluids in the real world don't produce random singularities, so the result can't really have much physical meaning. What it illustrates is that the Navier-Stokes equations fail to model physical fluids in some yet to be characterized way.
Re: A misalignment of AI in mathematics
#455Earlier quoted context omitted.
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.
I am very specifically addressing what I have read Terrence Tao say on AI and mathematics, as that is the subject of this submission.
Are we on the same page?
Re: A misalignment of AI in mathematics
#456Mathematics is about discovering and understanding the logical implications of assumed axioms under various inference rules. Alternatively, some claim that mathematics is about understanding these implications. Under the first definition, AI is already, and forevermore will be faster and better at proving theorems. Just like it is better at checkers, chess, and now go. The author asserts that AI proofs are incomprehe…
Dont confuse mathematics with the formal system. If you beleive mathematics = formal system then AI is obviously better at it, and we dont need humans.
But then who decides why a statement is mor important than another? In the eyes of a formal systems all statements are born equal.
Re: A misalignment of AI in mathematics
#457It's good to start a conversation, and the number of Fields Medalists behind this certainly lends a lot of weight to it. But I'm not seeing a strong argument for misaligned incentives beyond the specific plagiarism allegations. The job of an AI company is to build systems that solve problems. The job of a mathematician is to advance the state of human knowledge. If anything, an influx of solved problems should increase the demand for human mathematicians who can convert them into conceptual understanding.
Re: A misalignment of AI in mathematics
#458Re: A misalignment of AI in mathematics
#459To 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 statement is not about AI but about the behaviour of AI companies. OpenAI have put vast resource into solving open maths problems: many millions of dollars of compute just on the Navier-Stokes result, plus whatever they spent on the broader Millenium Prize problems initiative and the other results they have published. Anthropic are doing the same. The statement is asking them to stop doing this. AI companies are…
> There is no near term commercial value
How much do you think other AI companies would offer to get access to the transcripts of the generation that led to the proof? No doubt OpenAI will include it in their training data somehow and use it to build the next generation.
There is already economic value.
Re: A misalignment of AI in mathematics
#460Earlier quoted context omitted.
But computers have destroyed chess as a "sport". Nobody will sit to watch two chess programs compete, or analyze their tactics. Kinda like how now, anybody can construct a "game" over the weekend or a new song or a slop video. The value of each of these decreases to 0 as the slop overwhelms.
>Nobody will sit to watch two chess programs compete, or analyze their tactics. I know nothing about chess yet I dare say that I'd doubt this. Surely chess enthusiasts would be interested in analyzing how a superior chess program came out victorious, no?
People do: https://tcec-chess.com/