5 ms·

I think his comparison to previous machine-assistance is misleading. In previous cases, the use of machines was never creative, whereas now AI has the ability t

I think his comparison to previous machine-assistance is misleading. In previous cases, the use of machines was never creative, whereas now AI has the ability to suggest creative lines. In the short-term, this sounds exciting. But I also think it reduces the beauty of math because it is mechanizing it into a production line for truth, and reduces the emphasis on the human experience in the search for truth. The same thing has happened in chess, with more people advocating for Fischer random because of the boring aspect of preparing openings with a computer, and studying games with a computer. Of course, the computer didn't initiate the process of in-depth opening preparation but it launched it to the next level. The point is that mechanization is boring except for pure utility. My point is that math as a thing of beauty is becoming mechanized and it will lead to the same level of apathy in math amongst the potentially interested. Of course, now it's exciting because it's still the wild west and there are things to figure out, but what of the future? Using advanced AI in math is a mistake in my opinion. The search for truth as a human endeavor is inspiring. The production of truth in an industrialized fashion is boring.

jebarker 2y ago
> Using advanced AI in math is a mistake in my opinion. I too feel saddened by the idea of automating math if it leads to inscrutable proofs or theories. But it seems essential that we advance the tools used for mathematical discovery if we hope to keep advancing. Hopefully we can find a balance where the advancement of mathematical understanding continues to be a human story, but we're not artificially held back by pretending new tools don't exist.
brap 2y ago
Human chess players are still incredibly valuable because we want to see what humans are capable of. For the same reason athletes are valuable even though a car can outrun them. With mathematicians, and others working in intelligence-intensive tasks (most of us here probably), I’m not sure what the value would be post-AGI.
- vouaobrasil 2y ago
  The point is that even with mathematics and programming, there is an underlying community aspect that cannot be ignored, but is hidden under layers of utility. For example, even in programming, people getting together to code, collaborating, and sharing their projects is a small but significant drop in people creating a community. With mathematics, the sharing of ideas and slaving over the proof of a theorem brings meaning to lives by forging friendships. Same with any intellectual discipline: before generative AI, all the art around us was primarily from human minds and were echoes of other people through society. Post-AGI, we abandon that sense of community in exchange for pure utility, a sort of final stage of human mechanization that rejects the very idea of community.
  - williamcotton 2y ago
    I don’t think AGI is going to have any impact on the communities of open mic folk singers of the world.
  - zmgsabst 2y ago
    Chess has never had a larger community — entirely because computers enable streaming and exciting faster games.
    - vouaobrasil 2y ago
      Again, I am not arguing against ALL computer use of chess. Just the chess engine/AI itself. Why do you insist on taking all of technology as an indivisible unit in your argument?
      - zmgsabst 2y ago
        They’re the same technology: you don’t get to select only some of the applications, which appeal to your personal aesthetics. We arrived at engines before online chess, and the two have come up together — both being enabled by the growth of computers. You can choose not to use an engine, but it will exist either way because others will choose to use it when it’s enabled by those same things. To get rid of the engine, you have to get rid of computers — or in the case of Freestyle/Chess960, create so many openings a human can’t memorize them all so only has a short time to prepare.
_yb2s 2y ago
> The production of truth in an industrialized fashion is boring. Chess is a game, if it gets boring that defeats the point…. Math on the other hand is basic science research, and enables us to understand how the universe and our bodies work, to massive benefit. I don’t care how “boring” it is, the knowledge could have immense value or be critical for our survival and if AI can allow us to access it, all the better.
- vouaobrasil 2y ago
  I would argue with your "massive benefit", unqualified. Because while it is true that basic research HAS improved life, much of modern research and technical production has decreased it: less sense of community, microplastics, climate change, destabilization of the working force (AI), less sense of purpose. What's the use of an even longer life if our entire way of life is just a production to add incremental levels of safety, which hardly helps most anyway? While you might be right, it is VERY far from clear that the latest advanced research will really help us. It could also lead to our annihilation or at least dehumanization, which is really not much better than annihilation. In fact, due to the immense damage technology has caused, the burden of proof should be on the technologists to reliably demonstrate that new technology is even worth it beyond propping up our broken, global capitalistic system.
  - _yb2s 2y ago
    I’m not talking about technology, I’m talking about having an understanding of how reality works. I fully agree with you that one should have a sense of ethics and use the precautionary principle when deciding what to do with that knowledge. With deeper knowledge we can develop more humane and environmentally safe technology, and cure diseases that cause massive suffering… We’re past the point of just going back to preindustrial tech with less negative impacts- but with a deeper understanding of reality we could, e.g. pull carbon straight out of the atmosphere to manufacture almost anything in a renewable way, while also understanding biochemistry enough to make things that won’t be toxic or persist in the environment, and are readily broken down and reused.
    - 2y ago
zmgsabst 2y ago
Computers allow us to scale what we analyze in math — and that’s a good thing. Nobody examines structure of group diagrams because drawing interesting ones by hand is borderline impossible, but takes just a few minutes on a computer. However, they’re a natural way to arrive at algebraic/geometric equivalence. (And indeed, the first time I had an intuition for it.) To me, you sound like someone lamenting swimming is meaningless because we invented boats.
- vouaobrasil 2y ago
  Again, like so many, you are taking computer use in math as an indivisible whole. I never said that computers were NOT useful. Only that the use of creative AIs in math are counterproductive in the long run, hence implying a point of diminishing returns that we push towards (due to the peverse incentives of academia). There is also a fundamental difference between swimming and math. There is no prisoner's dilemma situation when it comes to swimming: with swimming, people CHOOSE to swim because they like it. But due to different incentives, people will CHOOSE to use AI only because others use it and it will become the only path eventually. In other words, swimming is still possible even though boats exist. People going into mathematics will not have the possibility of being of any use without AI, because the prisoner's dilemma (arms race) will ensure that math is no longer about anyone caring about math without AI.
  - zmgsabst 2y ago
    You ignored the thrust of my argument: You’re lamenting that inventing boats has destroyed the beauty of swimming. - - - Edit - - - Responding to your expanded argument: You could never swim to a new continent, which boats enabled. This is the same — people can choose to keep doing the same limited math themselves, in a slower way, but will never reach the places people can aided by tools. That’s simply how the world is. But we shouldn’t restrict the distance people can travel to adhere to the aesthetics of swimming. You’re arguing precisely that: we must limit our intellectual journey because you don’t approve of the aesthetics of the tool to travel further.
    - 2y ago
pepinator 2y ago
How is AI different from using a calculator? AI is just giving a new abstraction layer, in the same way that computers have done before AI. And these non-AI tools have allowed us to produce both deep research and beautiful theories. I'd be more worried about the problems related to a few companies concentrating all the tools and therefore the power.
- vouaobrasil 2y ago
  AI is different because its ability to suggest creative lines of thinking will change the entire structure of how mathematics is done. It's the same difference between "dumb" algorithms and "generative AI" algorithms. The generative AI has the capability to replace human thinking in some cases, whereas the dumb algorithms only replace rote work. Since creativity is not just what allows innovation but also forms the center of community and personal expression, we are also replacing those "soft" components of scentific exploration that eliminate the importance of the individual.
JonChesterfield 2y ago
Philosophy survived the rise of engineering. Informal mathematics will survive the rise of actually getting the answer right just the same.

jebarker 2y ago

> Using advanced AI in math is a mistake in my opinion. I too feel saddened by the idea of automating math if it leads to inscrutable proofs or theories. But it seems essential that we advance the tools used for mathematical discovery if we hope to keep advancing. Hopefully we can find a balance where the advancement of mathematical understanding continues to be a human story, but we're not artificially held back by pretending new tools don't exist.

brap 2y ago

Human chess players are still incredibly valuable because we want to see what humans are capable of. For the same reason athletes are valuable even though a car can outrun them. With mathematicians, and others working in intelligence-intensive tasks (most of us here probably), I’m not sure what the value would be post-AGI.

vouaobrasil 2y ago
The point is that even with mathematics and programming, there is an underlying community aspect that cannot be ignored, but is hidden under layers of utility. For example, even in programming, people getting together to code, collaborating, and sharing their projects is a small but significant drop in people creating a community. With mathematics, the sharing of ideas and slaving over the proof of a theorem brings meaning to lives by forging friendships. Same with any intellectual discipline: before generative AI, all the art around us was primarily from human minds and were echoes of other people through society. Post-AGI, we abandon that sense of community in exchange for pure utility, a sort of final stage of human mechanization that rejects the very idea of community.
- williamcotton 2y ago
  I don’t think AGI is going to have any impact on the communities of open mic folk singers of the world.
- zmgsabst 2y ago
  Chess has never had a larger community — entirely because computers enable streaming and exciting faster games.
  - vouaobrasil 2y ago
    Again, I am not arguing against ALL computer use of chess. Just the chess engine/AI itself. Why do you insist on taking all of technology as an indivisible unit in your argument?
    - zmgsabst 2y ago
      They’re the same technology: you don’t get to select only some of the applications, which appeal to your personal aesthetics. We arrived at engines before online chess, and the two have come up together — both being enabled by the growth of computers. You can choose not to use an engine, but it will exist either way because others will choose to use it when it’s enabled by those same things. To get rid of the engine, you have to get rid of computers — or in the case of Freestyle/Chess960, create so many openings a human can’t memorize them all so only has a short time to prepare.

_yb2s 2y ago

> The production of truth in an industrialized fashion is boring. Chess is a game, if it gets boring that defeats the point…. Math on the other hand is basic science research, and enables us to understand how the universe and our bodies work, to massive benefit. I don’t care how “boring” it is, the knowledge could have immense value or be critical for our survival and if AI can allow us to access it, all the better.

vouaobrasil 2y ago
I would argue with your "massive benefit", unqualified. Because while it is true that basic research HAS improved life, much of modern research and technical production has decreased it: less sense of community, microplastics, climate change, destabilization of the working force (AI), less sense of purpose. What's the use of an even longer life if our entire way of life is just a production to add incremental levels of safety, which hardly helps most anyway? While you might be right, it is VERY far from clear that the latest advanced research will really help us. It could also lead to our annihilation or at least dehumanization, which is really not much better than annihilation. In fact, due to the immense damage technology has caused, the burden of proof should be on the technologists to reliably demonstrate that new technology is even worth it beyond propping up our broken, global capitalistic system.
- _yb2s 2y ago
  I’m not talking about technology, I’m talking about having an understanding of how reality works. I fully agree with you that one should have a sense of ethics and use the precautionary principle when deciding what to do with that knowledge. With deeper knowledge we can develop more humane and environmentally safe technology, and cure diseases that cause massive suffering… We’re past the point of just going back to preindustrial tech with less negative impacts- but with a deeper understanding of reality we could, e.g. pull carbon straight out of the atmosphere to manufacture almost anything in a renewable way, while also understanding biochemistry enough to make things that won’t be toxic or persist in the environment, and are readily broken down and reused.
  - 2y ago

zmgsabst 2y ago

Computers allow us to scale what we analyze in math — and that’s a good thing. Nobody examines structure of group diagrams because drawing interesting ones by hand is borderline impossible, but takes just a few minutes on a computer. However, they’re a natural way to arrive at algebraic/geometric equivalence. (And indeed, the first time I had an intuition for it.) To me, you sound like someone lamenting swimming is meaningless because we invented boats.

vouaobrasil 2y ago
Again, like so many, you are taking computer use in math as an indivisible whole. I never said that computers were NOT useful. Only that the use of creative AIs in math are counterproductive in the long run, hence implying a point of diminishing returns that we push towards (due to the peverse incentives of academia). There is also a fundamental difference between swimming and math. There is no prisoner's dilemma situation when it comes to swimming: with swimming, people CHOOSE to swim because they like it. But due to different incentives, people will CHOOSE to use AI only because others use it and it will become the only path eventually. In other words, swimming is still possible even though boats exist. People going into mathematics will not have the possibility of being of any use without AI, because the prisoner's dilemma (arms race) will ensure that math is no longer about anyone caring about math without AI.
- zmgsabst 2y ago
  You ignored the thrust of my argument: You’re lamenting that inventing boats has destroyed the beauty of swimming. - - - Edit - - - Responding to your expanded argument: You could never swim to a new continent, which boats enabled. This is the same — people can choose to keep doing the same limited math themselves, in a slower way, but will never reach the places people can aided by tools. That’s simply how the world is. But we shouldn’t restrict the distance people can travel to adhere to the aesthetics of swimming. You’re arguing precisely that: we must limit our intellectual journey because you don’t approve of the aesthetics of the tool to travel further.
  - 2y ago

pepinator 2y ago

How is AI different from using a calculator? AI is just giving a new abstraction layer, in the same way that computers have done before AI. And these non-AI tools have allowed us to produce both deep research and beautiful theories. I'd be more worried about the problems related to a few companies concentrating all the tools and therefore the power.

vouaobrasil 2y ago
AI is different because its ability to suggest creative lines of thinking will change the entire structure of how mathematics is done. It's the same difference between "dumb" algorithms and "generative AI" algorithms. The generative AI has the capability to replace human thinking in some cases, whereas the dumb algorithms only replace rote work. Since creativity is not just what allows innovation but also forms the center of community and personal expression, we are also replacing those "soft" components of scentific exploration that eliminate the importance of the individual.

JonChesterfield 2y ago

Philosophy survived the rise of engineering. Informal mathematics will survive the rise of actually getting the answer right just the same.