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If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment. There is a real, undeniable possibility of AI beco

If it's worth anything: I have a PhD in (theoretical) mathematics and I entirely stand by stabbles' comment. There is a real, undeniable possibility of AI becoming better at mathematics in the same way that it became better at chess and Go, and in such a scenario, one may expect the community's response to be comparable.

3ash14 5d ago
Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish. Stockfish does not steal research or scoop researchers. The concentration of computing resources and capital should be examined by the math community.
- coderenegade 5d ago
  This is the real problem. We're looking at a future where those who control AI have an insurmountable advantage in everything. They can control the amount of intelligence the masses have access to -- for their own safety, of course -- and they will never, ever be able to close the gap.
  - tomrod 5d ago
    Say they do. What then? Will people buy from them? What if we decide not to?
    - coderenegade 5d ago
      At a certain point, you don't have a choice. Before China got into the game, the only way to avoid giving Luxotica money if you wanted a pair of glasses was to essentially not buy glasses. This is the same for many industries -- consolidation behind the scenes.
      - eru 5d ago
        Huh? I've been able to buy reasonably priced glasses for all my life. (However, I've never lived in the US nor China.)
        rvba 5d ago
        What is reasonably priced? Lenses are lenses so one vould debate the real cost, but the frames are incredibly overpriced for a piece of metal or plastic with two joints and those components that land on your nose. Frames could literally cost 1 dollar (only happened after china entered this market), but good luck finding ones like this with good lenses. You need to buy from one supplier who intentionally offers cheapest frames for 50+ dollars and those frames look like crap. The ones that look better (even if same plastic) cost 500+ dollars - and all due to price gouging. For lenses I am not sure, but suspect something similar.
        eru 5d ago
        I grew up in Germany, but I got frames in UK and Singapore and Australia, too. Fielmann in Germany has been offering very reasonably priced glasses and frames for ages.
      - ndriscoll 5d ago
        e.g. Zenni has sold $7 glasses for like 20+ years. They appeared shortly after Luxotica started buying retailers. If there's a problem, it's that advertising reduces consumer information (basically economic jamming) and distorts markets.
  - eru 5d ago
    There's lots of competition in AI. Where do you see the 'insurmountable advantage in everything'?
    - dns_snek 5d ago
      They said "We're looking at a future". And if that future ends up developing the way these companies want it to then we're looking at extremely dystopian future where AI is essential to all work and people have to buy their "intelligence" from an oligopoly of large providers who have total control over the price and capabilities whilst simultaneously having unfiltered read/write access to people's stream-of-consciousness - their work life, their personal problems, their political opinions. This level of access and power is unprecedented in our society.
      - Marha01 5d ago
        Open AI models are just a few months behind closed models, and the gap is actually getting more narrow.
        eru 5d ago
        Yes. And for most applications it's more important that the open models get better in absolute terms and perhaps that they are competitive on a per-Watt basis.
        dns_snek 5d ago
        Two concerns: - I think competitive open models are just an artifact of the AI race we're witnessing right now. What's the incentive for a company to spend billions researching, developing, and training a model, only to release it for free? Leading to the next point. - Even if open models are good enough to be competitive, how are we going to run them? Doing so locally is next to impossible and I don't see that changing. The capabilities of models that you can run locally will always get better, of course, but the level of quality that is considered essential for work will always stay pinned at "near-frontier". Datacenters will always have better optimization and economies of scale, the industry will consolidate over time and eventually we'll end up with a handful of companies that operate the hardware serving 95% of all inference needs. I'm not convinced that we can reach the fantasy world that they're trying to sell without killing the entire planet, but if we somehow do I don't see how we can avoid the world turning into a dystopian hellscape. We would need extremely radical interventions to avoid that scenario, such that these models and the hardware to run them would be owned and governed democratically, i.e. the end of capitalism.
- eru 5d ago
  The trailing edge of AI is catching up fast. There's plenty of open source (and even more open weight) AI models and they are getting better and better. If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?
  - robotpepi 5d ago
    The problem with your opinions is that you tend to state certain very quesitonable ideas with 100% confidence. Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. We don't even know how much of creative work they are able to do. We cannot make decisions that could destroy decades of progress just because of hype.
    - Dylan16807 5d ago
      We don't know how good models will get, but the pattern of open weight models keeping up on a relatively short delay has been holding pretty well. And even among the proprietary models there's healthy competition. The concentration of resources is pretty well counteracted by these factors.
    - eru 5d ago
      > Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. For the latter: I assume that having a whole data centre will always be an advantage. I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink. And, yes, the Rieman hypothesis hasn't been proven yet. So to take your fears into account, replace my example with something they've already done, like constructing a solution to the Navier-Stokes-problem.
      - robotpepi 5d ago
        > I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink. Yes, but to what point the hardware will shrink? There are several orders of magnitude of difference in what in your mind AI will become and what more conservative people believe. You take your view as granted...
- azan_ 5d ago
  Note that there are no trillionaires anymore - spacex stock went down and musk „lost” a lot of money so rejoice, poor must be much better off now that we do not have any trillionaire.
robotpepi 5d ago
It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they don't think on the externalities.
- flatline 5d ago
  Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be. Tech companies are as much the topic of this post as AI, I think that's the immediacy.
  - jeremyjh 5d ago
    To a significant extent, the pursuit of mathematics research is a pursuit of human understanding of mathematics, without knowing where it might lead, or whether it might lead anywhere at all. I don't see how the motivation for that goes away on its own, but the institution supporting it is certainly threatened by the potential loss of grant money and graduate student applications.
  - eru 5d ago
    > Does mathematics still have a practical impact without humans in the loop? There's a single answer to that question: yes, math very much has an impact without humans in the loop. Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
    - robotpepi 5d ago
      We can't be sure AI will be able to ask the questions of the future. At least right now, AI is not capable of that.

3ash14 5d ago

Stockfish isn't owned by a club of three trillionaires. It does not cost $15 million to achieve a result in Stockfish. Stockfish does not steal research or scoop researchers. The concentration of computing resources and capital should be examined by the math community.

coderenegade 5d ago
This is the real problem. We're looking at a future where those who control AI have an insurmountable advantage in everything. They can control the amount of intelligence the masses have access to -- for their own safety, of course -- and they will never, ever be able to close the gap.
- tomrod 5d ago
  Say they do. What then? Will people buy from them? What if we decide not to?
  - coderenegade 5d ago
    At a certain point, you don't have a choice. Before China got into the game, the only way to avoid giving Luxotica money if you wanted a pair of glasses was to essentially not buy glasses. This is the same for many industries -- consolidation behind the scenes.
    - eru 5d ago
      Huh? I've been able to buy reasonably priced glasses for all my life. (However, I've never lived in the US nor China.)
      - rvba 5d ago
        What is reasonably priced? Lenses are lenses so one vould debate the real cost, but the frames are incredibly overpriced for a piece of metal or plastic with two joints and those components that land on your nose. Frames could literally cost 1 dollar (only happened after china entered this market), but good luck finding ones like this with good lenses. You need to buy from one supplier who intentionally offers cheapest frames for 50+ dollars and those frames look like crap. The ones that look better (even if same plastic) cost 500+ dollars - and all due to price gouging. For lenses I am not sure, but suspect something similar.
        eru 5d ago
        I grew up in Germany, but I got frames in UK and Singapore and Australia, too. Fielmann in Germany has been offering very reasonably priced glasses and frames for ages.
    - ndriscoll 5d ago
      e.g. Zenni has sold $7 glasses for like 20+ years. They appeared shortly after Luxotica started buying retailers. If there's a problem, it's that advertising reduces consumer information (basically economic jamming) and distorts markets.
- eru 5d ago
  There's lots of competition in AI. Where do you see the 'insurmountable advantage in everything'?
  - dns_snek 5d ago
    They said "We're looking at a future". And if that future ends up developing the way these companies want it to then we're looking at extremely dystopian future where AI is essential to all work and people have to buy their "intelligence" from an oligopoly of large providers who have total control over the price and capabilities whilst simultaneously having unfiltered read/write access to people's stream-of-consciousness - their work life, their personal problems, their political opinions. This level of access and power is unprecedented in our society.
    - Marha01 5d ago
      Open AI models are just a few months behind closed models, and the gap is actually getting more narrow.
      - eru 5d ago
        Yes. And for most applications it's more important that the open models get better in absolute terms and perhaps that they are competitive on a per-Watt basis.
      - dns_snek 5d ago
        Two concerns: - I think competitive open models are just an artifact of the AI race we're witnessing right now. What's the incentive for a company to spend billions researching, developing, and training a model, only to release it for free? Leading to the next point. - Even if open models are good enough to be competitive, how are we going to run them? Doing so locally is next to impossible and I don't see that changing. The capabilities of models that you can run locally will always get better, of course, but the level of quality that is considered essential for work will always stay pinned at "near-frontier". Datacenters will always have better optimization and economies of scale, the industry will consolidate over time and eventually we'll end up with a handful of companies that operate the hardware serving 95% of all inference needs. I'm not convinced that we can reach the fantasy world that they're trying to sell without killing the entire planet, but if we somehow do I don't see how we can avoid the world turning into a dystopian hellscape. We would need extremely radical interventions to avoid that scenario, such that these models and the hardware to run them would be owned and governed democratically, i.e. the end of capitalism.
eru 5d ago
The trailing edge of AI is catching up fast. There's plenty of open source (and even more open weight) AI models and they are getting better and better. If that's your only objection: in a few years you can prove Rieman's hypothesis on your smartphone, no need for any trillionaires to give you permission. Does that make any change to your argument, or did it not actually matter?
- robotpepi 5d ago
  The problem with your opinions is that you tend to state certain very quesitonable ideas with 100% confidence. Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. We don't even know how much of creative work they are able to do. We cannot make decisions that could destroy decades of progress just because of hype.
  - Dylan16807 5d ago
    We don't know how good models will get, but the pattern of open weight models keeping up on a relatively short delay has been holding pretty well. And even among the proprietary models there's healthy competition. The concentration of resources is pretty well counteracted by these factors.
  - eru 5d ago
    > Right now, we don't know if AI will be able to solve bigger problems, or if they'll be so efficients that you no longer need a whole datacenter for running them. For the latter: I assume that having a whole data centre will always be an advantage. I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink. And, yes, the Rieman hypothesis hasn't been proven yet. So to take your fears into account, replace my example with something they've already done, like constructing a solution to the Navier-Stokes-problem.
    - robotpepi 5d ago
      > I am saying that for a fixed target, like proving the Rieman hypothesis from scratch, the required hardware will shrink. Yes, but to what point the hardware will shrink? There are several orders of magnitude of difference in what in your mind AI will become and what more conservative people believe. You take your view as granted...
azan_ 5d ago
Note that there are no trillionaires anymore - spacex stock went down and musk „lost” a lot of money so rejoice, poor must be much better off now that we do not have any trillionaire.

robotpepi 5d ago

It makes no sense to compare mathematics with chess. Chess is a sport. No one is interested in watching two machines compete. Chess doesn't have a practical impact. Etc. What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. It could be the case in the future, but no one knows right now, and more importantly: tech companies don't even think about it! they don't think on the externalities.

flatline 5d ago
Does mathematics still have a practical impact without humans in the loop? I don't think there's one single answer to that question, but I think it's worth considering exactly what that impact may be. Tech companies are as much the topic of this post as AI, I think that's the immediacy.
- jeremyjh 5d ago
  To a significant extent, the pursuit of mathematics research is a pursuit of human understanding of mathematics, without knowing where it might lead, or whether it might lead anywhere at all. I don't see how the motivation for that goes away on its own, but the institution supporting it is certainly threatened by the potential loss of grant money and graduate student applications.
- eru 5d ago
  > Does mathematics still have a practical impact without humans in the loop? There's a single answer to that question: yes, math very much has an impact without humans in the loop. Math has a lot of applications, and those applications don't care whether eg the new faster matrix multiplication algorithm was found and proven correct by a machine or a meatbag.
  - robotpepi 5d ago
    We can't be sure AI will be able to ask the questions of the future. At least right now, AI is not capable of that.