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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 cons

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 21d 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 21d 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 21d 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.
  - eru 21d ago
    Why do you need AI to ask the questions? You give your AI the problem, like 'make this computer program faster and more reliable', and it'll go off and do the math necessary to make it so.
    - robotpepi 21d ago
      so you're 100% sure that AI will solve every intellectual problem in the future, since as long as that's not the case, it's us who need to ask the questions. I don't know man, I wouldn't bet on that. What if we end up being wrong and then there is not research community?
      - eru 21d ago
        Huh? Where do I say that AI needs to solve every intellectual problem? For all we know, P vs NP will never be resolved neither by human nor AI, and the world will just keep turning.
        robotpepi 21d ago
        I don't understand what you're proposing then. We can ask AI to solve practical problems of interest (making a computer faster for instance), but I'd say no one really believes that this is an unlimited resource. At some point we'll reach a plateau, and then AI will be an important tool but to continue advancing we'll need someone to ask the right questions.
        eru 20d ago
        What is 'asking the right questions' supposed to mean? I am saying that applications supplied and supply an inexhaustible amount of good problems and questions to consider. Purely theoretical concerns also supply some questions, but even if that well dries up for some reason, applications persist.
    - fn-mote 21d ago
      > Why do you need AI to ask the questions? As the US has offshored manufacturing, the number of patents issued for those processes has fallen. Innovation occurs where the foundational understanding is applied; they arise from a desire to do the required work more efficiently. Similarly in math, attempting to solve a problem leads to new questions. IF you actually do the work. You need to have done enough of the work to know what the correct next question are, or you need to rely on AI for everything.
- Dylan16807 21d ago
  We're way into diminishing returns in matrix multiplication, and being clever about ALUs and cache layout is likely to dwarf any asymptotic improvements you're going to find. Any better examples of improvements in the last decade? The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.
  - eru 21d ago
    You can have a look at eg improvements in solving linear programming problems or in mixed integer linear programming or SAT solvers.
  - subsistence234 21d ago
    >hmm let's see... important applications of math... i guess there's matrix multiplication and fourier transform. anything else? probably not. t. low information voter.
    - Dylan16807 21d ago
      Wow that's a terrible paraphrase! I asked about algorithms where recent/ongoing improvements were important and they already replied with a list. If you tell someone they can't use a matrix multiplication with better asymptotic performance than n^2.3755 from 1990 they're going to shrug and not care.

jeremyjh 21d 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 21d 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 21d 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.
- eru 21d ago
  Why do you need AI to ask the questions? You give your AI the problem, like 'make this computer program faster and more reliable', and it'll go off and do the math necessary to make it so.
  - robotpepi 21d ago
    so you're 100% sure that AI will solve every intellectual problem in the future, since as long as that's not the case, it's us who need to ask the questions. I don't know man, I wouldn't bet on that. What if we end up being wrong and then there is not research community?
    - eru 21d ago
      Huh? Where do I say that AI needs to solve every intellectual problem? For all we know, P vs NP will never be resolved neither by human nor AI, and the world will just keep turning.
      - robotpepi 21d ago
        I don't understand what you're proposing then. We can ask AI to solve practical problems of interest (making a computer faster for instance), but I'd say no one really believes that this is an unlimited resource. At some point we'll reach a plateau, and then AI will be an important tool but to continue advancing we'll need someone to ask the right questions.
        eru 20d ago
        What is 'asking the right questions' supposed to mean? I am saying that applications supplied and supply an inexhaustible amount of good problems and questions to consider. Purely theoretical concerns also supply some questions, but even if that well dries up for some reason, applications persist.
  - fn-mote 21d ago
    > Why do you need AI to ask the questions? As the US has offshored manufacturing, the number of patents issued for those processes has fallen. Innovation occurs where the foundational understanding is applied; they arise from a desire to do the required work more efficiently. Similarly in math, attempting to solve a problem leads to new questions. IF you actually do the work. You need to have done enough of the work to know what the correct next question are, or you need to rely on AI for everything.
Dylan16807 21d ago
We're way into diminishing returns in matrix multiplication, and being clever about ALUs and cache layout is likely to dwarf any asymptotic improvements you're going to find. Any better examples of improvements in the last decade? The main situation I can think of where better calculations have a really visible effect is video and image compression, and that stuff is very far away from mathematical proof territory.
- eru 21d ago
  You can have a look at eg improvements in solving linear programming problems or in mixed integer linear programming or SAT solvers.
- subsistence234 21d ago
  >hmm let's see... important applications of math... i guess there's matrix multiplication and fourier transform. anything else? probably not. t. low information voter.
  - Dylan16807 21d ago
    Wow that's a terrible paraphrase! I asked about algorithms where recent/ongoing improvements were important and they already replied with a list. If you tell someone they can't use a matrix multiplication with better asymptotic performance than n^2.3755 from 1990 they're going to shrug and not care.