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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 imp

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.
    - eru 5d 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 5d 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 5d 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 4d 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 4d 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 5d 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 5d 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 5d ago
      You can have a look at eg improvements in solving linear programming problems or in mixed integer linear programming or SAT solvers.
    - subsistence234 5d 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 5d 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.
phoghed 5d ago
> No one is interested in watching two machines compete I’ve watched quite a lot of YouTube videos where two machines compete, so you may not be completely right here
- sebastiansm7 5d ago
  https://tcec-chess.com/ https://tcec-chess.com/ Top chess engine championship is pretty fun to watch.
- mikepurvis 5d ago
  The Square One commentary on the AlphaZero v Stockfish game from 2017 is pretty entertaining: https://www.youtube.com/watch?v=LnVDUQksIDk https://www.youtube.com/watch?v=LnVDUQksIDk In other videos he's called out the influence that this and similar games have had on human players in recent years, particularly around square denial and thorn pawn strategies.
- rvba 5d ago
  There are chess engine tournaments too, to see who can build the best one
JoshTriplett 5d ago
> What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. There is no bound on the amibitions of AI. AI is set to replace anything done by people, and there won't be any room left for people. There isn't any task done by humans that AI won't be better at. This is not a tenable outcome. We should never have built machines with agency, rather than optimization processes that operate as subroutines of humans.
- esafak 5d ago
  > We should never have built machines with agency... We haven't quite crossed that bridge, but we do appear to be standing on it.
- eru 5d ago
  You say it like it's a bad thing.
  - JoshTriplett 5d ago
    Replacing people leaves no room for people.
    - eru 5d ago
      Even aggregate employment of translators has held up well in the US. Even though machines do a much better job of what used to be the most basic job of a translator.
    - user43928 5d ago
      Out of 3.5 billion employed people globally, only 10% are professionals. Do you really think making labor obsolete and giving humans back their time is such a bad thing?
      - JoshTriplett 5d ago
        When cars made horses obsolete, it didn't go so well for horses. In the short term, AI is disempowering the vast majority of people in favor of a very small subset. In the also way too short term, AI is disempowering all people.
eru 5d ago
Well, what you are saying that the situation is even better for math than for chess? Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess. But with math, everyone in the world would gain from computers becoming really, really good at it.
- thayne 5d ago
  But solving math problems is not the same as increasing understanding of math concepts.
  - eru 5d ago
    Applications don't care whether the math was proven and understood by humans or computers. Your algorithm will get faster no matter where the insight came from.
    - freehorse 5d ago
      Applications do not care about 99.999% of theoretical math production anyway. And especially most of the big results in theoretical math nowadays are really inconsequential in applications.
      - eru 5d ago
        Applications don't care about Navier Stokes, yes. But they care about eg proving crytographics secure, or proving that your algorithm doesn't blow up under adversarial input.
        freehorse 5d ago
        Formal verification, cryptography and the like is far from what the vast majority of theoretical mathematicians are doing (if those who do them even see themselves as that vs computer scientists or applied mathematicians) especially when it has to do with specific, production systems, and there are not many other examples like this in general outside compsci and statistics. Moreover, I can imagine that these fields will actually flourish more now that AI can make verification and proofs more viable in scale. But even much theoretical work related to cryptography etc is often not very applicable in itself.

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.
  - eru 5d 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 5d 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 5d 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 4d 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 4d 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 5d 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 5d 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 5d ago
    You can have a look at eg improvements in solving linear programming problems or in mixed integer linear programming or SAT solvers.
  - subsistence234 5d 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 5d 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.

phoghed 5d ago

> No one is interested in watching two machines compete I’ve watched quite a lot of YouTube videos where two machines compete, so you may not be completely right here

sebastiansm7 5d ago
https://tcec-chess.com/ https://tcec-chess.com/ Top chess engine championship is pretty fun to watch.
mikepurvis 5d ago
The Square One commentary on the AlphaZero v Stockfish game from 2017 is pretty entertaining: https://www.youtube.com/watch?v=LnVDUQksIDk https://www.youtube.com/watch?v=LnVDUQksIDk In other videos he's called out the influence that this and similar games have had on human players in recent years, particularly around square denial and thorn pawn strategies.
rvba 5d ago
There are chess engine tournaments too, to see who can build the best one

JoshTriplett 5d ago

> What you seem to suggest is that AI will be able to completely (or at least in a great part) replace mathematicians. There is no bound on the amibitions of AI. AI is set to replace anything done by people, and there won't be any room left for people. There isn't any task done by humans that AI won't be better at. This is not a tenable outcome. We should never have built machines with agency, rather than optimization processes that operate as subroutines of humans.

esafak 5d ago
> We should never have built machines with agency... We haven't quite crossed that bridge, but we do appear to be standing on it.
eru 5d ago
You say it like it's a bad thing.
- JoshTriplett 5d ago
  Replacing people leaves no room for people.
  - eru 5d ago
    Even aggregate employment of translators has held up well in the US. Even though machines do a much better job of what used to be the most basic job of a translator.
  - user43928 5d ago
    Out of 3.5 billion employed people globally, only 10% are professionals. Do you really think making labor obsolete and giving humans back their time is such a bad thing?
    - JoshTriplett 5d ago
      When cars made horses obsolete, it didn't go so well for horses. In the short term, AI is disempowering the vast majority of people in favor of a very small subset. In the also way too short term, AI is disempowering all people.

eru 5d ago

Well, what you are saying that the situation is even better for math than for chess? Chess is only valuable as an entertainment. So no one really gains anything from computers becoming really good at chess. But with math, everyone in the world would gain from computers becoming really, really good at it.

thayne 5d ago
But solving math problems is not the same as increasing understanding of math concepts.
- eru 5d ago
  Applications don't care whether the math was proven and understood by humans or computers. Your algorithm will get faster no matter where the insight came from.
  - freehorse 5d ago
    Applications do not care about 99.999% of theoretical math production anyway. And especially most of the big results in theoretical math nowadays are really inconsequential in applications.
    - eru 5d ago
      Applications don't care about Navier Stokes, yes. But they care about eg proving crytographics secure, or proving that your algorithm doesn't blow up under adversarial input.
      - freehorse 5d ago
        Formal verification, cryptography and the like is far from what the vast majority of theoretical mathematicians are doing (if those who do them even see themselves as that vs computer scientists or applied mathematicians) especially when it has to do with specific, production systems, and there are not many other examples like this in general outside compsci and statistics. Moreover, I can imagine that these fields will actually flourish more now that AI can make verification and proofs more viable in scale. But even much theoretical work related to cryptography etc is often not very applicable in itself.