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I thought one of the implicit points of the open letter was that unsolved problems are not something that falls out of the sky, they are a curated resource that

I thought one of the implicit points of the open letter was that unsolved problems are not something that falls out of the sky, they are a curated resource that people have spent time on and shared for the benefit of like-minded peers and humanity as a whole. And the AI companies treat them like they treat absolutely everything else: natural resources, literature, art, code etc. as something to be chucked into the ravening maw and pooped out the back as profit. They don't care if mathematics advances, they don't care if they strip-mine the available problems and damage the field. In fact, as with programming I think they see that as in their long-term interest - soon there will be no intelligence or creativity but the one that Sam Altman bills you for.

junofan 15d ago
Yes, and here towards the bottom the author gets to the reason he didn’t sign with the other medalists: > I felt that there was nothing to be gained from criticizing AI companies for generating too many solutions too quickly. > Under the circumstances, I think the best we can do is recognise the changes that are coming and try to work out the least unsatisfactory way of dealing with them. Basically let’s make it a short-term problem and deal with it. Groups of people can deal with short term emergencies. Don’t turn it into a structural issue. And in my view what’s the alternative in the letter exactly? The tools exist. Is there going to be drama every time somebody decides to use them?
- GPerson 15d ago
  The tools exist, so let’s try to figure out as humans the best way to use them to promote humanity, and let’s advocate against ways of using them which are a detriment to humanity, which is exactly the charge the letter makes. There are cultural norms around the use of every technology.
  - pfdietz 15d ago
    Let's figure out how to use the iron fist of the state to keep people from doing things the math establishment doesn't like? Yeah, that's really great for humanity. Just super.
    - GPerson 14d ago
      An obvious misrepresentation of the letter and my comment. For what purpose, I don’t know.
      - pfdietz 14d ago
        I'd like to hear how your comment isn't irrelevant noise, then. How does one implement these grand ideas except by state action? Otherwise, people will do what people will do, including proving theorems by machine.
        deleted 14d ago
        [deleted]
        GPerson 13d ago
        Your comments are irrelevant noise because you’re just making up a bunch of nonsense out of nowhere. Are you a vegetable?
- fruitl00p 15d ago
  Well I think in response to 'what are you going to do', what people are probably going to do is stop sharing on-going work, stop bothering to curate problems that are just going to inflate someone's IPO valuation, basically accelerating the tragedy of the commons that the AI companies are driving.
  - NonHyloMorph 15d ago
    Seems legit. I speculate their are emergent mechanisms for the development of memory that are not dependent on what ever mechanism is behind the "improve $model for 'everyone'"* Is someone knowlegeable on research that engages the question on the development of something that could be considered as some emergent mechanism of memory, that is independent of instances and their contextwindow an specifically also independent of the use of conversations for trainingsdata? *(This is regarding the value of selfhosted models - maybe small selforganisations that share ressources to do though to do so? Generally the value of machine learning seems to be to big to reject)
aurareturn 15d ago
I don't understand this logic. Ok, so unresolved math problems are often something people discover while trying to solve a different math problem. However, math problems are really there to solve a real world problem. We have unlimited real world problems no matter how smart AI gets. Therefore, we will always have unresolved math problems.
- tempfile 15d ago
  > math problems are really there to solve a real world problem I think this is totally wrong. Math problems are almost by definition problems with a particular theory. That theory might be inspired by the real world, but the problem itself is purely theoretical. I can't think of any theoretical problems like this that actually support a practical problem, as opposed to being an internal knot in the theory that indicates something is wrong with it. Not to say that cannot happen - certain optimization problems were historically actually hard to solve and solving them helped us to genuinely optimize a real thing (rather than just explain why the answer we already had was correct, which is much more common). In particular, none of the millennium problems have anything to do with a "real" problem, including the Navier Stokes one.
  - GPerson 15d ago
    Agreed, though for the hn audience I want to advocate a bit for the utility of mathematics. The development of applicable mathematics has often not been through the direct means of solving an open problem. It has however often depended on theory which was developed for the purpose of human understanding. It is difficult to pull concepts out of the aether on demand, but when there is a general milieu of human understanding economic applications can be developed in post. I have in mind GPS, cryptography, numerical fluid simulation, lasers, etc…
    - aurareturn 15d ago
      Question: Did the theoretical math lead to the invention of GPS, cryptography, lasers, etc? Or did we encounter a real physical problem, then we found that someone had done some theoretical math before that would be useful for this application? If we run into a real physical problem today, can we just have AI invent the math on the spot to solve the problem without a human having done the theoretical math in the past?

junofan 15d ago

Yes, and here towards the bottom the author gets to the reason he didn’t sign with the other medalists: > I felt that there was nothing to be gained from criticizing AI companies for generating too many solutions too quickly. > Under the circumstances, I think the best we can do is recognise the changes that are coming and try to work out the least unsatisfactory way of dealing with them. Basically let’s make it a short-term problem and deal with it. Groups of people can deal with short term emergencies. Don’t turn it into a structural issue. And in my view what’s the alternative in the letter exactly? The tools exist. Is there going to be drama every time somebody decides to use them?

GPerson 15d ago
The tools exist, so let’s try to figure out as humans the best way to use them to promote humanity, and let’s advocate against ways of using them which are a detriment to humanity, which is exactly the charge the letter makes. There are cultural norms around the use of every technology.
- pfdietz 15d ago
  Let's figure out how to use the iron fist of the state to keep people from doing things the math establishment doesn't like? Yeah, that's really great for humanity. Just super.
  - GPerson 14d ago
    An obvious misrepresentation of the letter and my comment. For what purpose, I don’t know.
    - pfdietz 14d ago
      I'd like to hear how your comment isn't irrelevant noise, then. How does one implement these grand ideas except by state action? Otherwise, people will do what people will do, including proving theorems by machine.
      - deleted 14d ago
        [deleted]
      - GPerson 13d ago
        Your comments are irrelevant noise because you’re just making up a bunch of nonsense out of nowhere. Are you a vegetable?
fruitl00p 15d ago
Well I think in response to 'what are you going to do', what people are probably going to do is stop sharing on-going work, stop bothering to curate problems that are just going to inflate someone's IPO valuation, basically accelerating the tragedy of the commons that the AI companies are driving.
- NonHyloMorph 15d ago
  Seems legit. I speculate their are emergent mechanisms for the development of memory that are not dependent on what ever mechanism is behind the "improve $model for 'everyone'"* Is someone knowlegeable on research that engages the question on the development of something that could be considered as some emergent mechanism of memory, that is independent of instances and their contextwindow an specifically also independent of the use of conversations for trainingsdata? *(This is regarding the value of selfhosted models - maybe small selforganisations that share ressources to do though to do so? Generally the value of machine learning seems to be to big to reject)

aurareturn 15d ago

I don't understand this logic. Ok, so unresolved math problems are often something people discover while trying to solve a different math problem. However, math problems are really there to solve a real world problem. We have unlimited real world problems no matter how smart AI gets. Therefore, we will always have unresolved math problems.

tempfile 15d ago
> math problems are really there to solve a real world problem I think this is totally wrong. Math problems are almost by definition problems with a particular theory. That theory might be inspired by the real world, but the problem itself is purely theoretical. I can't think of any theoretical problems like this that actually support a practical problem, as opposed to being an internal knot in the theory that indicates something is wrong with it. Not to say that cannot happen - certain optimization problems were historically actually hard to solve and solving them helped us to genuinely optimize a real thing (rather than just explain why the answer we already had was correct, which is much more common). In particular, none of the millennium problems have anything to do with a "real" problem, including the Navier Stokes one.
- GPerson 15d ago
  Agreed, though for the hn audience I want to advocate a bit for the utility of mathematics. The development of applicable mathematics has often not been through the direct means of solving an open problem. It has however often depended on theory which was developed for the purpose of human understanding. It is difficult to pull concepts out of the aether on demand, but when there is a general milieu of human understanding economic applications can be developed in post. I have in mind GPS, cryptography, numerical fluid simulation, lasers, etc…
  - aurareturn 15d ago
    Question: Did the theoretical math lead to the invention of GPS, cryptography, lasers, etc? Or did we encounter a real physical problem, then we found that someone had done some theoretical math before that would be useful for this application? If we run into a real physical problem today, can we just have AI invent the math on the spot to solve the problem without a human having done the theoretical math in the past?