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.
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.
> 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.
>Humans only invest in solving problems that matter one way or another.
Fermat's Last Theorem was one of the most famous open problems in math for centuries, and it has no direct applicability to any tangible problems here in the physical world.
Oh some few. No right triangle with rational sides has area equal to a perfect square depends on N=4 for instance.
And it can be used to form other theorems that are terribly actionable. Every elliptical curve over Q is modular, which has consequences throughout number theory.
But yes, none of those are very tangible, until applied to problem solutions that are tangible.
fruitl00p · · focus · HN ↗
aurareturn · · focus · HN ↗
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 · · focus · HN ↗
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.
aurareturn · · focus · HN ↗
I also disagree that none of them solve "real" problems. They clearly do. Solving them have implications on real world problems.
jplusequalt · · focus · HN ↗
Fermat's Last Theorem was one of the most famous open problems in math for centuries, and it has no direct applicability to any tangible problems here in the physical world.
JoeAltmaier · · focus · HN ↗
But yes, none of those are very tangible, until applied to problem solutions that are tangible.