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.
> However, math problems are really there to solve a real world problem.
this is ABSOLUTELY not how actual mathematicians see their field. A problem in mathematics is just that: its interest to a pure mathematician is not related to any applications in other disciplines.
I don't really understand what makes a mathematical problem "interesting" because of my bias as an engineer. Nothing is interesting to me unless I can use it to solve a "real world problem". But, I'm willing to concede that "solving real world problems" is really not how mathematics advances.
Things like complex numbers or quaternions were often thought about way outside of the context of their modern applications in physics and engineering. When Hamilton thought about quaternions I really doubt he cared that it would make some programmer's life easier 200 years later:
> Every morning in the early part of October 1843, on my coming down to breakfast,
> your brother William Edwin and yourself used to ask me:
> "Well, Papa, can you multiply triples?"
> Whereto I was always obliged to reply, with a sad shake of the head,
> "No, I can only add and subtract them." [1]
If we go back further, Pythagoreans weren't trying to solve "real problems" either, they were like a weird religious cult.
My point is, the practice of "real" mathematics is really something that odd people feel driven to do, not unlike painting or playing an instrument. All the applied stuff is just a byproduct (not unlike ad billboards or elevator music).
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.
nicebyte · · focus · HN ↗
this is ABSOLUTELY not how actual mathematicians see their field. A problem in mathematics is just that: its interest to a pure mathematician is not related to any applications in other disciplines.
I don't really understand what makes a mathematical problem "interesting" because of my bias as an engineer. Nothing is interesting to me unless I can use it to solve a "real world problem". But, I'm willing to concede that "solving real world problems" is really not how mathematics advances.
Things like complex numbers or quaternions were often thought about way outside of the context of their modern applications in physics and engineering. When Hamilton thought about quaternions I really doubt he cared that it would make some programmer's life easier 200 years later:
> Every morning in the early part of October 1843, on my coming down to breakfast,
> your brother William Edwin and yourself used to ask me:
> "Well, Papa, can you multiply triples?"
> Whereto I was always obliged to reply, with a sad shake of the head,
> "No, I can only add and subtract them." [1]
If we go back further, Pythagoreans weren't trying to solve "real problems" either, they were like a weird religious cult.
My point is, the practice of "real" mathematics is really something that odd people feel driven to do, not unlike painting or playing an instrument. All the applied stuff is just a byproduct (not unlike ad billboards or elevator music).
[1] <a href="https://en.wikipedia.org/wiki/History_of_quaternions" rel="nofollow">https://en.wikipedia.org/wiki/History_of_quaternions
kurtis_reed · · focus · HN ↗
Yeah and they should start seeing it differently