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.
If we are talking about pure/theoretical mathematics, then the vast majority of the problems people pose and solve have at best tangential relationship with applications, and a big part even is only related to other math problems. Of course quite a bit of mathematics historically emerged as this kind of intellectual endeavour to find applications later, but there is neither a way to predict which ones are that and how to get them, nor is there indication of this thing going on to the same proportion nowadays as it was, considering the mathematical production is much higher. In mathematics human mathematicians have to decide which problems matter, it does not come from somewhere.
Solving "real" problems in theoretical mathematics (as in problems directly related to applications) is a very small proportion compared to the vast majority of math work that does not. So if we are discussing about the future of mathematics as a field, we have to understand what the field of theoretical mathematics is actually about.
"The FT’s Gillian Tett reported that a senior financier’s New York firm now seeks out humanities students, because “AI-native” Stem graduates are entering the job market with “alarmingly shallow ideas”."*
I don't advocate for the dichotomy of stem and humanities. A good counterecample from the 20th century being Ernst Mach (Mach-speeds are named after him) and his work in phenomenology ("bodies do not produce sensations, sensations produce bodies")
Your incatation of contextless 'technological progress' still kinda calls for a quote like the above
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.
freehorse · · focus · HN ↗
Solving "real" problems in theoretical mathematics (as in problems directly related to applications) is a very small proportion compared to the vast majority of math work that does not. So if we are discussing about the future of mathematics as a field, we have to understand what the field of theoretical mathematics is actually about.
aurareturn · · focus · HN ↗
Would this slow technological progress? Or make it go faster?
That math problems are found and solved as we run into real physical problems.
NonHyloMorph · · focus · HN ↗
I don't advocate for the dichotomy of stem and humanities. A good counterecample from the 20th century being Ernst Mach (Mach-speeds are named after him) and his work in phenomenology ("bodies do not produce sensations, sensations produce bodies")
Your incatation of contextless 'technological progress' still kinda calls for a quote like the above
*<a href="https://www.theguardian.com/books/ng-interactive/2026/aug/08/i-hate-what-ai-is-doing-to-the-minds-and-happiness-of-the-young-katherine-rundell-on-the-view-from-the-classroom" rel="nofollow">https://www.theguardian.com/books/ng-interactive/2026/aug/08...