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> Most of modern pure mathematics doesn't look like it has any chance of being that.

The stuff powering current tech (incl LLMs), the very foundational math, could have been described in exactly that way when it was new. Number theory, basis of most cryptography, was "pure math" not too long ago. It's only useful in hindsight.

by renyicircle13 hours ago|

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Yes, there's so many applications that we couldn't even imagine until we got modern computers, and most of us couldn't imagine them either until we got them. What didn't sit right with me is that these concepts are a very small subset of mathematics, and look like "basic" stuff, while the branches got developed much further than what the applications could catch up with. You don't need Fermat's last theorem for cryptography, for example. I have no idea if we'll ever need homotopy groups of high-dimensional spheres, etc.

Either way it seems like nobody is in a position to say "this branch of math will surely stay arcane abstract nonsense forever", so the argument for continuing specialized math research comes down to "we might lose out on some cool stuff if we stop", even if most of it will indeed remain useless for a long time.

by teiferer12 hours ago|

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Exactly. Most results will stay "useless" in the sense of not having a direct application. But the process of having figured out those results is a necessary step on the way of figuring out those few things that eventually do have a direct application. And you don't know which is which beforehand.

(Besides, it's not more useless than playing the piano. But that's a whole other type of conversation. Though it shares resemblance if you think about it long enough.)

by viccis13 hours ago|

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There's been some knot theory applied to molecule analysis chemistry as well as things like topological quantum field theory, with both of those being examples of fields that benefit greatly from previously unapplied mathematics introducing tools to use.

by renyicircle13 hours ago|

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Thanks, that sounds interesting. As I said in a parallel comment after some thought on this, nobody can really say with absolute certainty that a particular branch will forever stay useless, so that should be good enough to keep going.

Sometimes one can be convinced that their mathematics will be useful, too. I've just recalled a rather motivating (though his life story is rather sad) quote by Grassmann, the inventor of modern linear algebra, whose mathematical work was not appreciated during his lifetime.

"I remain completely confident that the labour I have expended on the science presented here and which has demanded a significant part of my life as well as the most strenuous application of my powers, will not be lost. It is true that I am aware that the form which I have given the science is imperfect and must be imperfect. But I know and feel obliged to state (though I run the risk of seeming arrogant) that even if this work should again remain unused for another seventeen years or even longer, without entering into the actual development of science, still that time will come when it will be brought forth from the dust of oblivion and when ideas now dormant will bring forth fruit. I know that if I also fail to gather around me (as I have until now desired in vain) a circle of scholars, whom I could fructify with these ideas, and whom I could stimulate to develop and enrich them further, yet there will come a time when these ideas, perhaps in a new form, will arise anew and will enter into a living communication with contemporary developments. For truth is eternal and divine."