[jstanley]

Applications for pure mathematics can't necessarily be known until the underlying mathematics is solved.

Just because we can't imagine applications today doesn't mean there won't be applications in the future which depend on discoveries that are made today.

[cubefox]

Well, read the linked comment. The possible future applications of useless science can't be known either. I still argue that it has intrinsic value apart from that, unlike pure mathematics.

[Thorrez]

There are many cases where pure mathematics became useful later.

https://www.reddit.com/r/math/comments/dfw3by/is_there_any_e...

[cubefox]

So what? There are probably also many cases where seemingly useless science became useful later.

[glenstein]

Exactly, you're almost getting it. Hence the value of "pure" research in both science and math.

[cubefox]

You are not yet getting it I'm afraid. The point of the linked post was that, even assuming an equal degree of expected uselessness, scientific explanations have intrinsic epistemic value, while proving pure math theorems hasn't.

[glenstein]

I think you lost track of what I was replying to. Thorrez noted that "There are many cases where pure mathematics became useful later." You replied by saying "So what? There are probably also many cases where seemingly useless science became useful later." You seemed to be treating the latter as if it negated the former which doesn't follow. The utility of pure math research isn't negated by noting there's also value in pure science research, any more than "hot dogs are tasty" is negated by replying "so what? hamburgers are also tasty". That's the point you made, and that's what I was responding to, and I'm not confused on this point despite your insistence to the contrary.

Instead of addressing any of that you're insisting I'm misunderstanding and pointing me back to a linked comment of yours drawing a distinction between epistemic value of science research vs math research. Epistemic value counts for many things, but one thing it can't do is negate the significance of pure math turning into applied research on account of pure science doing the same.