There are many cases where pure mathematics became useful later.

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

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

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

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.

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.

"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"

No, "so what" doesn't indicate disagreement, just that something isn't relevant.

Anyway, assume hot dogs taste not good at all, except in rare circumstances. It would then be wrong to say "hot dogs taste good", but it would be right to say "hot dogs don't taste good". Now substitute pure math for hot dogs. Pure math can be generally useless even if it isn't always useless. Men are taller than women. That's the difference between applied and pure math. The difference between math and science is something else: Even useless science has value, while most useless math (which consists of pure math) doesn't. (I would say the axiomatization of new theories, like probability theory, can also have inherent value, independent of any uselessness, insofar as it is conceptual progress, but that's different from proving pure math conjectures.)

It really speaks to the weakness of your original claim that you're applying this level of sophistry to your backpedaling.

There are 1135 Erdős problems. The solution to how many of them do you expect to be practically useless? 99%? More? 100%? Calling something useful merely because it might be in rare exceptions is the real sophistry.

So when you said "so what, hamburgers (science) taste good (is useful)", you were implicitly making a point about how bad (mostly not useful) the hot dogs (math research) was? And that's the thing that supposedly wasn't being followed on the first pass?

That brings us full circle, because you're now saying you were using one to negate the other, yet you were claiming that interpretation was a "failure to follow" what you were saying the first time around.