[spekcular]

Yes, I expect practitioners to care about something useful, assuming the result has been properly written up and explained in a way they can understand. Scientists want good results and will adopt new tools if you can make a case that they will help them publish impactful papers.

Again, it's pretty telling specific applications aren't mentioned, and instead there's just vague gesturing. How can we expect scientists to "do the field work" necessary to bring the applications to fruition if we can't even tell them what those applications are?

Also, regarding your first sentence, the vast majority of influential mathematics was indeed "immediately acknowledged," because it made progress on some important problem. Perfectoid spaces are a recent example.

[FabGenovese]

Nice, if everyone thought like you do, number theory wouldn't have existed, elliptic curves along with it, and hence much of public key cryptography as well. Indeed, number theory has been exquisitely useless for a couple of millennia, give or take.

I feel you are one of those people that just hate category theory because they consider it too abstract and useless for any purpose. We get that a lot, from a lot of people. Still, since Grothendieck, categorical methods are absolutely central in modern algebraic geometry and topology, and this centrality is only destined to grow, because CT is the best theory we have to manage emerging complexity in describing systems. In my opinion, the approach of "if it's not immediately useful then it's useless" really will lead you farther and farther away to understand modern developments in applied mathematics.

[spekcular]

This mischaracterizes my position. I'm not against pure mathematics research, but I am against claiming applications exist when they don't.