Hey /sci/, 2nd year math student, I'm really into math and wouldn't mind dedicating a big part of my life to the more "pure" parts of it. Still, I also like to think about the real world applications of mathematical constructs, and this brings me to the topic of this post.

Let me preface this by saying that there are many areas that are arguably far more abstract than mathematical analysis - just think about cathegory theory or foundations of mathematics or stuff like that. Yet, I think these "more abstract" fields have much more in store for the future than what I can imagine math analysis has.

For me, the 19th and early 20th centuries were the "golden age" of "continuous" mathematics. But, for some time already, I think we have entered in a new age, the "age of the discrete". Don't get me wrong: I don't mean that we're gonna throw all of the "continuous" parts of math out of the window, like some extremist people do. What I mean, though, is that, at least for some time, we're gonna be seeing a lot less of the "delta-epsilon" and "supremum" and "measure theory-esque" kind of math, and we're gonna turn towards a more "algebra-like" approach. I know most algebra isn't exactly "discrete", but in some intuitive sense it does seem more like it. I know homology theory, for example, is quite relevant (even in data analyisis, for example) and it talks precisely about continuous transformations. However, it's not the "analytical" approach to continuity - it's the topological one, which, even though in some cases equivalent, is in general much more abstract. Though, what immediate uses do highly specific results in differential operator theory have? Of course, I'm just a second year student, so there's probably a lot of stuff that I just don't know - that's why I'm putting this out there.