Not really. Riemann just had the idea of generalizing what Gauss did for surfaces to higher dimensions. So, if you look at it as an extension of Gauss's work, it deals with pretty concrete physical things: surfaces. It's one step removed from reality. It's necessary to be a little playful and not always be thinking directly of solving some particular practical problem. That's sort of the nature of math, if you have some experience with it.
Never the less, after getting a PhD in topology, I became a little bit skeptical of the value of a lot of the research that is being done in math. Skeptical doesn't mean I dismiss it as useless, it just means, I'm skeptical about its use, in that I don't take it as a given. Historically, there are good reasons to be concerned about this. A lot of research from the 19th century that people thought was so important back then ended up being pretty much forgotten. Apparently, according to Thurston, even work from the 1980s on foliations has been forgotten. It might not be such a bad idea to say, maybe we should only allow X degrees of separation from reality, or at least that we should put more emphasis on things with less separation from reality. You can easily argue that mathematicians should have some freedom to play around with stuff that isn't directly useful, but once you accept that, it is not at all clear HOW MUCH they should do that. I would contend that they ought to do it less than is the case right now.
It's very frustrating to study pure math sometimes if you have the even the slightest hint of scientific/applied curiosity because you hear these vague hints that so and so is doing research on protein-folding or using topology to determine the chirality of molecules, but it takes a gargantuan effort to actually read about these things and understand them in detail and figure out exactly what role the math is playing and how it important it might be. Learning about such things could could take effort that will make it harder for you to succeed in your absurdly competitive pure math world, unless you change your entire focus to those applications.
Math is so vast and requires so much effort that it seems strange to devote your whole life to things that are so far from reality and only have an extremely hypothetical potential for application. Some mathematicians might just think of it as fun, rather than work, but after writing a big fat dissertation and finding out what it's like to come up with substantial new ideas and try to write it all down, trying to read ridiculously obscure and formal papers, and attending obscure talks, I can't really see it as fun anymore, at least not the way most mathematicians are doing it these days. It was when I was an undergrad and to some extent earlier on in grad school. I can always understand anything, if I put enough effort into, but increasingly, as I went on, I found it wasn't worth the effort. I found the excessive complexity of it all to be sickening. The usual way to deal with this complexity is to take more theorems on faith and not understand them for yourself, but for me, because the only pleasure I get out of math is in understanding, that defeats the whole purpose. I found out that it wasn't that I wasn't smart enough, it was that I was the one who insisted that I had to understand everything and not build on top of stuff I don't understand. There just isn't enough time for that, so no one does that. Also, people tend to be so specialized, so they are going into these very narrow little pigeon holes. They still have to learn the basics of a lot of different fields, but they tend to dig their holes excessively deep and narrow for my tastes. Math is not the same as it was 100 years ago. It was only through 6 or 7 years of painstaking effort that I was finally able to admit that math, in its current state, was not for me.
Actually, Ed Witten even gave a talk to a general audience that's somewhere on youtube where he talks about how there's this feeling of understanding that is what would make someone want to be a mathematician in the first, but a lot of mathematicians are not working in a way that allows that to happen.
It's a very easy trap to fall into because these sorts of issues don't really have their full force until you're almost done with a PhD. I thought it was just unbelievably awful, personally, and I'm far from being alone in that. I still think classical math is great, though.
