Background: I have studied mathematics at university (mainly algebraic and arithmetic geometry), but for many reasons I am now a PhD student in computer science. However, at the end of the first year all PhD students have to pass an interview, and if they don't they can't continue with the process. During the preparation to this interview, I have understood that I was missing to explain why my research was relevant within the field; more specifically, which impact it can have, which applications can be developed from this. And I was wondering: is this a matter of being somehow different from my collegues? I mean, I am enthusiastic about the project I'm working on because it's an interesting project, and not because I'm sure it'll have many applications (well, now I'm a bit more convinced about its applications too). So the question is: what am I?

More in general, what is a mathematician? Of course, for most of you it's clear that you are. But what about those who work in some "in-between" field?

I guess that also being recognized as mathematicians by a community is a big part of beeing / feeling a mathematician. But for example, the questions generally posted on Mathoverflow are often out-of-my-reach. However, I feel that the methods I use for solving problems in the area I'm studying now use mathematical methods, in a non-trivial way (I mean, I don't just solve an integral to find a number, I'm building a formal theory behind this approach to the problem).

More in general, I imagine that there should be plenty of people, with a mathematical background, who work in applications, like economics for example, who do something similar to what I do: are they mathematicians?