Mathematics
It is rather ironic that a subject so devoted to precision and the avoidance of circular reasoning should find itself in such a predicament, but pretty much the only universally-accepted definition of mathematics and mathematicians is the following:
“Mathematics is that which mathematicians study.”
So, for what it's worth, I am a mathematician.
Partly as a result of my mathematical upbringing (at the University of Warwick), I reject the common distinction between “pure” and “applied” mathematics. However, I will describe myself as an analyst, and not an algebraist (although I've always liked the neatness of algebra), nor a geometer (although there's something irresistibly classical about geometry), nor a combinatoricist, nor a number theorist. I'm not sure what “applied mathematics” is, but I definitely like mathematics that has (potential) applications.
Most of my recent work has been strongly probabilistic in nature. I have also developed some interests in theoretical computer science, particularly the implications of massive parallelism for optimization problems. For more information on my past and present research projects, see the research page.