As an undergraduate, I was very pure---I hated applied mathematics. I outgrew that in graduate school, and was trained in classical applied mathematics in the usual way in North America---namely in an engineering department. Though I still enjoy an occasional foray into pure mathematics (which I am often as helpless to resist as a Belgian chocolate or other self-indulgence) I firmly regard myself as an applied mathematician, and I am pleased that most of the work that I have done in the past ten years is solidly applied.
But there is another dichotomy in mathematics, that of analysis versus algebra, and I was never sure which side I inclined to most. I'm still nearly balanced, but as I write this I feel that over the past year I have learned that I incline ever so slightly to the algebra side. I can do analysis (indeed my `heaviest' papers, in J. Math. Anal. and Applications, with S. Yu. Pilyugin, are pure analysis---and obviously mostly Sergei's work---and my Error Backward paper is also heavy on analysis), but I think what I enjoy doing most and am most competent at is algebra.
This fence-sitting has its uses, though, and my most serious critiques of computer algebra (``Well, It Isn't Quite That Simple...'' and ``What is a Solution of an ODE...'') are from the point of view of an analyst. So I will continue to stay close to analysis.