I am not exclusively interested in mathematics. The following are topics to which I have devoted a not inconsiderable amount of thought*:

• When I'm out of sight of other mathematicians, I often wonder about the logico-philosophical foundations of the field, it's position in the hierarchy of human knowledge, and precisely what kind of activity one is engaging in when one does mathematics. Just between you and I, I am also rather uncomfortable with the Axiom of Choice (and its equivalents), and would probably be an intuitionist if I actually had the courage of my convictions.
• Problems in the historiography of revolutionary Russia and the Third Reich. In the first case, how does one balance the tendency to write a "top-down" account emphasizing the ideology and aims of the revolutionary leadership with the opposite tack: a history grounded in the details of everyday life, of the socio-economic underpinnings of the ambient society? How is official ideology and practice mediated, thwarted, even amplified, by popular opinion and facts on the ground? In the latter case, where does one strike the balance between moral condemnation, the cataloguing of atrocities, and the attribution of guilt, and the relatively dispassionate style of inquiry practiced by historians like Martin Broszat, in which one occasionally finds partial causes for the grotesqueries of the period not merely in the deranged Weltanschauung and general criminality of the Nazis, but also in concrete historical realities and in the very structure of the regime? To what extent is the writing of history a moral enterprise, to what extent a political enterprise, and to what extent a scientific one? See, in particular, the Historikerstreit, and the subsequent exchange between Martin Broszat and Saul Friedländer.
• The early work of the so-called Fifth Generation of Chinese filmmakers, the role of filmic representations of China's ethnic minorities in the Han majority's self-examination, and the intersection of these two areas, most clearly manifested in Tian Zhuangzhuang's film "Horse Thief."
• More generally (and more existentially), the maniacal obsession with the Other, and how and to what extent figurations of the aforementioned reflect back upon the Self. What is ethnography, really, and who could possibly have ever considered it a science?
• I appreciate, and have given some thought to, extreme and avant-gardist tendencies in music, having once been a member of the seminal noise-jazz-thrash-drone band centipede, and also a longtime confidant of noisy nihilist Johannes Silentio. I also enjoy a wide variety of more conventional music, from hardcore to twee to thrash to Nordic folk.
• Bergman, Bergman, Bergman.

* Monstrously self-indulgent, I know. But to be otherwise on this, my website, would be an intolerable violation of the unwritten rules of the internet.