I think I have absorbed more abstract mathematics over the course of today than during my entire undergraduate degree. In need of some compelling formal arguments to round out my latest paper, I've been trawling the web trying to answer the big questions of life ("Does the set of equivalence classes of first-order sentences form a complete boolean lattice? Is logical consequence over this set a well-founded partial order?") while maintaining my sanity. The later was helped immensely when I stumbled upon what has officially become (despite not understanding a lick of it) my favourite branch of mathematics: Pointless Topology.
Yes, Pointless Topology.
Literally, the study of topology without points. Oh sure, they could call it "point-free topology" or some-such, but I like to think that the topologists are making a little in-joke about the reputation of their profession, which is often (as in, even by other mathematicians) treated to adjectives such as "ugly", "pathological" and "useless".
If only other academic pursuits were named so honestly.