Rick, thanks for this morning mind opener. I loved my courses in set theory and the philosophical foundations of mathematics -- in particular, countably vs. uncountably infinite sets. I just never understood why discussing these important concepts never got me anywhere at college parties. (The topic seemed perfectly interesting to me.)

Another favorite is Godel's incompleteness theorems (which are given a short and accessible exposition in the great book "Godel's Proof" by Nagel and Newman).