I just love things that I can't understand --- and since there are so many such things in the world, I'm usually a pretty happy camper. Two examples, inadequately explained because, beneath the first few millimeters of their surface, they remain quite opaque to me:
Some day, if I am lucky enough, I'd like to know a bit about what the above really mean ... not in any great detail, but enough to be able to be able to talk about them semi-coherently. For instance, I would like to know what the sentences after the first three mean in Ron Soloman's paper "On Finite Simple Groups and Their Classification" (Notices of the AMS, February 1995) when he writes:
The pace of the Classification in the '70s was exhilarating. Not a single leading group theorist besides Gorenstein believed in 1972 that the Classification would be completed this century. By 1976, almost everyone believed that the Classification problem was "busted". The principal reason was Michael Aschbacher's lightning assaults on the B-conjecture, the Thin Group Problem, and the Strongly p-embedded 2-local problem. Also, in 1976 Timmesfield announced a breakthrough in the "O2 extraspecial" problem. ...
Greek to me --- I sure wish that I could learn a little Greek! (And the above, of course, are trivial compared to comprehending people ... including myself.)