I divide proofs into two groups: 1) Clever little things 2) Long, hard slogs Cantor's proof is a clever little thing. These sorts of proofs can be daunting a

I divide proofs into two groups: 1) Clever little things 2) Long, hard slogs Cantor's proof is a clever little thing. These sorts of proofs can be daunting at first but they become easier, even delightful, as one becomes more familiar with their kind. If you studied the foundations of math in school for as long as an American student takes English literature courses then these proofs would be second nature to you. They aren't really hard, just written in a language unfamiliar to most people. Then there are the long, hard slogs. Lemma after lemma, with no clue as to where the author is leading, until finally, after an exhausting march, he bludgeons the reader into accepting his conclusions. These are pretty hard for anybody to understand because you can't hold the whole thing in your head. You just have to convince yourself of the truth of each step.