For me, the key to understanding was to realize that reality is only a figment of your imagination ;) On a more serious note, it was understanding the Axiom of

For me, the key to understanding was to realize that reality is only a figment of your imagination ;) On a more serious note, it was understanding the Axiom of Choice, or that our "intuitive" notions of reality aren't really consistent with themselves: http://en.wikipedia.org/wiki/Nonmeasurable_set http://en.wikipedia.org/wiki/Nonmeasurable_set