In high school, I remember learned this from reading James Gleick's book about Feynman. Feynman had written in one of his notebooks, as a fifteen year-old: THE MOST REMARKABLE FORMULA IN MATH: e^(i*pi) + 1 = 0

I marched in to my calculus teacher the next day and stammered about how unbelievable this was. A few weeks later he helped us work through why it's true.

(Edit: ha, typo. Thanks BoppreH.)