Math people, you know this already, and please don't contradict my Gauss anecdote. It's part of math culture, so shhhhhhhh.
The target audience is general - not for math know-it-alls. But since so many of you do know-it-all, I'm certainly taking recommendations. I'm going to do stuff like the infinitude of primes, irrationality of square root of 2, the classics. I thought I'd start with something conceptually simple.