[wetmore]

You may recall that one can use the quadratic formula to find solutions to a quadratic equation (polynomial with highest term being x^2). Did you know that (one) guy that proved there is no such formula for quintic equations (highest term x^5) died in a duel when he was only 20? [1]

There is a town with a particular rule when it comes to facial hair: those who do not shave themselves are shaved by the barber. But then who shaves the barber? [2]

The other poster mentioned different infinities. One "size" of infinity is called "countable infinity" and is the infinity describing the size of the natural numbers (1,2,3,...). Say we have a hotel with a countable infinite number of rooms. I've been travelling all day and I show up at the hotel, and talk to the clerk at the front desk. He tells me every room is full, but when he sees the sad look on my face he tells me not to worry - he can make room for me. He simply moves the person in room 1 to room 2, the person in room 2 to room 3, room 3 to room 4, etc... And then the first room is empty for me, and everyone still has a room. [3]

[1] http://en.wikipedia.org/wiki/%C3%89variste_Galois [2] http://en.wikipedia.org/wiki/Russell's_paradox [3] http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_...