The Hairy Ball Theorem

http://commons.wikimedia.org/wiki/File:Hairy_ball.png

A hairy ball can’t be combed flat — it must always have a cowlick.

This result arose originally in algebraic topology, but it has intriguing applications elsewhere. For example, it can’t be windy everywhere at once on Earth’s surface — at any given moment, the horizontal wind speed somewhere must be zero.