- 6635 South Hall
The Hairy Ball Theorem states that an even-dimensional sphere cannot admit a nonvanishing continuous vector field. One fun consequence is that the wind is *not* blowing at some point on the surface of the Earth. There are multiple proofs, but most require a bit of machinery (e.g., homology theory or differential forms). John Milnor provided what he calls a "strange" proof that only uses elementary real analysis.