Hairy ball theorem

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Hairy ball theorem

Summary

The Hairy Ball Theorem is a famous rule in mathematics that says, quite literally, you can’t smoothly comb a hairy, spherical ball without leaving at least one messy cowlick, whorl, or bald spot somewhere on its surface. While it sounds a bit silly, this concept from topology describes how vectors behave on curved, closed shapes, proving that it's impossible to create a perfectly flat, continuous flow over a sphere. 

Because of this rule, we see fascinating real-world side effects all around us: for instance, if you look at the Earth's global wind patterns as a giant "hairy ball," the theorem proves there must always be a cyclone or completely calm eye of a storm brewing somewhere on the planet.

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