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Mathematics

The Hairy Ball Theorem and Its Topological Implications

Quick fact

The Hairy Ball Theorem guarantees that every continuous vector field on a sphere must have at least one point where the vector is zero—like a cowlick or a whirlpool—no matter how you try to arrange it.

Why this is interesting

Have you ever tried to perfectly flatten your hair on a round ball? No matter how you brush, there's always a tuft that sticks up. Why can't you get it smooth?