The Hairy Ball Theorem

The podcast explores the hairy ball theorem, a mathematical concept stating that one cannot comb all the hair on a sphere without creating a tuft. It connects this theorem to practical problems, such as orienting a 3D airplane model in a game, where a continuous function for wing direction is impossible without glitches. The discussion extends to wind velocity on Earth and radio signal propagation, illustrating the theorem's unexpected relevance. The podcast then transitions to a puzzle: proving that a continuous vector field on a sphere must have at least one point with a zero vector, using a proof by contradiction involving the deformation of a sphere and the concept of flux.