Abandon perfectionism, because of the Hairy Ball Theorem

Abstract

Abstract “Abandon perfectionism, because of the Hairy Ball Theorem” explains the mathematics behind the Hairy Ball Theorem, including a basic introduction to topological equivalence, vectors, and continuous vector fields. The discussion is illustrated with numerous hand-drawn sketches. Readers will understand the meaning of mathematical sayings arising from the theorem, including, “you can’t comb a hairy ball,” “every cow has a cowlick,” and “there is always one place on Earth where the wind is not blowing.” Mathematics students and enthusiasts are encouraged to let the Hairy Ball Theorem serve as a reminder that perfection in mathematics and life is often an impossible goal and that it is often enough, maybe even desirable, to do one’s very best. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.