This strangely-named theorem has a rarefied theoretical background, arising from a perfectly round ball covered with perfectly fine hair. Despite that, it has real-world applications, including the ability to build gold nanowires â€” and finding the one spot on earth where there is no wind.

Top image: BryceGuy72 on Deviant Art.

The Hairy Ball Theorem springs from an early 20th century mathematician's thoughts about vector fields applied to ideal shapes. I know, it sounds fascinating. But Luitzen Brouwer took that ridiculously abstract idea and gave it an easily understood form - especially since Koosh balls were invented.

According to Brouwer, to understand this, people should picture a perfectly round ball covered with perfectly fine hair all over. Next, imagine taking a brush and brushing the hair on the ball in continuous strokes, trying to flatten it to the body of the ball. After the brushing, the hair is essentially a vector field. Each hair shows the motion of the brush, since each hair has been tugged in whatever direction the brush was moving as it tugged the hair into place. From the point of view of someone standing on the surface of the ball, the hairs drawn perpendicular to the surface of the ball received the most vigorous motion, while those standing up and down, just the way they were before the brush moved through, show no motion at all. They are 'zero vectors.'