This theorem comes from a branch of math known as
Topology, and was discovered by Luitzen Brouwer. While its technical expression
is quite abstract, it has many fascinating real world implications. Let’s say
we have a picture (for example, the Mona Lisa) and we take a copy of it. We can
then do whatever we want to this copy—make it bigger, make it smaller, rotate
it, crumple it up, anything. Brouwer’s Fixed Point Theorem says that if we put
this copy overtop of our original picture, there has to be at least one point
on the copy that is exactly overtop the same point on the original. It could be
part of Mona’s eye, ear, or possible smile, but it has to exist.
This also works in three
dimensions: imagine we have a glass of water, and we take a spoon and stir it
up as much as we want. By Brouwer’s theorem, there will be at least one water
molecule that is in the exact same place as it was before we started stirring.