# brouwer's fixed-point theorem

i want to share an elegant piece of mathematical theory from the branch of topology that has always fascinated me. it's called brouwer's fixed-point theorem.

here's the idea in a nutshell:

imagine you have a cup of coffee. when you stir it, you're applying a continuous transformation – each point moves somewhere, but the coffee stays in the cup and doesn't move around continuously. the theorem proves that at least one molecule of coffee will end up exactly where it started before it was stirred.

kinda cool. 🤓