Mathematics
The Cauchy-Schwarz Inequality and Its Many Uses
Quick fact
The Cauchy-Schwarz inequality is so fundamental that it appears in almost every branch of mathematics, and it even underlies Heisenberg's uncertainty principle in quantum mechanics.
Why this is interesting
You've probably heard that the shortest path between two points is a straight line. But did you know that a simple algebraic inequality can tell you how close any two vectors are to being aligned?