ฺBy any standard, the Pythagorean the is the most well-known in all of mathematics. It shows up, direcly or in disguise, in almost every branch of it, pure or applied. It is also a record breaker in terms of the number of proofs it has generated since Pythagoras allegedly proved it around 500 BCE. And it is the one theorem that almost everyone can remember from his or her high school geometry class.