Pythagoras's Theorem

Theorem
Let $\triangle ABC$ be a right triangle with $c$ as the hypotenuse.

Then:
 * $a^2 + b^2 = c^2$

The Classic Proof
However, little is known about him, and it is uncertain whether he actually proved it or not.

Also see

 * Pythagorean Theorem (Hilbert Space), a generalisation to the context of Hilbert spaces.