The Pythagorean Theorem
The Pythagorean theorem is one of the most famous in all of mathematics. It states:
Theorem: The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the legs.
There are many different proofs of the theorem (even one supplied by President Garfield in 1876!), and we know that the Babylonians knew about the Pythagorean theorem about 1000 years before the time of Pythagoras (born in 572 B.C.).
Nonetheless, a rigorous, general proof of the theorem requires the development of deductive geometry, and thus it is thought that Pythagoras probably supplied the first proof. Most math historians credit him with a proof by dissection, which relies on the use of two squares, one inscribed inside the other.