Pythagoras of Samos was the leader of a mystical cult-like sect that believed that the harmony of everything in the universe can be expressed in numbers. He did not discover the Pythagorean theorem, but it is likely that he was one of the few mathematicians who proved it. How he proved the theorem is not known since his sect was extremely secretive and never wrote anything down. The Pythagorean theorem led to the discovery of irrational numbers, which became a huge problem for the Pythagoreans who believed in the absolute perfection of numbers.
A thousand years before Pythagoras, the Babylonians in the second millenium B.C. knew the relationship among the sides of a right triangle. Clay tablets with cuneiform writing provide evidence that the Babylonians were skilled in geometry and knew how to generate Pythagorean triples -- a set of three numbers that could be the lengths of the sides of a right triangle. The Pythagorean theorem was used by Babylonian master builders.
The ancient Indian mathematician Baudhayana wrote down a formulation of the Pythagorean theorem in 800 B.C. He was one of the authors of the Sulbasutras, a set of rules for making altars for sacrificial ceremonies. The ancient Indians believed that areas, orientations and shapes of the altars had to be perfect for the religious ceremonies to be effective. They developed various rules, including the Pythagorean theorem, for creating accurate geometric shapes.
A Chinese mathematical and astronomical treatise named the Chou Pei Suan Ching, written sometime between 1100 and 200 B.C. (the dating is uncertain), gives a statement and geometrical proof of the Pythagorean theorem. The diagram demonstrating the proof is known as hsuan-thu and is well-known throughout China. Another mathematical text, the Chiu chang suan shu, also provides evidence that the ancient Chinese were aware of the relationship among the sides of a right triangle.