Pythagoras

Pythagoras was born on Samos, a Greek island off the coast of Asia Minor, around 580 B.C. Like Thales, he travelled in his youth. He likely visited both Egypt and Babylon, like Thales. He also went to the Ionian school founded by Thales. It is unlikely that he studied directly under Thales though, because Thales would have been quite old by then.

Pythagoras later founded his own school/cult in the Greek colony of Croton in Magna Graecia (southern Italy). His cult had about 300 members, divided into two groups: mathematikoi (Greek for "scientists"; this is from where English gets the word mathematics), the elite of the school, who were privy to Pythagoras' mathematical truths, and the akousmatikoi (Greek for "those who hear"), who followed the sect's rules but didn't know about the mathematical mysteries of the cult.

Pythagoras believed that the natural numbers were the basis of all reality. For example, he felt that musical harmonies were not merely related to ratios of whole numbers; they were ratios of whole numbers. Pythagoras said that "all is number", and he fostered a number mysticism which classified numbers as male (odd numbers), female (even numbers), triangular, square, prime, composite, perfect, deficient, abundant, amicable, or into other categories.

Pythagoras is most famous for his proof of the Pythagorean Theorem. The ancient Egyptians had known that a right triangle could be made with sides of lengths 3, 4, and 5, but were not aware of the general rule. The Babylonians knew that a² + b² = c², but they never attempted to prove this theorem. Pythagoras was the first person to do so. This theorem led Pythagoras to a sensational discovery when applied to a right triangle whose two legs were of length 1.