Pythagoras of Samos

Pythagoras founded a religious and mathematical brotherhood and is credited with a theorem that predates him. Born on Samos around 570 BC, he is said to have travelled to Egypt and Babylon before settling around 530 BC at Croton in southern Italy, where the local aristocracy took him up. The community he founded was closer to a monastic order than a school. Members held property in common, followed dietary rules including a celebrated prohibition on beans, observed silence for years as novices, and attributed every discovery to the founder — which is why nothing can be assigned to him personally with confidence. He wrote nothing, and the earliest accounts are centuries later. Their central doctrine was that number is the principle of reality. The evidence they cited was musical: strings whose lengths stand in simple whole-number ratios sound consonant, so harmony is arithmetic made audible, and the cosmos itself was held to sound. They also taught the transmigration of souls, which is why the diet mattered. The theorem about the squares on the sides of a right triangle was known to Babylonian and Indian mathematicians long before, and the Pythagoreans are credited with proving it rather than finding it. Their discovery that the diagonal of a square is incommensurable with its side — that some magnitudes cannot be expressed as ratios of whole numbers — undermined their own doctrine. The tradition that Hippasus was drowned for revealing it is a later story. The brotherhood was attacked and dispersed, and Pythagoras died around 495 BC, probably at Metapontum.

• Lived: 570 BCE – 495 BCE
• Nationality: Greek
• Roles: mathematician, philosopher