Pythagoras

Pythagoras was born on Samos and at about forty, fleeing its tyrant, settled in Croton in southern Italy, where he founded a community that was at once a school, a religious brotherhood and a political faction. Members held property in common and kept rules of silence, vegetarianism and taboos such as never eating beans. The group later became entangled in politics; Pythagoras himself was driven into exile and died at Metapontum.

He left nothing written, and what later tradition attributes to him is hard to separate from the work of other members. What is certain is the core belief of the school: the soul is immortal and transmigrates, so it must be purified from the body, and the highest purification is the study of mathematics, because number is the very order of the cosmos. They found that simple ratios of string length yield the concordant musical intervals and inferred that the whole universe is built on numerical proportion, the planets sounding a 'music of the spheres' that human ears cannot hear.

The theorem that bears his name was already known to the Babylonians; the school's contribution may have been the proof. Within the school someone discovered incommensurable magnitudes, that is, irrational numbers, a fatal blow to 'all is number'; the discloser was said to have been thrown into the sea. Plato took from the Pythagoreans the immortality of the soul and mathematics as the road to reality.