Pythagoras was born around 570 BC on the island of Samos in the eastern Aegean. He wrote nothing, and all we know comes from authors writing centuries later, when he had already become legendary: he was said to have a golden thigh, to talk to animals and to be able to appear in two places at once.
From Samos to Croton
Tradition says Pythagoras travelled to Egypt and Babylon, learning mathematics and astronomy. To escape the tyranny of Polycrates he left Samos and around 530 BC settled at Croton in Calabria, one of the richest Greek colonies of Magna Graecia. There he founded a community of followers, men and women, which also became an influential political group. A revolt against the Pythagoreans forced him to flee to Metapontum, where he died.
The Pythagorean community
The Pythagoreans lived by strict rules: they shared property, kept silence during years of apprenticeship, ate no meat, perhaps because of their belief in reincarnation, and had odd taboos, such as not eating beans. The teachings were secret; disciples quoted their master with autos epha, "he himself said it", in Latin ipse dixit.
All is number
The Pythagoreans' central idea was that the deep nature of things is number. They found it in music: on a stretched string, harmonic intervals match simple ratios of length (the octave is 2:1, the fifth 3:2, the fourth 4:3). The cosmos too must follow harmonious proportions: the moving planets would produce a "music of the spheres". The number 10, the sum of 1+2+3+4, was sacred, shown as the tetraktys, a triangle of ten dots.
The theorem
Pythagoras' theorem states that in a right-angled triangle the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c². Babylonians and Egyptians knew particular cases, such as the 3-4-5 triangle, but the Pythagoreans are credited with the general proof.
Legacy
Pythagoras inspired Plato and, many centuries later, Copernicus and Kepler, convinced the universe was written in mathematical language. On Samos his birthplace is now called Pythagoreio, a UNESCO site along with the Heraion and the Tunnel of Eupalinos. In Croton a park and many events recall his school.
See also Greek philosophy and Greek science.