Pythagorean Theorem

Pythagoras

[Samos, 582 - 500 BC]

Like Thales, Pythagoras is rather known for mathematics than for philosophy. Anyone who can recall math classes will remember the first lessons of plane geometry that usually start with the Pythagorean theorem about right-angled triangles: a²+b²=c². In spite of its name, the Pythagorean theorem was not discovered by Pythagoras. The earliest known formulation of the theorem was written down by the Indian mathematician Baudhāyana in 800BC. The principle was also known to the earlier Egyptian and the Babylonian master builders. However, Pythagoras may have proved the theorem and popularised it in the Greek world. With it, his name and his philosophy have survived the turbulences of history.

His immediate followers were strongly influenced by him, and even until today Pythagoras shines through the mist of ages as one of the brightest figures of early Greek antiquity. The Pythagorean theorem is often cited as the beginning of mathematics in Western culture, and ever since mathematics -the art of demonstrative and deductive reasoning- has had a profound influence on Western philosophy, which can be observed down to Russell and Wittgenstein.

Pythagoras' influence found an expression in visual art and music as well, particularly in the renaissance and baroque epoch. The far-reaching imprint of his ideas is yet more impressive if we consider that he did not leave any original writings. Instead, all what is known about Pythagoras was handed down by generations of philosophers and historiographers, some of whom, like Heraclitus, opposed his views. In this light it is remarkable that Pythagoras' teachings have survived relatively undistorted until the present day.

Pythagoras was a native of the island of Samos. During his early life, Samos was governed by the powerful, unscrupulous tyrant Polycrates. Pythagoras did not sympathise with his government and thus emigrated to Croton in Southern Italy. Like the ancient Greek cities in Ionia, Croton was a flourishing commercial city that lived from importing and exporting goods. Obviously it was in Croton where Pythagoras developed most of his important ideas and theories.

Pythagoras founded a society of disciples which has been very influential for some time. Men and women in the society were treated equally -an unusual thing at the time- and all property was held in common. Members of the society practised the master's teachings, a religion the tenets of which included the transmigration of souls and the sinfulness of eating beans. Pythagoras' followers had to obey strict religious orders where it was forbidden to eat beans, to touch white cocks, or to look into a mirror beside a light.

If all of this seems a bit odd, it might lead us to suspect that Pythagoras' personality reflects the inseparable blend of genius and madness that we associate with many other great men. It is said that once Pythagoras was walking up a lane in Croton when he came by a dog being ill-treated. Seeing this he raised his voice: "Stop, don't hit it! It is a soul of a friend. I knew it when I heard its voice." Spirits, ghosts, souls, and transmigration were obviously things he believed in deeply.

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