Pythagoras

569?-475? B.C.

Greek Philosopher and Mathematician

Despite the fact that he is famous for the discovery of the theorem that bears his name, Pythagoras did not view himself primarily as a mathematician; nor did the members of the society he founded, whose principles addressed nonscientific subjects such as reincarnation, or metempsychosis. Yet Pythagoras and his followers, the Pythagoreans, viewed the concept of the number as fundamental to the universe, and with their focus on numerical properties virtually inaugurated the serious study of mathematics in the West.

The son of Mnesarchus, a merchant from Tyre (now in Lebanon), and his wife Pythias, Pythagoras grew up in Samos, Ionia, on what is now the western part of Turkey. His father's profession gave him reason to travel widely, and apparently the boy accompanied him on trips as far away as Italy. During his youth, Pythagoras fell under the influence of several great teachers, most notably Thales (625?-547? B.C.).

Around the year 535 B.C., Pythagoras visited Egypt, where he became interested in various mystical rites while studying at the temple of Diospolis. Following the Persian invasion of Egypt in 525 B.C. he was taken back to Babylon as a prisoner, which placed him in that city alongside the Israelites during the Captivity. Like the Israelites, who adopted the idea of Satan from Zoroastrian scriptures, Pythagoras came under the influence of Zoroastrianism and the much older religion of the Magi.

By 520 B.C., he had made his way back to Samos, where he founded a school based on his emerging mystical worldview. It appears that Samian students were not interested in his rather unusual, Egyptian-influenced teaching style, and in an effort to avoid being forced into a life of public service in his hometown, Pythagoras used this lack of interest as an excuse to move to Italy. In 518 B.C. he settled in Croton, at the eastern tip of the peninsula's boot heel, where he established the Pythagorean society.

His followers, a group that grew steadily after his arrival in Croton, called themselves mathematikoi. They believed that mathematics was at the heart of reality, and that symbols possessed a mystical significance that drew the human closer to the divine. One of the world's first secret societies, the Pythagoreans lived communally, practiced vegetarianism, and practiced vows of secrecy and loyalty. Aside from all their other unusual qualities, they stood apart from much of the ancient world in that women were allowed to enjoy full participation in their society, and did so as full intellectual equals of men.

From a mathematical standpoint, one of the most significant contributions made by Pythagoras was his treatment of number as an abstract entity separable from all specifics. Perhaps for the first time, 2 was just two—not two pebbles or two horses or two ships. As for his famous theorem—that the square of a right triangle's hypotenuse is equal to the sum of the squares of its other two sides—it appears that the Babylonians a millennium before him recognized this principle, and that Pythagoras was simply the first to prove the theorem. He and his followers also showed that the sum of the angles in a triangle is equal to two right angles.

The Pythagoreans—and specifically Hippasus of Metapontum (fl. c. 500 B.C.)—are also credited with the discovery of irrational numbers, or infinite decimals with no indefinitely repeating digits. The idea of an irrational, however, went against Pythagorean precepts, which maintained at all things can be expressed in terms of whole numbers, or the ratios of whole numbers. Similar reasoning led to the Pythagorean rejection of concepts such as the infinite and the infinitesimal. These positions highlight the fact that though he and his followers made many mathematical discoveries, Pythagoras—who believed that each number had a "personality"—was at heart a mystic and not a mathematician.

In 508 B.C., a noble named Cylon tried to force his way into the society, and Pythagoras rejected him because he did not regard Cylon as having a pure interest in mathematics for its own sake. Cylon then set out to destroy the society, and Pythagoras fled to the Italian city of Metapontum, where according to some accounts he committed suicide rather than allow Cylon to take over the society he had founded. In later years, the Pythagoreans became a powerful force in southern Italy, so much so that in the mid-fifth century B.C. they came under severe attack from enemies, and had to flee to Thebes and other cities in Greece.

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