wheel of birth.This belief also led them to regard the sexes as equal, to treat slaves humanely, and to respect animals. The highest purification was
philosophy,and tradition credits Pythagoras with the first use of the term. Beginning with the discovery that the relationship between musical notes could be expressed in numerical ratios (see Greek music ), the Pythagoreans elaborated a theory of numbers, the exact meaning of which is still disputed by scholars. Briefly, they taught that all things were numbers, meaning that the essence of things was number, and that all relationships—even abstract ethical concepts like justice—could be expressed numerically. They held that numbers set a limit to the unlimited—thus foreshadowing the distinction between form and matter that plays a key role in all later philosophy. The Pythagoreans were influential mathematicians and geometricians, and the theorem that bears their name is witness to their influence on the initial part of Euclidian geometry. They made important contributions to medicine and astronomy and were among the first to teach that the earth was a spherical planet, revolving about a fixed point. At the end of the 5th cent. BC the Pythagoreans were forced to flee Magna Graecia when people grew enraged at their interference with traditional religious customs; many were killed. A short-lived
See biographies by P. Gorman (1978) and T. Stanley (1988); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (1989).
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