Pythagoras

Pythagoras , c.582-c.507 BC, pre-Socratic Greek philosopher, founder of the Pythagorean school. He migrated from his native Samos to Crotona and established a secret religious society or order similar to, and possibly influenced by, the earlier Orphic cult. We know little of his life and nothing of his writings. Since his disciples came to worship him as a demigod and to attribute all the doctrines of their order to its founder, it is virtually impossible to distinguish his teachings from those of his followers. The Pythagoreans are best known for two teachings: the transmigration of souls and the theory that numbers constitute the true nature of things. The believers performed purification rites and followed moral, ascetic, and dietary rules to enable their souls to achieve a higher rank in their subsequent lives and thus eventually be liberated from the "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 Neo-Pythagoreanism developed at the beginning of the Christian era; it borrowed some elements from Jewish and Hellenistic thought and greatly emphasized the mystical element in Pythagorean ideas.

Bibliography: See biographies by P. Gorman (1978) and T. Stanley (1988); D. J. O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (1989).

Pythagoras (c.580–500 bc), Greek philosopher; known as Pythagoras of Samos. Pythagoras sought to interpret the entire physical world in terms of numbers, and founded their systematic and mystical study; he is best known for the theorem of the right-angled triangle. His analysis of the courses of the sun, moon, and stars into circular motions was not set aside until the 17th century.

Pythagoras also founded a secret religious, political, and scientific sect in Italy: the Pythagoreans held that the soul is condemned to a cycle of reincarnation, from which it may escape by attaining a state of purity.
Pythagoras' theorem the theorem attributed to Pythagoras that the square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.
Pythagorean letter the Greek letter Y, used by Pythagoras as a symbol of the two divergent paths of virtue and of vice.
Pythagorean system the system of astronomy proposed by Pythagoras, in which all celestial bodies, including the earth, were held to revolve around a central fire (not the sun, but presumably identified with the sun, resulting in the system being assumed identical with the Copernican system).