PYTHAGORAS (582?-500? BC), Greek philosopher and mathematician, whose doctrines strongly influenced Plato.on the island of Sámos, Pythagoras was instructed in the teachings of the early Ionian philosophers Thales, Anaximander, and Anaximenes. He is said to have been driven from Sámos by his disgust for the tyranny of Polycrates (r. about 533-522 BC). About 530 BC he settled in Crotona, a Greek colony in southern Italy, where he founded a movement with religious, political, and philosophical aims, known as Pythagoreanism. The philosophy of Pythagor as is known only through the work of his disciples.Basic Doctrines. The Pythagoreans adhered to certain mysteries, similar in many respects to the Orphic mysteries. Obedience and silence, abstinence from food, simplicity in dress and possessions, and the habit of frequent self-examination were prescribed. The Pythagoreans believed in immortality and in the transmigration of souls. Pythagor as himself was said to have claimed that he had been Euphorbus, a warrior in the Trojan War, and that he had been permitted to bring into his earthly life the memory of all his previous existences.Theory of Numbers. Among the extensive mathematical investigations carried on by the Pythagoreans were their studies of odd and even numbers and of prime and square numbers. From this arithmetical standpoint they cultivated the concept of number, which became for them the ultimate principle of all proportion, order, and harmony in the universe. Through such studies they established a scientific foundation for mathematics. In geometry the great discovery of the school was the hypotenuse theorem, or Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares on the other two sides; Pythagorean numbers are numbers so related, for instance, 5, 4, and 3 (52 = 42 + 32).Astronomy. The astronomy of the Pythagoreans marked an important advance in ancient scientific thought, for they were the first to consider the earth as a globe revolving with the other planets, including the sun, around a central fire. They explained the harmonious arrangement of things as that of bodies in a single, all-inclusive sphere of reality, moving according to a numerical scheme. Because the Pythagoreans thought that the heavenly bodies are separated from one another by intervals corresponding to the harmonic lengths of strings, they held that the movement of the spheres gives rise to a musical sound the "harmony of the spheres."
