Pythagoras, a Greek mathematician and philosopher who lived in the sixth century B.C., and gave his name to a body of facts and theories. Since his followers attributed all discoveries to the master, it is impossible to know what accomplishments were actually his. Even the facts of his life are little known. He was born on the island of Samos, according to legend, and came to the Greek city of Croton in southern Italy about 530 B.C., when he was 50 years old. Gathering a group of pupils, he organized them into a brotherhood devoted to both learning and virtuous living.
Of long-lasting influence were the Pythagorean doctrines that numbers were the basis of all things and possessed a mystic significance; and that the universe was a sphere in which the planets revolved. The revolving planets were thought to produce musical notes—"the music of the spheres." The Pythagoreans believed also in transmigration (that the soul, after death, passes into another living thing).
Pythagoras encouraged his followers to become active in politics, a field in which they gained great influence and aroused violent opposition. According to one legend, Pythagoras was killed during an attack on the brotherhood; according to another, he was exiled. The Pythagorean brotherhoods remained active, however, for several centuries.
The Pythagorean Theorem, representing a major step in the development of geometry, is that the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the two other sides. A second theorem is that the sum of the angles within any triangle is 180 degrees. A discovery which was the origin of the science of acoustics was that the notes sounded by a stringed instrument are related to the length of the strings. The Pythagoreans recognized that the earth is round.