The Greek philosopher, scientist, and religious teacher Pythagoras (ca. 575-ca. 495 BC) evolved a school of thought that accepted the transmigration of souls and established number as the principle in the universe.

Born on the island of Samos, Pythagoras was the son of Mnesarchus. He fled to southern Italy to escape the tyranny of Polycrates, who came to power about 538, and he is said to have traveled to Egypt and Babylon. He and his followers became politically powerful in Croton in southern Italy, where Pythagoras had established a school for his newly formed sect. It is probable that the Pythagoreans took positions in the local government in order to lead men to the pure life which their teachings set forth. Eventually, however, a rival faction launched an attack on the Pythagoreans at a gathering of the sect, and the group was almost completely annihilated. Pythagoras either had been banished from Croton or had left voluntarily shortly before this attack. He died in Metapontum early in the 5th century.

Religious Teachings

Pythagoras and his followers were important for their contributions to both religion and science. His religious teachings were based on the doctrine of metempsychosis, which held that the soul was immortal and was destined to a cycle of rebirths until it could liberate itself from the cycle through the purity of its life. A number of precepts were drawn up as inviolable rules by which initiates must live.

Pythagoreanism differed from the other philosophical systems of its time in being not merely an intellectual search for truth but a whole way of life which would lead to salvation. In this respect it had more in common with the mystery religions than with philosophy. Several taboos and mystical beliefs were taught which sprang from a variety of primitive sources such as folk taboo, ritual, and sympathetic magic and were examples of the traditional beliefs that the Greeks continued to hold while developing highly imaginative and rational scientific systems.

An important underlying tenet of Pythagoreanism was the kinship of all life. A universal life spirit was thought to be present in animal and vegetable life, although there is no evidence to show that Pythagoras believed that the soul could be born in the form of a plant. It could be born, however, in the body of an animal, and Pythagoras claimed to have heard the voice of a dead friend in the howl of a dog being beaten.

The number of lives which the soul had to live before being liberated from the cycle is uncertain. Its liberation came through an ascetic life of high moral and ethical standards and strict adherence to the teachings and practices of the sect. Pythagoras himself claimed to remember four different lives. Followers of the sect were enjoined to secrecy, although the discussions of Pythagoras's teachings in other writers proved that the injunction was not faithfully observed.

Mathematical Teachings

The Pythagoreans posited the dualism between Limited and Unlimited. It was probably Pythagoras himself who declared that number was the principle in the universe, limiting and giving shape to matter. His study of musical intervals, leading to the discovery that the chief intervals can be expressed in numerical ratios between the first four integers, also led to the theory that the number 10, the sum of the first four integers, embraced the whole nature of number.

So great was the Pythagoreans' veneration for the "Tetractys of the Decad" (the sum of 1 + 2 + 3 + 4) that they swore their oaths by it rather than by the gods, as was conventional. Pythagoras may have discovered the theorem which still bears his name (in right triangles, the square on the hypotenuse equals the sum of the squares on the other sides), although this proposition has been discovered on a tablet dating from the time of the Babylonian king Hammurabi. Regardless of their sources, the Pythagoreans did important work in systematizing and extending the body of mathematical knowledge.

As a more general scheme, the Pythagoreans posited the two contraries, Limited and Unlimited, as ultimate principles. Numerical oddness and evenness are equated with Limited and Unlimited, as are one and plurality, right and left, male and female, motionlessness and movement, straight and crooked, light and darkness, good and bad, and square and oblong. It is not clear whether an ultimate One, or Monad, was posited as the cause of the two categories.

Cosmological Views

As a result of their religious beliefs and their careful study of mathematics, the Pythagoreans developed a cosmology which differed in some important respects from the world views of their contemporaries, the most important of which was their view of the earth as a sphere which circled the center of the universe. The center of this system was fire, which was invisible to man because his side of the earth was turned from it. The sun reflected that fire; there was a counterearth closer to the center, and the other five planets were farther away and followed longer courses around the center. It is not known how much of this theory was attributable to Pythagoras himself. Later writers ascribe much of it to Philolaos (active 400 BC), although it circulated as a view of the school as a whole.

The systematization of mathematical knowledge carried out by Pythagoras and his followers would have sufficed to make him an important figure in the history of Western thought. However, his religious sect and the asceticism which he taught, embracing as it did a vast number of ancient beliefs, make him one of the great teachers of religion in the ancient Greek world.

Further Reading

• Pythagoras left no written works. A first-rate technical book, J. A. Philip, Pythagoras and Early Pythagoreanism (1966), separates the valid from the spurious among the legends that surround Pythagoras and his views. An excellent and thorough treatment of the evidence for his life and teachings is in W. K. C. Guthrie, A History of Greek Philosophy (3 vols., 1962-1969). A good account of Pythagoras and his followers is in Kathleen Freeman, The Pre-Socratic Philosophers (1946; 3d ed. 1953), and G. S. Kirk and J. E. Raven, The Presocratic Philosophers (1962). Briefer treatments of the Pythagoreans and the intellectual currents of their time are in the standard histories of Greek literature, such as Albin Lesky, A History of Greek Literature (trans. 1966), or in accounts of Greek philosophy, such as John Burnet, Greek Philosophy (1914).