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575-ca. 495 B.C.

The Greek philosopher, scientist, and religious teacher Pythagoras 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 travelled 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 centre of the universe. The centre 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 counter earth closer to the centre, and the other five planets were farther away and followed longer courses around the centre. It is not known how much of this theory was attributable to Pythagoras himself. Later writers ascribe much of it to Philolaos (active 400 B.C.), 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.


Pythagoras, Greek polymath, philosopher, and mystic of the sixth century BC. He wrote no books, but so impressive were his doctrines, his learning, and his way of life that by the end of the fifth century he had become a figure of mystery and legend with a reputation as a great sage and a possessor of miraculous powers (as well as of a golden thigh). The traditions concerning his life are contradictory and confused, but it is believed that he was born at Samos c.580 BC and emigrated (perhaps through hostility to the tyranny of Polycrates) to Croton in Magna Graecia. There he attracted followers, both men and women, who formed a community and lived according to his rule of life. Even after his death, c.500 BC, Pythagorean societies continued to flourish in Croton and elsewhere in Magna Graecia. The members seem to have been active in the politics of the time and, presenting a united front, were no doubt a powerful force; they became unpopular and eventually (c.450 BC) the societies were broken up and the members killed or exiled.

Part of Pythagoras' teaching was religious and mystical, and it was presumably this aspect which led his contemporary Heracleitus to regard him as a fraud. Another contemporary, Xenophanes, mocked the most celebrated aspect of his teaching, his doctrine of reincarnation or the transmigration of souls (metempsychosis), with the story that Pythagoras once claimed to recognize a friend's voice in the howling of a puppy which was being beaten. Pythagoras also declared that he remembered his own previous incarnations, including that as the Trojan Euphorbus, killed in the siege. Pythagoras taught that the soul (a combination of life-principle, self, and mind) is immortal, a fallen divinity imprisoned in the body as in a tomb. Since the soul is rational and responsible for its actions, the choices it makes determine the kind of body into which it is reincarnated, human or animal (perhaps even plant; Empedocles, who was greatly influenced by Pythagorean ideas, declares that in one of his incarnations he was a bush). By keeping itself pure from the pollutions of the body the soul may eventually win release from it (see also ORPHEUS and compare Orphic beliefs, with which Pythagoras obviously had much in common). Pythagoras and his followers adhered to a rule of life by which release for the soul might be attained; this was an austere regimen the details of which are not clear but which perhaps entailed silence, self-examination, and abstention from eating flesh and beans (no reason is known for this latter prohibition). The idea of metempsychosis is foreign to Greek tradition and its source uncertain; it may have reached Greece from central Asia or even India. Many precepts of Pythagoras were collected at some time under the name of acusmata (Gk. akousmata, ‘ (oral) instructions’). Some sound like taboo-prohibitions, e.g. ‘Do not poke the fire with a sword’ (which Porphyry interpreted as meaning, ‘Do not vex with sharp words a man swollen with anger’). Others sound like traditional wisdom: ‘What is the wisest of the things in our power? Medicine. What is the fairest thing? Harmony. What is the most powerful? Knowledge. What is the best? Happiness.’

Pythagoras' name is also linked to the study of numbers and proportions as well as astronomy. It is impossible to ascertain what discoveries should be attributed to him personally, but he is credited with the discovery that the relation between the chief musical intervals produced on a vibrating string can be expressed as ratios between the first four whole numbers: octave, 2 : 1; fifth, 3 : 2; fourth, 4 : 3. From this evolved the idea that the explanation of the universe is to be sought in numbers and their relations, of which the objects of sense are representations. According to Aristotle, even abstracts like ‘opinion’ or ‘opportunity’ or ‘injustice’ were numbers in the Pythagorean system, and had their place in the cosmos. Since the first four whole numbers are important in expressing musical harmonies and since their sum can be represented as an equilateral triangular array of ten dots in rows of one, two, three, and four, it was thought that this pattern, the tetraktys, ‘foursome’, of the decad, was of mystical significance, embracing the whole nature of number: the number one could be identified with the point, two with the line, three with the surface, and four with the solid. Pythagoras is also credited with the theorem that still goes under his name, namely that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides; on discovering it he is said to have made the important sacrifice of a hecatomb. The Pythagoreans believed that the earth is a sphere; later Pythagoreans had an astronomical system in which the heavenly bodies (the sphere of the fixed stars, the five planets, the sun, moon, earth, and counter-earth, the last included to bring the number of bodies up to ten) revolve around a central fire, a system to which an earlier belief in a ‘harmony of the spheres’ was accommodated.

Pythagoreanism influenced not only Empedocles but also Plato, whose science and metaphysics are infused with Pythagorean ideas. Later the doctrines were revived at Rome under the early empire, and became confused with Orphic beliefs with which they had affinities.










This web page was last updated on: 15 December, 2008