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Pythagoras, the Greek philosopher and mathematician and founder of the Pythagorean school, flourished about 530 B. C. Very little is known about the life and personality of Pythagoras. There is an abundance of biographical material dating from the first centuries of the Christian era, from the age of neo-Pythagoreanism, but, when we go back to the centuries nearer to Pythagoras's time, our material becomes very scanty. It seems to be certain that Pythagoras was born at Samos about the year 550 or 560 B. C. , that he travelled to Magna Græcia in Southern Italy about the year 530, that he founded there a school of philosophy and that he died at Metapontum in Sicily. The detailed accounts of how he invented the musical scale, performed miracles, pronounced prophecies, and did many other wonderful things, belong to legend, and seem to have no historical foundation. Similarly the story of his journey into Egypt, Asia Minor , and even to Babylon is not attested by reliable historians. To the region of fable belongs also the description of the learned works which he wrote and which were long kept secret in his school. It is certain, however, that he founded a school, or, rather, a religious philosophical society, for which he drew up a rule of life. In this rule are said to have been regulations imposing secrecy, a protracted period of silence, celibacy, and various kinds of abstinence. The time-honoured tradition that Pythagoras forbade his disciples to eat beans, for which various reasons, more or less ingenious, were assigned by ancient and medieval writers, has been upset by some recent writers, who understand the phrase, "Abstain from beans" ( kyamon apechete ), to refer to a measure of practical prudence, and not to a gastronomic principle. Beans, black and white, were, according to this interpretation, the means of voting in Magna Græcia, and "Abstain from beans" would, therefore, mean merely "Avoid politics"— warning which, we know, was warranted by the troubles in which the school was involved on account of the active share which it took during the founder's lifetime in the struggles of the popular with the aristocratic party in Southern Italy. The school was instructed by its founder to devote itself to the cultivation of philosophy, mathematics, music, and gymnastics, the aim of the organization being primarily ethical. The theoretical doctrines taught by the master were strictly adhered to, so much so that the Pythagoreans were known for their frequent citation of the ipse dixit of the founder. Naturally, as soon as the legends began to grow up around the name of Pythagoras, many tenets were ascribed him which were in fact introduced by later Pythagoreans, such as Philolaus and Archytas of Tarentum.

It seems to be certain that, besides prescribing the rules that were to govern the society, Pythagoras taught:

a doctrine of transmigration of souls which he probably borrowed from the Bacchic and Orphic mysteries, the whole spirit of thedoctrine being religious andethical, intended to show, by successive incarnations of the soul in the bodies of different animals a system by which certain vices and virtues were to be punished and rewarded after death;
in a general way, the doctrine that mathematics contains the key to all philosophical knowledge, a germ, so to speak, which was afterwards developed into an elaborate number-theory by his followers; and
the notion that virtue is a harmony, and may be cultivated not only by contemplation and meditation but also by the practice of gymnastics and music. he subsequent elaboration of these three central doctrines into a complicated system is the work of the followers of Pythagoras. The Pythagorean philosophy in its later elaboration is dominated by the number-theory. Being the first, apparently, to observe that natural phenomena, especially the phenomena of the astronomical world, may be expressed in mathematical formulas, the Pythagoreans were carried on by the enthusiasm characteristic of discoverers to maintain that numbers are not only the symbols of reality, but the verysubstance of real things. They held, for example, that one is the point, two the line, three the surface, and four the solid. Seven they considered to be the fate that dominates human life, because infancy ceases at seven, maturity begins at fourteen, marriage takes place in the twenty-first year, and seventy years is the span of life usually allotted to man. Ten is the perfect number, because it is the sum of one, two, three, and four-the point, the line, the surface, and the solid. Having, naturally, observed that all numbers may be ranged in parallel columns under "odd" and "even", they were led to attempt a similar arrangement of the qualities of things. Under odd they placed light, straight, good, right, masculine; under even, dark, crooked, evil, left, feminine. These opposites, they contended, are found everywhere Innature, and the union of them constitutes the harmony of the real world.

The account given by the Pythagoreans of the "harmony of the spheres" is the best illustration of their method. There are, they said, ten heavenly bodies, namely, the heaven of the fixed stars, the five planets, the sun, the moon, the earth, and the counter-earth. The counter-earth is added because it is necessary to make up the number ten, the perfect number. It is a body under the earth, moving parallel with it, and, since it moves at the same rate of speed, it is invisible to us. The five planets, the sun, the moon, and the earth with its counter-earth, moving from west to east at rates of speed proportionate to the distance of each from the central fire, produce eight tones which give an octave, and, therefore, a harmony. We are not conscious of the harmony, either because it is too great to be perceptible by human ears, or because, like the blacksmith who has grown accustomed to the noise of his hammer on the anvil, we have lived since our first conscious moments in the sound of the heavenly music and can no longer perceive it. In their psychology and their ethics the Pythagoreans used the idea of harmony and the notion of number as the explanation of the mind and its states, and also of virtue and its various kinds. It was not these particular doctrines of the school so much as the general notion which prevailed among the Pythagoreans of the scope and aim of philosophy, that influenced the subsequent course of speculation among the Greeks. Unlike the Ionians, who were scientists and related philosophy to knowledge merely, the Pythagoreans were religiously and ethically inclined, and strove to bring philosophy into relation with life as well as with knowledge. Aristotelianism, which reduced philosophy to knowledge, never could compete, in the estimation of its advocates, with Christianity, as neo-Pythagoreanism did, by setting up the claim that in the teachings of its founder it had a "way of life" preferable to that taught by the Founder of Christianity.

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