PYTHAGORAS. - The historical figure of P., philosopher and founder of the school that bears his name, was so distorted by later legends that it is difficult, amid the accumulation of traditions, to sift the true from the fabulous. It is certain that he, born at Samos to Mnesarchus, in the first half of the 6th century B.C. (c. 580), moved in his mature years (after perhaps having stayed in Egypt in his youth) from his island to the Italian city of Croton, and here established a philosophical-religious community that later also became a political party. P. taught only orally: Empedocles celebrates him as ἀνὴρ περιώσια εἰδώς... πάντων δὲ μάλιστα σοφῶν ἐπιήφανος ἔργων (fr. 129), while Heraclitus speaks of his πολυμαθίη (fr. 40, 129); Xenophanes of Colophon attests (fr. 7) P.'s belief in reincarnation, not without a veil of irony. By Herodotus (IV, 95) he is described as an eminent σοφιστής. Having carried out his teaching in Croton, P. emigrated, following the political opposition of a part of the Crotonian citizenry, to Metapontum, where he died (around 500?).
The Pythagoreans formed an association characterized by a strict ethical-religious discipline: they observed the practice of prolonged silence (ἐχειυθία), abstinence at least in part from meat and, it seems, from beans, and various precepts partly ethical and partly ritual (these latter too interpreted later as ethical symbols); and they were accustomed to examine their conscience each evening. According to later testimonies, the sect would have comprised two classes of disciples, the exoteric and the esoteric (the former not initiated into the secrets of the doctrine, that is, mere hearers, ἀκουσματικοί; the latter initiated into wisdom, μαθηματικοί), while others distinguish three categories (ἀκουστικοί, μαθηματικοί, φυσικοί). The master's views were accepted as indisputable truth (according to the famous motto αὐτὸς ἔφα). Having spread from Croton to other places of Magna Graecia, the school acquired great political power and held the government of various cities. But soon a violent hostility of the democratic parties arose against the aristocratizing Pythagoreans: the first uprising broke out while P. was still alive (hence his flight from Croton); and other seditions occurred subsequently, until at a moment that cannot be precisely determined (between 460 and 400) a revolution took place by which the Pythagorean order was utterly destroyed, and its members for the most part killed. Of the survivors, some moved to Thebes (Lysis and Philolaus), others to Phlius. Some later returned from exile to Tarentum, and in this city Pythagoreanism flourished anew with Archytas, until it died out in the last years of the 4th century B.C. Among the principal ancient Pythagoreans figure, besides Philolaus (who was the first to set forth the doctrine in writing), Simmias and Cebes (known through Plato), Occlus of Lucania, Timaeus of Locri, Lysis and Archytas (a distinguished mathematician and physicist).
How much of the Pythagorean theories goes back to P. himself is difficult to determine; one may state with certainty that he professed the belief in reincarnation (v.), transmitted to his disciples the fundamental core of the ethical-religious precepts destined to constitute the most characteristic heritage of Pythagoreanism, and gave rise to those mathematical studies from which the school itself later derived its greatest glory (it may be that the "theorem of P." goes back to him personally). In any case it is better to speak, rather than of P., of the Pythagoreans in general. Their metaphysical conception was closely bound to the aforementioned mathematical studies. Observing the importance that numerical relations have in the universe, since nothing is knowable without number (πάντα γε μὰν τὰ γεγνωσκόμενα ἀριθμὸν ἔχοντι: Philolaus, fr. 4), they affirmed that the principle of things is precisely number: which seems to have to be understood, according to the testimony of Aristotle (cf. in particular Met., I, 5, 985 b 23 ff., 986 a 15), in the sense that number is the intimate substance, the ὕλη of things themselves: nor does the fact that the Pythagoreans at the same time considered numbers as models of things (ibid., 987 b) conflict with this interpretation. Of number there are two fundamental categories, the odd (περισσόν) and the even (ἄρτιον), to which Philolaus adds the ἄρτιον-περισσόν, the even-odd, equivalent, it seems, to the One. The odd is limited (πεπερασμένον) and the principle of limit (πέρας); the even is unlimited (ἄπειρον) and the principle of unlimitedness (ἀπειρία). The Universe is a harmony of these contrary principles, with which are then connected other antithetical pairs (cf. the Pythagorean "table" of oppositions in Aristotle, Met., I, 5, 986: πέρας-ἄπειρον; περιττόν-ἄρτιον; ἓν-πλῆθος; δεξιόν-ἀριστερόν;... φῶς-σκότος; ἀγαθόν-κακόν, etc.). The discords are reconciled in an accord that is numerical accord: so that it results that "the whole heaven is harmony and number" (cf. Aristotle, Met., I, 5). The Pythagoreans then, speculating on individual numbers, attributed to them particular virtues and significations: and they held in special account, besides the One and the Two, principles respectively of the odd and the even, the Four and the Ten, perfect numbers. To this arithmology, so to speak, metaphysical, was moreover associated positive mathematics (discovery of the incommensurable, successive approximations to √3, method of application of areas, etc.).
The Pythagorean theology was, it appears, oriented in a monotheistic sense: that is, it admitted a supreme God above the gods; but it is doubtful whether this doctrine was developed philosophically in connection with arithmology, and whether God was for them identical with the One understood as the original principle (cf. Zeller-Mondolfo, I, 2 [v. bibl.], pp. 457-74). The cosmology of the school, at first akin to the conceptions of the early Ionians, later developed into a system that considered the earth as rotating like the sun and a supposed "counter-earth," around a central fire. Icetas admitted the rotation of the earth around its own axis and thus explained the alternation of day and night (Cicero, Acad. prior., 2, 39, 123). Another Pythagorean theory is that of the harmony of the spheres.
In psychology, the school considered the human soul as an eternal substance, of divine origin, joined by way of penalty to a body and destined to transmigrate from body to body, and not only into bodies of men, but also of beasts or plants (παλιγγενεσία, not μετεμψύχωσις, is the word probably used by the ancient Pythagoreans). In its union with the body, the soul is enclosed as in a tomb (Philolaus, fr. 14 D; Plato, Gorg., 493 A). The incarnations will last until the soul itself has been purified and made worthy of returning to its heavenly homeland. How this conception itself (which was later taken up by Plato) was connected by the Pythagoreans with arithmology is not very clear.
Pythagorean ethics, religiously inspired, prescribed for man the imitation of the Divinity, and inculcated purity of life, measure and harmony in all activities, and furthermore the cultivation of wisdom as a means of salvation.
Pythagoreanism had great influence on Greek thought, and especially on Platonism (v.). The school, extinct in the 4th century B.C., rose again later, from the 1st century onward, in an eclectic form (v. NEO-PYTHAGOREANISM).