Pythagoreans and Plato
Pythagoras (6th century B.C.) was a religious leader, and a proponent of a new way of living. We are not aware of the exact content of his teachings. In examining the Pythagoreans of the classical times, we discern two characteristics of the Pythagorean School: the conviction that numbers are the principles of beings; and the doctrine of reincarnation.
The Pythagoreans had already established their position in the spiritual life of the time of Plato and Aristotle. The most advanced achievements in the fields of mathematics and astronomy were induced by Pythagoreans. The theory of music, an advantageous discipline for the Pythagoreans, was brought forward as an autonomous branch of mathematics. Lastly, appreciable was the idiosyncrasy of the Pythagorean tradition in philosophy; a tradition defined by the primordial significance it ascribed to numbers.
It is generally assumed that Plato was influenced by the Pythagorean world-view: he affirms the immortality of the soul and the doctrine of reincarnation; he introduces the "hypothetical method" of mathematics into philosophy; he submits the prospective governors of his ideal city to a ten-year study of mathematics; and, via Timaeus, a philosopher from South Italy, he proffers a fascinating -and Pythagorean in origin- mathematical cosmology. Moreover, Plato establishes the Academy in the same way that the closed Pythagorean communities were organized. Therefore, it has been said, and not without good reason, that Plato, especially in his late period, was "Pythagorizing". In support to that claim, Plato in his so-called "unwritten doctrines" -that is, his oral, unregistered teachings- appeals to numbers which he identifies with the Forms. The number yields the organic relation between One and Many, unity and multitude.