Pythagorean School of Ancient Greek Philosophy Texts

Pythagoras (c. 570–c. 490 BCE) founded the school after leaving Samos for Croton in southern Italy around 530 BCE, where he gathered a secretive community that joined philosophical inquiry to religious practice and political activity. The community prescribed a structured way of life under the maxim that all things are common among friends, and its members were traditionally divided into the ἀκουσματικοί, who held to the founder's rules and sayings, and the μαθηματικοί, who pursued mathematical inquiry.

The community's central religious doctrine was μετεμψύχωσις, the passage of the ψυχή into a new body after death. Because the ψυχή outlives the body, its condition had to be purified through ascetic practice and intellectual study in the hope of liberation. Alongside this stood the school's characteristic teaching about number: the Pythagoreans held that ἀριθμοί, numbers, are what things most truly are, and that the cosmos is ordered by mathematical ratio. The discovery that harmonious musical intervals answer to simple whole-number ratios became their standing example, extended into the claim that all natural phenomena belong to a single intelligible order.

Later doctrine worked these insights into a scheme of principles. Philolaus (fl. late 5th century BCE) wrote of limiters (πέρας) and unlimiteds (ἄπειρον), with number as the means by which the limiter structures the unlimited, and another group drew up a table of ten opposite principles, such as limit and unlimited, odd and even, one and many.

The brotherhood flourished at Croton until the mid-5th century BCE, when violent political opposition, including an attack on a meeting house in 510 BCE, broke its power. Its influence in Magna Graecia waned, though it was re-established in the 4th century BCE at Tarentum under Archytas (c. 420–c. 350 BCE), whose work in mathematics, harmonics, and mechanics gave the school renewed standing. Thereafter the ἀκουσματικοί largely dissolved or merged with movements such as Cynicism, while the μαθηματικοί were increasingly absorbed into the Platonic tradition. After a long dormancy Pythagorean ideas were revived in the 1st century BCE under the name Neopythagoreanism.