PYTHAGORAS. The ancient tradition presents different images of Pythagoras (c. 570 BCE–c. 500 BCE) that hardly square with one another: philosopher and initiator of rational inquiry, scientist and mathematician, politician and lawgiver, and religious wonderworker and leader of a sect of initiates. Surely he was an extraordinary personality and a charismatic chief, venerated by his followers and desecrated by his opponents. Soon he became a legend, whose historical nucleus is difficult to ascertain. The very nature of the association he founded is consequently controversial: it is mainly described as a philosophical school where scientific inquiries were practiced, as a political party, or as a religious confra-ternity.

The main sources on Pythagoras, while plentiful, are late and rarely impartial; for the most part they are cast in the distorting light of hostile polemic or religious veneration. Whether Pythagoras left any writing was in ancient times already controversial and is still...