The Pythagoreans were both a religious society and a school of philosophers. They were originally located in Kroton, a Greek colony on the toe of the Italian peninsula. Their name was taken from the reputed head of the school who contributed to both the field of philosophy and the field of mathematics. (You may recall "the Pythagorean Theorem" from high school geometry.) Among other things, the Pythagoreans believed in transmigration of the soul, spiritual purification through study, and the identification of reality with number.