All that is known of the life of Pythagoras with any certainty is that he left his birthplace, Samos, in about 520 bc to settle in Croton (now Crotone) in southern Italy and, as a result of political trouble, made a final move to Metapontum in about 500.

In Croton Pythagoras established his academy and became a cult leader. His community was governed by a large number of rules, some dietary, such as those commanding abstinence from meat and from beans, and others of obscure origin, such as the commands not to let a swallow nest under the roof or not to sit on a quart measure.

The movement was united by the belief that “all is number.” While the exact meaning of this may be none too clear, that it led to one of the great periods of mathematics is beyond doubt. Not only were the properties of numbers explored in a totally new way and important theorems discovered, of which the familiar theorem of Pythagoras is the best example, but there also emerged what is arguably the first really deep mathematical truth – the discovery of irrational numbers with the realization of the incommensurability of the square root of 2.