COSMOS. Like many philosophers of the 6c & 5c B.C.E. he was an agnostic on theological questions. His great fame in the history of philosophy stems partly from his personal integrity and partly from his famous doctrine that:
A human being is the measure of all things--of things that are, that they are, and of things that are not, that they are not. (McKirahan translation)Despite a long and continuing scholarly debate as to what he may precisely have meant by this, there can be little doubt that he intended this precept to establish both the centrality of practical, moral & socio-political questions in philosophical reflection and a deep and abiding skepticism about all efforts to arrive at ultimate or absolute truths about the nature of things
PERI PHYSEOS. Unlike some of the more radical sophists, such as Thrasymachus azs repredented by Plato in Republic. Bk. I, Protagoras does not seem to have employed his skeptical relativism in wholesale attacks on coventional morality and tradition. His adopted countrymen, the Athenians, confirmed this judgment when they appointed him lawgiver to their colony at Thurii, etstablished in 444/43.
Pythagoras seems to have believed that the soul is sentenced to a cycle of reincarnations, in plant, animal, and human form, from which release and immortality can be achieved through purity of life. He held that inquiry (HISTORIA) is an essential element of the pure life. A strong ancient tradition attributes the discovery of the mathematical ratios underlying consonant intervals to Pythagoras. He may also have dicovered the theorem of geometry that bears his name, although it is almost certain that Euclid's proof of that theorem comes from a later source.
When he left Samos and migrated to Croton where he established a community based in a religious life. It soon became one of the most prosperous cities in the western Greek world, but civil strife seems eventually to have convinced him to move once again. He died in Metapontum.