Philolaus comes almost a century after Pythagoras; he was a contemporary of Socrates and Democritus, but carried on a tradition more at home in the mode of thought of earlier thinkers.
He seems to have written a book, On Nature, the first by a Pythagorean. He has emerged from the shadow of Pythagoras and come to be recognized as an important Pre-Socratic thicker.
Philolaus is thought to be the first Pythagorean to have left a written work. It is for this reason that he has been included, achronistically, along with the Pythagorean School.
Philolaus taught philosophy and mathematics as well as engaging in political life. When the activity of the Pythagorean order became intolerable to the democracy, the order was ousted and Philolaus fled first to Lucania and then to Thebes for refuge.
He seems to have been deeply interested in number theory and mathematics, which he used to interpret man’s purpose and place in the state and the universe.
By applying mathematical concepts to cosmology, Philolaus seems to have brought Pythagorean traditions into the mainstream of Greek intellectual development.
He is also credited with the view that ‘soul’ is a mixture and harmony of the parts of the body.
Philolaus of Croton (470-385 BC)
