Pythagoras (c570-c495 BCE) was an ancient Greek philosopher and mathematician, and the founder of a religious community in southern Italy. The adjective from Pythagoras is Pythagorean, and the noun for Pythagoras’ distinctive beliefs is Pythagoreanism.
Pythagoras was born on the island of Samos (in the eastern Aegean Sea) and in c 530 BCE emigrated to the city of Croton (modern Crotone in southern Italy), where he founded an ascetic religious community. Pythagoras and his followers established themselves as the government of the city, but eventually the local population rose up against them. Pythagoras was forced to leave Croton and retired to the neighbouring city of Metapontum, where he died.
Although Pythagoras, like Socrates, wrote nothing, aspects of his teaching – in particular, his interest in numbers and his religious beliefs – exercised a considerable influence on many later thinkers in the ancient world.
Pythagoras was interested in numbers and the relations between them. He discovered the numerical basis of the principal intervals of the musical scale (i.e., that the octave is based on the ratio 2:1, the fifth on the ratio 3:2, and the fourth on the ratio 4:3). He may also have discovered what has come to be called Pythagoras’ theorem (i.e., that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides)- though it is unlikely that he was familiar with the theorem in this geometrical formulation. No doubt encouraged by these discoveries, Pythagoras believed that numbers provide the key to a proper understanding of the world. As Aristotle says in his summary history of Greek philosophy in Metaphysics I, ‘the Pythagoreans assumed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number’ (I 5, 986a1-3).
Pythagoras believed that a person’s soul and body are two distinct and separable entities; that our souls are divine in origin but have fallen from grace and must be punished by undergoing a series of embodiments, sometimes in human form, sometimes in the body of another species of animal, and sometimes as a plant; and that salvation, escape from this cycle of reincarnation, is possible only when the soul has attained its original state of purity, which is to be achieved through certain ascetic practices and through study – intellectual activity thus having for Pythagoras a religious aspect.
The religious community which Pythagoras founded in Croton reflected these beliefs. Its members, who, remarkably for the period, included women, followed an austere way of life: they abstained from eating meat, observed periods of silence and self-examination, and devoted much of their time to study. The community survived Pythagoras’ death but did not outlast the fifth century BCE.
Neopythagoreanism is the term applied to the revival of Pythagoreanism in Rome and Alexandria in the first century BCE and the first and second centuries CE, when a number of philosophers (such as Apollonius of Tyana (c15-c100 CE) and Nicomachus of Gerasa (c60-c120 CE)) combined aspects of Pythagoras’ thought with elements from the philosophies of Plato, Aristotle, and the Stoics.