Pythagoras was a mystic who believed in immortality

It is well known that Pythagoras – supposedly – came up with the theorem that allows us to calculate the length of the hypotenuse of a right-angled triangle from the length of its sides. It is less well-known that he was a mystic who founded a religion that emphasised a belief in immortality and the transmigration of souls (a kind of reincarnation, in which the soul enters an already existing body rather than a newborn).

Pythagoras’s ideas about the triangle were only a small part of the contribution he made to the history of mathematics. His work on the mathematical foundations of music is probably the most significant. Legend has it that he first came to an understanding of the link between music and maths while observing a blacksmith at work. He noticed that there was a relationship between the size and weight of the blacksmith's hammer and the pitch of the note that was produced as it struck the anvil. It appeared that music was governed by maths.

For Pythagoras and his followers, this was indicative of the ultimate nature of reality: behind the play of appearances, they believed, “all things are number”. Precisely what this means, however, isn't entirely clear, since history has not been kind in leaving us clues to Pythagoras’s precise thinking. All that we know of him comes from fragments, apparently written by his disciples.

The significance of Pythagorean ideas reaches out in at least two different directions. The notion that the structure of reality is ultimately mathematical was a precursor to attempts to analyse the universe in mathematical and scientific terms.

Plato noted that there was a certain style of living associated with the followers of Pythagoras, defined by an interest in philosophy, music, mathematics and astronomy. Although we know little about the details of the ideas of the Pythagoreans, we do know that these had an impact on the development of early Greek philosophy.