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).

Pythagorass 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 Pythagorass precise thinking. All that we know of him comes from fragments, apparently written by his disciples.

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The Great Philosophers: Pythagoras was a mystic who believed in immortality - The Independent