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What Lies Behind Pythagoras' Theorem

Pythagoras has been upheld as the most influential of all thinkers.

Pythagoras (570-500 BC) was born on the island of Samos in what is now Greece. On the advice of Thales of Miletus, he travelled to Memphis in Egypt where he came into contact with priests renowned for their wisdom. At the age of 40, he fled the tyranny of Polycrates to Croton in Southern Italy, where he established a philosophical and religious community. Those who entered the community’s inner circle were governed by a strict set of ascetic and ethical rules, forsaking personal possessions, assuming a mainly vegetarian diet, and—since words are so often careless and misrepresentative—observing the strictest silence. Some of the community’s more eccentric rules, such as 'do not break bread' or 'do not poke the fire with a sword' may have been riddles or allegories that required interpreting. Pythagoras’ brotherly community has been hailed as a prototype for later philosophical institutions such as Plato’s Academy, Aristotle’s Lyceum, and Epicurus’ Garden, and, indeed, for the monastic life and associated early universities. 

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Music played an important role in Pythagoras’ community. Pythagoreans recited poetry, sang hymns to Apollo, and played on the lyre to cure illnesses of both body and soul. It is said that, one day, Pythagoras passed by some blacksmiths at work, and found that their hammering on anvils produced especially harmonious sounds. He then found that the anvils were simple ratios of one another, one being half the size of the first, another two thirds of the size, and so on. This discovery of a relationship between numerical ratios and musical intervals led Pythagoras to believe that the study of mathematics was the key to understanding the structure and order of the universe. According to his ‘harmony of the spheres’, the heavenly bodies move according to mathematical equations that correspond to musical notes and form part of a grand cosmic symphony.

Pythagoras never separated religion from science and philosophy, which, even in his day, left him open to accusations of mysticism. No doubt under the influence of Orphism, an Ancient Greek mystery religion that arose from pre-Hellenic beliefs and the Thracian cult of Zagreus, he believed in the transmigration of the soul; that is, in the reincarnation of the soul over time into the bodies of human beings, animals, or plants (metempsychosis) until such a time as it became moral. He claimed to have lived four lives and to remember them all in great detail, and once recognized the cry of his dead friend in the yelping of a puppy. After his death, the Pythagoreans deified him, and attributed him with a golden thigh and the gift of bilocation (being in two places at once). But in his own lifetime Pythagoras had always been a paragon of modesty, declining to be called a ‘wise man’ or 'sophos', and preferring instead to be called ‘a lover of wisdom’ or 'philosophos'—thereby coining the term 'philosopher'.

It is said that Numa Pompilius, the second king of Rome, had been schooled by Pythagoras, whence his great wisdom and piety. This story is referred to and discredited by Plutarch and Livy, not least because the dates do not tally, with Pythagoras having lived from about 570 to 500 BC, and so considerably later than the semi-legendary King Numa. Even though Pythagoras and Numa never met, Pythagoras and the Pythagoreans exerted a strong influence on the Roman mind. In the Tusculan Disputations, Cicero indicates that Pythagoras rose to fame in southern Italy at just the same time that Brutus brought an end to the monarchy, and that many Roman usages derived from the Pythagoreans. Unfortunately, he does not elaborate on the nature of these usages. In his Natural History, Pliny the Elder tells us that, in 343 BC, during the war with the Samnites, the god Apollo ordered the Romans to erect one statue to the wisest and another to the bravest of all Greeks, with their choices falling upon Pythagoras for the former and Alcibiades for the latter. Pliny expresses surprise that they picked Pythagoras over Socrates, whom Apollo himself had called the wisest of all men. But the fact is that the Romans liked to think of the Greek-Italian Pythagoras as their very own philosopher, and spun all sorts of stories, such as the one about Numa, to better appropriate him.

Apart from this, Pythagoras also exerted a strong indirect influence on Roman thinking, and indeed on all philosophy and theology, through the teachings of Plato, the principal architect of the western mind. Aristotle, who was Plato’s pupil of twenty years, claimed that his master’s teachings owed much to those of Pythagoras; so much, in fact, that, in his History of Western Philosophy, Bertrand Russell upheld not Plato but Pythagoras as the most influential of all Western philosophers. Pythagoras’ influence is especially evident in Plato’s mystical approach to the soul and in his emphasis on mathematics and, more generally, abstract thinking, as a secure basis for the practice of philosophy.

Neel Burton is author of The Meaning of MadnessThe Art of Failure: The Anti Self-Help GuideHide and Seek: The Psychology of Self-Deceptionand other books.

Find Neel Burton on Twitter and Facebook 


Neel Burton, M.D., is a psychiatrist, philosopher, and writer who lives and teaches in Oxford, England.


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