Pythagoras and His School at Croton (c. 530 BC)

Pythagoras of Samos was a Greek philosopher and religious teacher who, around 530 BC, settled in Croton in southern Italy and founded a community of followers that became one of the most influential schools of the ancient world. The Pythagoreans combined mathematics, music and a belief in the rebirth of souls with a strict way of life. Pythagoras himself wrote nothing, and separating the historical man from centuries of legend is one of the hardest problems in the history of philosophy.

The problem of the sources

Very little is known of Pythagoras for certain. The few early references, from writers who lived in or near his own time, are brief. The detailed Lives of Pythagoras were written by Diogenes Laertius, Porphyry and Iamblichus in the third and early fourth centuries AD, more than 700 years after his death, when he had become a semi-divine figure.

Aristotle, in the fourth century BC, wrote about the “so-called Pythagoreans” and seems careful not to credit Pythagoras with their mathematical ideas. Modern historians, following the work of Walter Burkert, generally see the historical Pythagoras as a religious teacher and charismatic leader more than a mathematician.

From Samos to Croton

Pythagoras was born on Samos, an island off the coast of Ionia, around 570 BC; his father Mnesarchus is said to have been a gem engraver. Later writers claim he studied in Egypt and Babylon and learned from Thales and Anaximander, but these stories cannot be confirmed.

Around 530 BC, perhaps to escape the rule of Polycrates, who became tyrant of Samos around 538 BC, Pythagoras moved to Croton. This was a prosperous Greek colony on the Ionian Sea coast of Calabria, one of the cities of Magna Graecia founded during the age of Greek colonization. Croton was famous for its doctors and athletes and for its great sanctuary of Hera Lacinia on a nearby headland.

The community at Croton

According to later accounts, Pythagoras quickly won influence through his speeches to the young men, the women and the city council of Croton. His followers formed a closed brotherhood. Members are said to have kept silent for long periods while learning, shared some property and kept the group’s teachings secret.

The community followed rules known as akousmata (“things heard”) or symbola. These included abstaining from beans, not stirring a fire with a knife, not stepping over a crossbar and wearing white clothing. Some rules may have had religious meanings now lost; others may be later inventions. Many sources say Pythagoreans avoided some or all meat, though the details vary.

Later tradition divided the followers into two groups: the akousmatikoi, who kept the rules and sayings, and the mathematikoi, who pursued deeper study. This division probably reflects disputes among Pythagoreans in the fifth century BC rather than the original organisation.

Unusually for a Greek philosophical group, women are said to have taken part. Later sources name several female Pythagoreans, above all Theano, described variously as Pythagoras’ wife or pupil. Letters and sayings attributed to her and other women survive, but most scholars think they were written centuries later, so they show how the tradition remembered women’s role rather than what the first members actually taught.

Teachings: souls, number and harmony

The best-attested teaching is the transmigration of souls, the belief that the soul is immortal and is reborn in new bodies, human or animal. A contemporary, the poet Xenophanes, mocked Pythagoras for supposedly stopping a man from beating a puppy because he recognised the voice of a dead friend in its cries. This joke is valuable evidence that the doctrine was linked with Pythagoras in his lifetime.

The early Pythagoreans are also associated with the discovery that musical intervals correspond to simple ratios of whole numbers: the octave to 2:1, the fifth to 3:2 and the fourth to 4:3. This finding encouraged the idea that number underlies the order of the cosmos, and later Pythagoreans spoke of the “harmony of the spheres”.

How much mathematics Pythagoras himself did is uncertain. The famous theorem about right-angled triangles was known in Babylonia over a thousand years earlier, as tablets such as Plimpton 322 show. It was attached to Pythagoras’ name by later writers, and there is no reliable evidence that he proved it.

Politics and the fall of the school

The Pythagoreans became politically powerful in Croton and other cities, and their influence was resented. In 510 BC Croton destroyed its rival Sybaris in war; the army, according to later sources, was led by the wrestler Milo of Croton, a six-time Olympic champion whom tradition counts as a follower of Pythagoras.

Soon afterwards an uprising led by a Crotoniate named Cylon turned against the brotherhood. Pythagoras left for Metapontum, where he is said to have died around 495 BC; dates as early as 500 BC and as late as 490 BC are given. Around the middle of the fifth century BC, violence against Pythagorean groups broke out across southern Italy and their meeting houses were burned, with many members killed.

Later Pythagoreans

Survivors carried the tradition to mainland Greece. Philolaus of Croton, active in the later fifth century BC, wrote the first known Pythagorean book, proposing that the earth moved around a central fire. Archytas of Tarentum, a friend of Plato in the fourth century BC, was a statesman, general and leading mathematician.

Plato was strongly influenced by Pythagorean ideas about the soul and mathematics. In the Roman period a Neopythagorean revival turned Pythagoras into a miracle-working sage, and much of the legend we know comes from this time. Euclid’s later Elements gathered geometry that owed something to Pythagorean work, though it is impossible to say how much.

Myths and facts

• Myth: Pythagoras invented the Pythagorean theorem. The relationship was known in Mesopotamia, and perhaps in India and China, long before him; the attribution comes from much later sources.
• Myth: Pythagoras discovered musical ratios by hearing a blacksmith’s hammers. This later story is physically impossible, because the pitch of a hammer blow does not depend on its weight in the way the tale claims.
• Myth: a Pythagorean was drowned for revealing irrational numbers. Late sources tell of Hippasus being punished for disclosing a secret, but the details differ and the story is regarded as legend.
• Fact: he was famous in his own lifetime. Xenophanes and Heraclitus both mention him, Heraclitus criticising his wide learning as lacking true understanding.

Timeline

• c. 570 BC: Pythagoras is born on Samos.
• c. 538 BC: Polycrates becomes tyrant of Samos.
• c. 530 BC: Pythagoras settles in Croton and founds his community.
• 510 BC: Croton destroys Sybaris.
• c. 509 BC or later: An uprising led by Cylon forces Pythagoras to leave for Metapontum (date uncertain).
• c. 495 BC: Approximate date of his death.
• c. 450 BC: Pythagorean meeting houses in southern Italy are attacked and burned.
• Late 5th century BC: Philolaus writes the first Pythagorean book.

Why it matters

Pythagoras and his followers gave Western thought one of its most powerful ideas: that the universe is ordered according to number and can be understood through mathematics. Their beliefs about the soul shaped Plato and later religion, and their name is still attached to a theorem taught in every school. Like Thales of Miletus before him, Pythagoras marks the moment when Greek thinkers began to seek the hidden structure of the world.