Pythagoras

Pythagoras of Samos was a Greek teacher of the sixth century BCE who founded a community of followers in southern Italy bound by a strict way of life and a belief in the immortality and rebirth of the soul. His name is attached to a famous theorem and to the idea that number underlies the order of the universe, but he wrote nothing, and both claims owe more to his later followers than to anything that can be traced to him. Few figures in Greek thought are so famous and so poorly documented.

Almost everything said about Pythagoras comes from writers who lived long after him. The earliest references, in Xenophanes, Heraclitus and Herodotus, are brief and show that he was already well known around 500 BCE as a man of wide learning and as a teacher about the fate of the soul. In the fourth century BCE, Plato mentions him only once by name, and Aristotle, who wrote a lost book on the Pythagoreans, usually speaks of "the so-called Pythagoreans" rather than of Pythagoras himself. Aristotle's pupils Aristoxenus and Dicaearchus collected traditions about his life that modern scholars treat as the most reliable available.

The full biographies, by Diogenes Laertius, Porphyry and Iamblichus, date from the third and fourth centuries CE. By then Pythagoras had become a semi-divine sage in Neoplatonist circles, and these lives credit him with miracles: appearing in two cities at once, being greeted by a river, having a golden thigh. Plato and his successors had also come to attribute to Pythagoras much of their own mathematical philosophy. The great modern study by Walter Burkert concluded that the picture of Pythagoras as a mathematician and scientist is largely a later construction, and most scholars now agree that he is best understood first as a religious and ethical teacher.

Pythagoras was born on the island of Samos, off the coast of Ionia, around 570 BCE; his father, Mnesarchus, is described as a gem engraver or merchant. Later writers say he travelled widely, studying in Egypt and Babylonia and meeting Thales, but these journeys may be inventions designed to explain where his wisdom came from. According to Aristoxenus, he left Samos at about forty to escape the tyranny of Polycrates, who seized power around 535 BCE.

He settled around 530 BCE in Croton, a Greek colony in the south of what is now Italy, where he quickly gained influence. Dicaearchus reports that he addressed the city's elders, its young men, its women and its children, and that a society of followers formed around him. The Pythagoreans gained political power in Croton and other cities of the region. Around 510 BCE a backlash against the group, perhaps provoked by its exclusive character, forced Pythagoras to move to Metapontum, where he is said to have died around 495 BCE. Violent attacks on Pythagorean meeting houses continued in the following decades, scattering the movement across the Greek world.

The best-attested teaching of Pythagoras is metempsychosis, the transmigration of souls: the belief that the soul is immortal and is reborn in new bodies, human or animal. Xenophanes mocked him for telling a man to stop beating a puppy because he recognised in its cries the voice of a dead friend. Later stories say Pythagoras claimed to remember his own previous lives, including as a warrior in the Trojan War.

This belief was tied to a disciplined way of life. Pythagoreans followed rules called akousmata, oral sayings that mixed moral advice with ritual taboos: abstain from beans, do not stir a fire with a knife, put on the right shoe first. Some sources say they avoided meat, or certain kinds of meat, which would fit a belief that animals may house human souls, though the ancient evidence is contradictory. Members were expected to keep the teachings secret, to share property in some form, and to examine their conduct daily. Women took part in the community, unusually for the time. After Pythagoras died, his followers reportedly split into two groups: the akousmatikoi, who kept the sayings and rituals, and the mathematikoi, who pursued mathematical study.

The idea most associated with Pythagoreanism is that the cosmos is ordered according to number. A traditional story credits Pythagoras with discovering that the main 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. Aristotle reports that the Pythagoreans took such discoveries as evidence that things are, in some sense, numbers, and developed a cosmology involving opposites such as limit and the unlimited. Much of this, however, is documented first in the work of Philolaus, a Pythagorean of the later fifth century BCE, and cannot be securely traced back to Pythagoras.

The theorem that bears his name, that in a right-angled triangle the square on the longest side equals the sum of the squares on the other two, was known in practice to Babylonian mathematicians more than a thousand years earlier. The story that Pythagoras proved it and sacrificed an ox in celebration appears only in late sources. He may have had an interest in numbers with a religious or symbolic dimension, but there is no reliable evidence that he produced the proof later set out by Euclid.

Whatever Pythagoras himself taught, the tradition that grew from him was deeply influential. Plato's dialogues, especially the Phaedo and the Timaeus, draw on Pythagorean ideas about the immortal soul and a mathematically ordered universe, and through Plato these themes became central to later ancient Greek philosophy. In the first centuries CE a Neopythagorean revival, and then Neoplatonists in the school of Plotinus, notably Porphyry and Iamblichus, turned Pythagoras into a model of the philosopher as holy man.

In the Renaissance and early modern period, the belief that nature is written in mathematics encouraged thinkers such as Nicolaus Copernicus and Johannes Kepler, who sought harmonic ratios in the orbits of the planets. Vegetarians were often called Pythagoreans until the nineteenth century. Pythagoras thus survives as several figures at once: a historical religious teacher in Croton, a founder claimed by later philosophers, and a symbol of the union of mathematics and mysticism.