Pythagoras

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Pythagoras of Samos (traditionally c. 570 – c. 495 BCE) was a Greek thinker and the founder of a religious and philosophical brotherhood at Croton, in southern Italy, remembered above all for the conviction that number is the key to the order of things. He wrote nothing that survives, and may have written nothing at all; what is known of him comes through followers and, increasingly, through admirers writing centuries after his death.

That distance is the central problem. The earliest near-contemporary references treat him less as a mathematician than as a teacher of the soul’s fate — a man who claimed to recall his former lives and who promised something about what happens after death. The full portrait of Pythagoras the geometer, musician, and cosmologist comes mainly from late sources, above all the Neoplatonist biographers Porphyry and Iamblichus, writing some eight centuries on, by which time he had become a near-divine sage to whom almost any ancient wisdom could be credited. Scholarship has therefore grown cautious: the theorem that bears his name was known to Babylonian calculators long before him, and how much of “Pythagorean” mathematics is his own remains genuinely uncertain.

What the tradition consistently ascribes to him are two linked ideas. The first is metempsychosis — the transmigration of souls — the teaching that the same soul is reborn across bodies, human and animal alike, which gave the community its vegetarianism and its rules of purity. The second is the discovery that musical concord rests on whole-number ratios: that a string halved sounds the octave, and simple proportions yield the harmonious intervals. From this the Pythagoreans drew the larger claim that number underlies everything, and that the cosmos itself is an ordered, sounding whole — the source of the later image of the harmony of the spheres.

The brotherhood was as much a way of life as a school: shared property, silence imposed on novices, dietary restriction, and a body of oral precepts. Its members became a political force in the Greek cities of Italy and were violently driven out, scattering the movement while spreading its ideas.

The afterlife of those ideas is long. Plato absorbed Pythagorean mathematics and soul-doctrine deeply enough that the two are hard to disentangle; later antiquity produced a revived Pythagoreanism that fed directly into Neoplatonism. The notion that mathematical proportion is the hidden script of the universe ran on through Kepler’s search for celestial harmonies and the early-modern study of musical ratios, and number-mysticism of every later kind has claimed him as ancestor. Across all of it the historical man stays out of reach, visible only in the doctrines others carried in his name.

→ In the library: Westcott — Numbers: Their Occult Power and Mystic Virtues (1911)

→ Related: Neopythagoreanism · Neoplatonism · Johannes Kepler · Marin Mersenne · The One