Pythagoras

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Pythagoras of Samos (traditionally c. 570 – c. 495 BCE) was a Greek sage and the founder of a religious and philosophical brotherhood at Croton, in southern Italy, remembered above all for two linked convictions: that the soul is immortal and passes through many births, and 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.

From Samos to Metapontum

He was born on Samos, off Miletus where Greek philosophy was being born; his father was Mnesarchus — the oldest fact on record, for Heraclitus already names “Pythagoras, son of Mnesarchus,” conceding that he “practiced inquiry most of all men.” The tradition sends him east for his wisdom, to Egypt above all and on to Babylon; the Egyptian thread is early — Herodotus and Isocrates gesture toward it — but the full itinerary, letter from Polycrates to the pharaoh Amasis included, is embroidery from Diogenes Laertius eight centuries later. Ion of Chios already ties him to Pherecydes of Syros, his remembered teacher.

At forty, by Aristoxenus’s reckoning, he found Polycrates’ tyranny unbearable and left — the anchor that sets his birth near 570. Around 530 BCE he arrived at Croton, where the following gathered. Diogenes Laertius reports nearly three hundred followers governing the city, “in effect a true aristocracy”; seventeen named women close Iamblichus’s catalogue of Pythagoreans.

The brotherhood was as much a way of life as a school: possessions in one common stock — Timaeus credits him with the saying “friends have all things in common” — five years of silence for novices, rules of purity, dietary restriction, and a body of oral precepts: an initiatory discipline closer to the mystery religions than to any later school. The famous vegetarianism, though, is a later simplification. Aristoxenus says he ate meat, abstaining only from plough oxen and rams, and even denies the bean taboo — the master valued beans “most of all vegetables”; Aristotle has the Pythagoreans shun the womb, the heart, the sea anemone, but “use all other animal food”; only Eudoxus makes him a total abstainer. The prudent verdict: he did not forbid all animal food — the strict vegetarian is the idealized later portrait.

The brotherhood became a political force in the Greek cities of Italy, and the reaction came in two waves later writers fused into one. Around 510 BCE the conspiracy of Cylon at Croton drove Pythagoras to Metapontum; the burning of the meeting house of Milo at Croton, which only Lysis and Archippus escaped, came around 450, forty years after his death — “the leading citizens of each city were destroyed,” Polybius records. The scattering that broke the movement also spread its ideas, a story that belongs to Pythagoreanism at large.

Diogenes Laertius collects four endings: caught at a bean field he would not cross, choosing to be “killed rather than prate about his doctrines”; starved forty days in the temple of the Muses at Metapontum (Dicaearchus); starved himself after burying Pherecydes on Delos (Heraclides); fell in a war of Agrigentum and Syracuse, again balked by a beanfield (Hermippus). The bean-field flight is a floating motif, told of other Pythagoreans too — legend shaped by the taboo, not memory. The soberest line, Aristoxenus and Dicaearchus, has him die at Metapontum around 490 BCE.

The sources problem

Pythagoras had no contemporary chronicler. Before Aristotle there are roughly twenty brief references, and they make him not a mathematician but an expert on the soul’s fate and ritual, a wonder-worker, the founder of a way of life — said to recall his former lives and to promise something about what happens after death. The first detailed accounts, a hundred and fifty years on, survive only in disagreeing fragments; the reliable fourth-century layer is Aristotle’s lost treatise, Aristoxenus, Dicaearchus, and Timaeus. The three extant Lives — by Diogenes Laertius, the most sober; by Porphyry; and by Iamblichus — come some eight hundred years after his death and lean on Neopythagorean intermediaries.

By the third century BCE three books circulated under his name, forgeries authenticated by a forged letter of Plato; by the first century BCE a whole pseudo-Pythagorean library existed; in the late Lives he is a near-divine sage to whom almost any ancient wisdom could be credited — “a soul sent from the gods to enlighten mankind,” Iamblichus says. The elevation had an edge in an age of advancing Christianity: Alexander Severus worshiped Apollonius of Tyana, heir to the whole Pythagoras pattern, alongside Christ, Abraham, and Orpheus, and the late Lives’ Pythagoras reads as a pagan counterpart to Christ. All three are in public-domain English: Taylor’s 1818 Iamblichus (https://www.gutenberg.org/files/63300/63300-h/63300-h.htm), Guthrie’s 1919 Porphyry with the Photius epitome (https://archive.org/details/1919-guthrie-life-of-pythagoras), and Hicks’s 1925 Diogenes Laertius VIII (https://en.wikisource.org/wiki/Lives_of_the_Eminent_Philosophers/Book_VIII).

The wandering soul

At the center of his teaching is metempsychosis: the soul is immortal, and at death it passes into another body, human or animal, to live again — the one doctrine the earliest evidence secures. Xenophanes, his contemporary, mocked it in verse: “once when he was present at the beating of a puppy, he pitied it and said ‘stop, don’t keep hitting him, since it is the soul of a man who is dear to me, which I recognized, when I heard it yelping.’” Herodotus already orbits him — the Hellespontine Greeks made the Thracian Zalmoxis his onetime slave, and the Egyptian doctrine of rebirth through every animal in three thousand years was, he says, adopted by “some Greeks both earlier and later” — read since antiquity as Pythagoras the earlier. Dicaearchus lists his four most recognized doctrines: the soul is immortal; it passes into other kinds of animals; what has happened happens again and “nothing is absolutely new”; all animate beings are kin. The chain of his own remembered lives — Aethalides, Euphorbus the Trojan, Hermotimus, Pyrrhus the fisherman, Pythagoras — is fourth-century elaboration from Heraclides and Dicaearchus. Its career across traditions is surveyed under reincarnation; among the Greeks it begins with him.

The akousmata and the tetraktys

The akousmata (“things heard”), or symbola, were the school’s oral maxims, quoted earliest by Aristotle: pour libations from the ear of the cup; enter temples barefoot; do not stir the fire with a knife. The bean prohibition, most famous of all, is first attested by Aristotle, who already guessed at its reason: the gates of Hades, the genitals, the lots of oligarchy. Some took question-and-answer form: What is the oracle at Delphi? The tetraktys, which is the harmony in which the Sirens sing.

That answer, preserved by Iamblichus and probably from Aristotle, carries the number-teaching as the tradition gives it to the Master: the tetraktys — the first four numbers, summing to the perfect ten — holds the harmony of the cosmos, and the school swore its oath by “the one who handed down the tetraktys to our generation”; the system built on it belongs to Pythagorean arithmology. After his death the movement divided between the akousmatikoi, who kept the maxims as a rule of life, and the mathēmatikoi, who pursued the demonstrations — the hearers insisting the mathematical philosophy descended from Hippasus, not Pythagoras — a fifth-century split among heirs, not the founder’s. Whether the akousmata governed a life hedged by taboo (Burkert), are largely later literary construction (Zhmud), or were followed and interpreted from the start remains a live question.

Number, harmony, and the heavens

The early formula is Aristoxenus’s: Pythagoras “honored and advanced the study concerned with numbers, having taken it away from the use of merchants and likening all things to numbers.” Likening, not calculating: in the earliest stratum numbers carry correspondences — three the male, two the female, five marriage — not theorems. Music anchored it: the octave, the fifth, and the fourth sound from the whole-number ratios 2:1, 3:2, and 4:3 — a string halved sounds the octave — and those four numbers are the tetraktys. The ratios are real, secure by Philolaus’s generation. The discovery legend is not: the blacksmith’s-shop tale — concords caught from hammers whose weights stood in the sacred proportions — first told by Nicomachus and repeated by Iamblichus, is acoustically impossible: pitch does not vary with hammer weight, and a string’s pitch varies as the square root of its tension. The first working experiment on record belongs to Hippasus, after his death — Pythagoras knew the relationship without having discovered or demonstrated it. The theorem that bears his name tells the same story: Babylonian calculators generated triples long before him, and no proof by Pythagoras is attested — only two lines of verse about an ox sacrificed for “that famous diagram.” How much of “Pythagorean” mathematics is his own remains genuinely uncertain.

What can be carried back to him is a cosmos of moral and numerical meaning: the sun and moon are the Isles of the Blest, the planets the hounds of Persephone, thunder a threat to the souls in Tartarus. The tradition is unanimous that the Master heard the music the heavens make, and the harmony of the spheres descends from that conviction; yet it is doubtful he himself thought in spheres. The first spheres-cosmology in the school is Philolaus’s; “number is the nature of things” as a system is Aristotle’s report on the Pythagoreans of Philolaus’s century. The ratio-cosmos and its long career are treated under Pythagorean–Platonic harmonics.

The wonder-worker

The marvels are not late ornament but the record’s earliest layer. Aristotle’s fragments already carry the golden thigh; the Crotoniates’ name for him, the Hyperborean Apollo; the secret teaching that “of rational beings, one sort is divine, one is human, and another such as Pythagoras”; bilocation at Metapontum and Croton on the same day and hour; the river that rose to greet him. Abaris the Hyperborean priest, presenting his arrow, may go back to Aristotle as well. Heraclitus’s sneer at the “chief of the charlatans” is the hostile reception of precisely this persona, admired and attacked in his own lifetime; the divine sage of the late Lives amplifies something genuinely old.

The figure’s afterlife

Plato names Pythagoras exactly once — in the Republic, as the founder of a way of life — yet he absorbed Pythagorean mathematics and soul-doctrine deeply enough that the two traditions are hard to disentangle. The conduit was the fifth-century school, Philolaus and Archytas, not any writing of the founder; and it soon ran the other way: Plato’s successors — Speusippus, Xenocrates, Heraclides — presented his late metaphysics of the One and the Indefinite Dyad as anciently Pythagorean, though Aristotle states plainly that the Dyad is Plato’s own. The Neopythagoreans completed the retrojection, and Platonism thereafter wore Pythagoras as its pedigree; later antiquity’s revived Pythagoreanism — Neopythagoreanism — fed directly into Neoplatonism.

The most read text under his name is the Golden Verses, seventy-one Greek hexameters of moral counsel — a compilation of materials of different dates, assigned anywhere from 350 BCE to 400 CE and not cited by name until about 200 CE. Hierocles of Alexandria, the fifth-century Neoplatonist, wrote the standard commentary; in the Renaissance the Verses became one of the most popular Greek texts, a schoolbook for learning the language. Marsilio Ficino translated Hierocles’s commentary and thirty-nine symbola and placed Pythagoras in the prisca theologia — the ancient theology descending through Zoroaster, Hermes Trismegistus, and Orpheus to Pythagoras, Plato’s immediate predecessor — taking the late-antique forgeries for genuine pre-Platonic wisdom. The sage of Samos thus became a hinge of esoteric genealogy, a revival that belongs to Renaissance Neoplatonism; Firth’s 1904 compilation of the Verses with Hierocles material is the accessible public-domain gathering (https://sacred-texts.com/cla/gvp/index.htm). The conviction that mathematical proportion is the hidden script of the universe ran on through Johannes Kepler’s celestial harmonies and Marin Mersenne’s early-modern musical ratios; numerology and number-mysticism of every later kind has claimed him as ancestor.

The scholarship

Modern study divides at Walter Burkert’s Lore and Science in Ancient Pythagoreanism (Harvard University Press, 1972; German original 1962), which tested every later report against the earliest evidence and reversed the picture: the Pythagoras the sources support is the religious founder and wonder-worker; mathematics and rational cosmology enter with Hippasus and Philolaus. Carl Huffman’s Stanford Encyclopedia of Philosophy article (https://plato.stanford.edu/entries/pythagoras/), the open reference of record, has all modern scholarship standing on Burkert’s shoulders — and notes that the consensus has lately received strong challenges. The strongest is Leonid Zhmud’s Pythagoras and the Early Pythagoreans (Oxford University Press, 2012; https://doi.org/10.1093/acprof:oso/9780199289318.001.0001), which rejects the travel legends wholesale yet restores Pythagoras as a genuine mathematician between Thales and Hippocrates of Chios, and argues the religious and miraculous elements grew over time rather than shrinking. Between them stand Charles Kahn’s Pythagoras and the Pythagoreans: A Brief History (Hackett, 2001), a compact conceptual history more generous toward early scientific content, and Christoph Riedweg’s Pythagoras: His Life, Teaching, and Influence (Cornell University Press, 2005), the standard one-volume biography, pressing the minority case that he wrote books and stands behind the very word “philosophy.” Huffman’s edited A History of Pythagoreanism (Cambridge University Press, 2014; https://doi.org/10.1017/CBO9781139028172) gives the per-topic state of the art, Johan Thom’s The Pythagorean Golden Verses (Brill, 1995; https://doi.org/10.1163/9789004295841) the standard edition and dating study, and Huffman’s companion Stanford article (https://plato.stanford.edu/entries/pythagoreanism/) the school’s later history.

Across all of it the historical man stays out of reach, visible only in the doctrines others carried in his name — the deathless, wandering soul; the number at the root of the world.

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

→ Related: Pythagoreanism · Neopythagoreanism · Pythagorean Arithmology · Pythagorean Platonic Harmonics · Plato · Reincarnation · Iamblichus · Apollonius Of Tyana · Neoplatonism · Johannes Kepler · Marin Mersenne · The One