Neopythagoreanism

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Nine meters under the Via Praenestina, just inside the Porta Maggiore where two aqueducts cross at the eastern edge of Rome, lies a hall that no ancient writer records. A railway cave-in exposed it in 1917: a long sloping corridor opening into a vaulted basilica of three naves, its white stucco worked with scenes of sea-crossings, abductions, and a figure leaping from a cliff into the waters of release. It was built in the first half of the first century and sealed, it seems, in the reign of Claudius — walled up and forgotten within a generation of its making. No inscription names its builders. Scholars have read it as a tomb, a nymphaeum, a meeting-place; the reading that holds is that here a circle of Romans gathered to practice a philosophy that promised the soul a passage out of the body and back to its source. It is the one structure that can be set beside the texts, and it stands for the whole movement: an underground revival, unannounced, that took an old name and made it speak again.

Neopythagoreanism is the modern label for that revival — the recovery of Pythagorean philosophy in the Roman world from about the first century BCE, gathering the teachings credited to Pythagoras and fusing them with the metaphysics of Plato. By that date the historical Pythagoras lay five centuries in the past, and his original brotherhood at Croton had long since dispersed; what survived was a reputation for hidden wisdom, a body of moral precepts, and the conviction that number is the key to the order of things. The man and his sixth-century community belong to their own account, as does the early school known through Philolaus and Archytas; the later movement gathered the surviving threads and made them speak in the philosophical language of its own age. The gap is the central fact. Almost nothing of the founder’s actual teaching could be reached directly across those five hundred years, so the revival did not so much continue Pythagoreanism as reconstruct it — and, where reconstruction failed, invent it.

A literature wearing the mask of age

The school’s origins are hard to fix, precisely because it prized antiquity and liked to disguise new work as old. A great deal of the Pythagorean literature circulating in this period is now judged to be pseudonymous: treatises issued under the names of Pythagoras, of his wife Theano, and of his early followers, but composed centuries after all of them were dead. The forgery was a settled genre with its own conventions. Most of the surviving pieces are written not in ordinary Greek but in a contrived Doric — the dialect the early Italian Pythagoreans would have spoken — so that the archaic sound of the prose would vouch for the age of its contents and persuade a reader that here was a voice older than Plato. A treatise On the Nature of the Cosmos went under the name of Timaeus of Locri, the speaker of Plato’s own cosmological dialogue; letters of moral counsel went out under the name of Theano; works on the soul and on household virtue were ascribed to women of the founder’s circle. The point of the disguise was not deception for its own sake but authority: to present Platonic and Academic doctrine as a recovery of something prior, so that Plato himself might be read as a late and faithful pupil of an Italian sage.

This is the textual base the revival rests on, and it sets the terms for everything that follows. When a Neopythagorean writer credits Pythagoras with the doctrine of the supreme One and the indefinite Dyad, the doctrine is in substance the metaphysics worked out in the old Academy after Plato; the attribution running backward to Pythagoras is the school’s founding move, half scholarship and half pious fiction. The instinct to honor a teaching by aging it — to find the new truth already spoken by the ancients — would outlast the movement and become a habit of the whole Western esoteric tradition.

The figures of the revival

Among the first named revivers stands the Roman senator Nigidius Figulus, a scholar of the late Republic ranked by ancient readers second only to Varro for learning, who is said to have gathered a Pythagorean circle on Roman soil and whose vast technical works — on the gods, on divination, on the heavens — pointed exactly where a Pythagorean’s interests were expected to run. Around him the revival took on its Roman coloring: the order of the cosmos, the reading of signs, the discipline of a life lived by rule. In the Greek-speaking East the metaphysical work went further. Eudorus of Alexandria, in the first century BCE, set above the Pythagorean pair of Monad and Dyad a single transcendent principle he called God; Moderatus of Gades, a century later, articulated a graded series of Ones — a first beyond being, a second bound up with the forms, a third with soul — a scheme whose shape the later tradition would inherit almost intact.

Two figures are most securely attached to the current. The first is the mathematician Nicomachus of Gerasa, active around the year 100 in the Roman province of Arabia, whose Introduction to Arithmetic and Manual of Harmonics set out the properties of number and the ratios of music as the foundation beneath geometry, music, and astronomy — the four mathematical arts the tradition traced to Pythagoras himself. His lost Theology of Arithmetic assigned a divine significance to each of the first ten numbers. The handbooks were read for more than a thousand years: rendered into Latin by Boethius in the early sixth century, the Introduction became the standard arithmetic of the medieval schools and the place where generations first met the idea that counting and contemplation might be a single act. The detail of that number-doctrine — the powers of the Monad and the Dyad, the perfection of the decad, the harmonic ratios of the cosmos — belongs to its own treatment in Pythagorean arithmology and the Pythagorean-Platonic harmonics; what matters here is that Nicomachus made it teachable, fixed it in handbook form, and so carried it forward.

The second is the philosopher Numenius of Apamea, of the Syrian city of Apamea, who taught in the middle of the second century and read Plato through Pythagoras as if they were one teaching, both of them heirs to a still older wisdom held in common by the great peoples of the East. He pressed toward a hierarchy of divine principles: a first god wholly at rest, pure being and the Good, identified with intellect; a second, active and turned toward the made world, ordering it as a craftsman; and a third bound up with the cosmos itself. The first imparts its thought to the second without losing it, as one mind shares knowledge with another. Almost nothing he wrote survives whole — he is known through fragments quoted by hostile or selective hands, chiefly the Christian scholars who copied him for their own ends — yet the pattern is unmistakable, and it is the architecture that Plotinus would raise a century later. In Plotinus’s own school the charge circulated that the master had merely repurposed Numenius; the relationship is now read as real influence, and Numenius as one of the bridges across which Pythagorean number, Platonic metaphysics, and the religious temper of the eastern provinces flowed toward what became Neoplatonism.

If Numenius gave the revival its metaphysics, the wandering sage Apollonius of Tyana gave it a face. Born in Cappadocia and devoted from youth to the Pythagorean discipline, he kept a five-year silence, ate no flesh, wore no wool, refused blood sacrifice, and traveled the world as a teacher and reputed wonder-worker. Three generations after his death the Severan empress Julia Domna commissioned the rhetorician Philostratus to write his Life, an eight-book romance that fixed his image for later ages: the holy man whose marvels flowed from purity and knowledge rather than from magic. In that portrait the Pythagorean ideal of a life made pure by abstinence and contemplation found its emblematic figure — so much so that, when a Roman official set him up around 303 as a pagan counter to Christ, the comparison was an attack precisely because the holy life was the recognized point.

A metaphysics built from number

What the school’s texts hold in common is a cosmology that begins in arithmetic. Reality descends from a supreme One, or Monad, with an indefinite Dyad standing beneath it as the principle of multiplicity, division, and matter; from the interplay of unity and plurality the ordered cosmos unfolds, as the series of numbers unfolds from one. This is the move that distinguishes the Neopythagorean register from a straight Platonism: where a Platonist might place Nous, divine intellect, at the summit of the intelligible order, the Pythagorizing thinkers tended to set the bare Monad-and-Dyad there instead, making first principles of the numbers themselves and treating the whole visible world as their working-out. The graded descent — a first principle held apart from all making, a second that acts, a hierarchy of being thinning toward matter — is the seed of the later doctrine of emanation, the procession of all things from a single source above being. The tension that ran through the revival, never fully resolved, was whether matter is a second ultimate principle standing eternally against the One, or whether even the Dyad must somehow be derived from unity so that the One alone is first; the attempts to derive the Dyad from the One, and so to make the system truly single, are among the revival’s most ambitious and most strained pages.

Bound to this metaphysics was a practical discipline, for the doctrine was never merely a theory of the cosmos but a regimen for the soul. The soul was held to be immortal and divine, fallen into the body and capable of ascent; the philosopher’s task was to purify it for the return. Hence the marks of the Pythagorean life: vegetarian abstinence, simplicity, silence, and the nightly examination of conscience in which one reviewed the day’s acts before sleep — what was done well, what done wrongly, what left undone. Mathematics itself was a part of this purification, not a separate study but a way of training the mind upon what does not change, drawing it from the world of becoming toward the stable order of number. The asceticism and the arithmetic were one project: the discipline cleared the soul, the numbers showed it the pattern it was climbing toward.

Tendency rather than sect

Neopythagoreanism is better understood as a tendency than as an organized school. It ran alongside, and finally merged into, the Platonism of the same centuries — the phase historians call Middle Platonism, the long stretch between the old Academy and Plotinus. The boundary between a Pythagorizing Platonist and a Platonizing Pythagorean is often impossible to draw; the figures placed on either side knew one another, answered one another, and drew on the same fund of texts. What set the Pythagorean accent apart was less a separate body of doctrine than a way of framing it: the appeal to a wisdom older than Plato, the elevation of number to first principle, the linking of metaphysics to a rule of life and to the eastern sages. By the time of Iamblichus in the early fourth century, who wrote a long work On the Pythagorean Life and gathered the school’s lore into a great synthesis, the Pythagorean current had been largely absorbed into the Neoplatonism it had helped to make possible.

Texts, fragments, and scholarship

The revival is recovered today from a difficult and uneven record. The pseudonymous Doric treatises were collected and dated by Holger Thesleff in The Pythagorean Texts of the Hellenistic Period (Åbo, 1965), the edition that remains the foundation of the field; later work has revised his geographic scheme for a chronological one, sorting the corpus into a first layer of Hellenistic forgeries ascribed to Pythagoras and his family and a later layer of philosophical treatises in pseudo-Doric — a sorting that turns on recognizing, as Leonid Zhmud argues in What is Pythagorean in the Pseudo-Pythagorean Literature? (Philologus 163, 2019), how little of the founder’s own thought the texts actually preserve and how much they import from the Academy. The wider state of the question is surveyed in the studies gathered as Pythagoras redivivus (Academia Verlag, 2021), reviewed in the Bryn Mawr Classical Review. For the movement as a whole the standard scholarly entrance is John Dillon’s The Middle Platonists (Cornell, 1977; revised 1996), which sets the Pythagorizing figures within their Platonic context; Charles Kahn’s Pythagoras and the Pythagoreans: A Brief History (Hackett, 2001) supplies the conceptual overview, and Dominic O’Meara’s Pythagoras Revived (Oxford, 1989) follows the number-theology forward into the later Neoplatonists. Carl Huffman’s article Pythagoreanism in the Stanford Encyclopedia of Philosophy (substantive revision 2024) gives the current account of the revival’s strands, and the open-access Middle Platonism article in the Internet Encyclopedia of Philosophy traces the doctrine of the transcendent One from Eudorus through Moderatus and Numenius.

The primary witnesses divide between the handbooks and the biographies. Nicomachus’s Introduction to Arithmetic survives in Richard Hoche’s Greek text (Teubner, 1866) and in Martin Luther D’Ooge’s annotated English translation (Macmillan, 1926). The Pythagorean ethical fragments — the Golden Verses and the sayings attributed to the school — are gathered in Florence Firth’s The Golden Verses of Pythagoras and Other Pythagorean Fragments (1904), hosted here in the Library; it is there, in the Golden Verses themselves, that the nightly self-examination is set down as a rule. The late-antique lives of Pythagoras by Iamblichus and Porphyry, the eighth book of Diogenes Laertius, and the Theology of Arithmetic transmitted under Iamblichus’s name carry the lore the revival assembled. The single biography that shaped the movement’s later reputation, Philostratus’s Life of Apollonius, reaches the modern reader in G. R. S. Mead’s study and translation, also held in the Library.

The current’s lasting effect was to deliver to Plotinus and his successors a Plato already read in Pythagorean terms: a One above being, a graded descent of principles, philosophy practiced as a way of life and not only a way of argument. When the later mystical traditions of the West speak of the powers of number, of the ascent of the soul, of a primordial wisdom shared among the ancient nations, they are drawing on a Pythagoras who was largely the work of this Roman revival — on the underground hall and the masked treatises rather than on the sixth-century master himself. Much that would afterward be called Pythagorean was first made so here, in the centuries when an old name was given new metaphysics and sent forward under the authority of age.

→ In the library: Mead — Apollonius of Tyana (1901) · Plato — The Dialogues (Jowett) · Plotinus — The Enneads (MacKenna)

→ Related: Pythagoras · Neoplatonism · The One · Nous · Emanation · Pythagoreanism · Platonism · Nicomachus Of Gerasa · Numenius Of Apamea · Nigidius Figulus · Apollonius Of Tyana · Asceticism · Soul · Iamblichus · Pythagorean Arithmology · Pythagorean Platonic Harmonics