Pythagoras

Separating historical fact from legend in the life of Pythagoras is an enterprise fraught with difficulty, for Pythagoras himself wrote nothing, and the earliest surviving extended accounts of his life — Porphyry's Life of Pythagoras and Iamblichus's Life of Pythagoras, both composed in the 3rd century CE — were written some eight centuries after his death. These late biographies are rich in miraculous anecdote and theological interpretation, drawing on earlier sources now largely lost, and it is impossible to determine with confidence how much of their content preserves genuine historical tradition and how much reflects the pious embellishment of later Neoplatonist admirers who regarded Pythagoras as the supreme philosopher-sage. What can be said with reasonable confidence is that Pythagoras was a real historical figure of tremendous intellectual and religious authority, born on the island of Samos c. 570 BCE, and that his influence on subsequent philosophy was both immense and enduring.

According to the ancient sources, Pythagoras's father was a man named Mnesarchus, a gem-engraver or merchant from Samos, and his extraordinary intellectual gifts manifested early. The tradition reports that he undertook extensive travels in pursuit of wisdom before settling in the West. Most prominently, he is said to have spent some twenty-two years studying with the priests of Egypt, learning geometry, astronomy, and the mysteries of the divine — an account that may reflect genuine historical contact between early Greek philosophy and Egyptian priestly learning, or may be a later attempt to provide the philosopher with the most venerable possible Eastern pedigree. He is also said to have studied with the Chaldean sages of Babylon, learning mathematics and astronomy, and traditions mention visits to Phoenicia and possibly India. Whether or not all these journeys occurred, they established Pythagoras in ancient imagination as the supreme synthesiser of the world's accumulated wisdom, a philosopher whose learning transcended any single cultural tradition.

Pythagoras eventually settled at Croton in the Greek colony of Magna Graecia in southern Italy c. 530 BCE, where he founded the community and school that would bear his name and carry his teachings forward. Ancient sources describe his personal presence as extraordinary — tall, golden-haired, possessed of a golden thigh (revealed by him to Abaris the Hyperborean as a sign of his divine nature), and endowed with a voice and bearing of such compelling authority that crowds would gather to hear him speak. His disciples held that he was a semi-divine being, perhaps a reincarnation of Apollo himself, or of the Trojan hero Euphorbus. Miraculous deeds were attributed to him: he reportedly predicted the arrival of a ship, tamed a savage bear, and was greeted by name by the river Cosas as he crossed it in full view of witnesses. Whether these stories preserve garbled memories of actual events or represent the mythologisation of an exceptional human personality, they testify to the profound impression Pythagoras made on those around him and on the generations that followed.

The Pythagorean community that Pythagoras established at Croton was a remarkable and historically unprecedented institution — simultaneously a philosophical school, a religious brotherhood, and a political association, bound together by shared doctrines, shared practices, and an intense communal loyalty that set its members apart from the wider society. The community operated on a two-tier structure that reflected both practical and initiatory distinctions. The outer circle, known as the akousmatikoi (hearers), received the moral and religious teachings in oral form without the mathematical and philosophical training that constituted the deeper teaching. The inner circle, the mathematikoi (learners), were admitted to the full curriculum of mathematics, music, astronomy, and philosophy, living communally with Pythagoras himself and subject to the most rigorous discipline of mind and body.

The daily life of the Pythagorean brotherhood was governed by an intricate set of rules and prohibitions whose full rationale was known only to the initiates. Members observed periods of meditative silence, sometimes lasting several years at the beginning of their training. They practised strict vegetarianism, grounded in the doctrine of metempsychosis — the belief that animal bodies might house the souls of former human beings. They refused to eat beans, a prohibition whose precise rationale was debated even in antiquity (explanations range from the beans' resemblance to human embryos to their role in political lot-casting). They wore white garments and avoided woollen clothing; they entered a house right foot first; they did not look into a mirror by lamplight; they did not touch a white cock or eat from a whole loaf. These rules, known as akousmata (things heard), were preserved and transmitted by the outer circle in cryptic form: "What is the oracle at Delphi? — the Tetractys, which is the Harmony in which the Sirens sing." Their enigmatic character suggests a symbolic or initiatory function beyond mere practical regulation.

The Pythagorean brotherhood exercised significant political influence in Croton and the surrounding cities of Magna Graecia, and this influence ultimately provoked a violent reaction. The precise circumstances are disputed, but the ancient sources agree that at some point — possibly in the late 5th century BCE, though the chronology is uncertain — anti-Pythagorean factions attacked and burned Pythagorean meeting houses, killing or driving into exile many members of the brotherhood. Pythagoras himself may have died in the aftermath of this persecution, either at Croton or at Metapontum, where he reportedly ended his days. The scatter of the Pythagorean communities, however, did not mean the end of Pythagorean philosophy. The tradition survived and developed through individual figures such as Philolaus of Croton (c. 470–385 BCE), whose writings are the earliest Pythagorean texts to survive in substantial fragments, and Archytas of Tarentum (c. 428–347 BCE), a brilliant mathematician and statesman who was a friend and influence on Plato. Through these thinkers the Pythagorean tradition was transmitted to Plato and through him to the entire subsequent history of Western philosophy.

At the heart of Pythagorean philosophy lies the audacious conviction that "number is all" — that number is not an abstract concept invented by human minds for practical convenience, but the fundamental structuring principle of reality itself, both physical and metaphysical. This insight, or rather this overwhelming intuition, sets Pythagorean thought apart from all earlier Greek philosophy and makes it the progenitor of the Western tradition of sacred mathematics. For the Pythagoreans, to understand number was not merely to perform arithmetic but to penetrate to the innermost structure of the cosmos and of the divine. Number was conceived as the rational form of all things — the reason why the world is intelligible, harmonious, and beautiful rather than chaotic and meaningless.

The special significance of the first four numbers — 1 (the Monad), 2 (the Dyad), 3 (the Triad), and 4 (the Tetrad) — and their sum of 10 (the Decad) was central to Pythagorean metaphysics. These four numbers were not merely arithmetical quantities but metaphysical principles: the Monad represented unity, the source from which all things proceed; the Dyad represented duality, difference, and matter; the Triad represented harmony and completeness (the first number with a beginning, middle, and end); and the Tetrad represented the physical world with its four elements and four seasons. Their visual and philosophical synthesis was the Tetractys — a triangular arrangement of ten points in rows of 1, 2, 3, and 4 — which the Pythagoreans regarded as the most sacred symbol of their philosophy. The solemn oath sworn by Pythagorean initiates was "by him who delivered to our souls the Tetractys, the source and root of ever-flowing Nature." This symbol was not a mere diagram but a direct representation of the mathematical structure of reality — the way in which the One unfolds through successive differentiations into the richness and multiplicity of the world.

The Pythagorean discovery — or perhaps systematic elaboration — of the mathematical ratios underlying musical harmony provided the most compelling empirical confirmation of the number-as-reality thesis. The octave corresponds to the ratio 2:1; the perfect fifth to 3:2; the perfect fourth to 4:3 — all derived from the sacred numbers of the Tetractys. This discovery that the most beautiful and emotionally powerful relationships in music are governed by simple numerical ratios seemed to demonstrate beyond doubt that number is not a human invention but a feature of reality itself. From this musical insight, Pythagorean cosmology developed the concept of the musica universalis or Harmony of the Spheres: the seven planets, moving at different velocities proportional to their distances from the earth, produce a cosmic music whose proportions mirror those of earthly musical harmony. This cosmic music was inaudible to ordinary human perception (numbed, as Pythagoreans held, by constant exposure since birth), but could be heard by the purified soul — a concept that Plato developed in the myth of Er in the Republic and that Kepler would revive in his Harmonices Mundi of 1619.

The doctrine of metempsychosis — the transmigration of souls through successive incarnations in human, animal, and vegetable bodies — was among the most distinctive, most controversial, and most historically influential of all the teachings attributed to Pythagoras. Unlike the number mysticism, which can be approached through mathematical reasoning, metempsychosis was grounded in personal religious conviction and in what Pythagoras claimed was direct experiential knowledge. He reportedly declared that he could recall his own previous lives in sequence, including an existence as the Trojan hero Euphorbus, whose shield — still preserved in a temple at Argos — he is said to have recognised and identified by the decorations on its inner surface as proof of his claim. Whether this story represents historical fact, symbolic teaching, or later legend, it illustrates the central role of personal spiritual authority in Pythagorean religion.

The soul, in Pythagorean teaching, was conceived as the true self — immortal, divine in origin, and temporarily imprisoned in the body, which the Pythagoreans described by the punning Greek phrase soma sema (the body is a tomb). The soul passes through a cycle of reincarnations in human and animal bodies — a process of purification and spiritual development — and the quality of each successive life is determined by the purity and virtue achieved in previous existences. The vegetarian diet and the prohibition against killing animals were not mere dietary preferences but ethical imperatives grounded in this belief: since the souls of former human beings might inhabit animal bodies, to kill and eat an animal was potentially an act of cannibalism or even murder of a kinsman. The ultimate goal of the soul's journey was purification sufficient to escape the cycle of reincarnation altogether and ascend to a permanent existence in a state of divine harmony — an eschatological vision that would exercise immense influence on subsequent religious thought.

The Pythagorean doctrine of metempsychosis did not arise in a cultural vacuum. It was closely related to the Orphic religious tradition — the complex of beliefs and practices associated with the mythical poet Orpheus, which included doctrines of the soul's divine origin, its fall into matter, and its cyclic reincarnation. Many scholars regard Pythagorean and Orphic eschatology as drawing on a common source, or as so closely intertwined that sharp distinctions are difficult to maintain. What is certain is that the Pythagorean doctrine of the soul profoundly shaped the thought of Empedocles, who adopted metempsychosis as a central principle of his philosophy, and — most consequentially for Western philosophy — of Plato. Plato drew extensively on Pythagorean eschatological ideas in dialogues including the Phaedrus, the Phaedo, the Republic, and the Timaeus, and through Plato these ideas entered the mainstream of Western philosophical and theological reflection, shaping Christian, Jewish, and Islamic conceptions of the soul's immortality and destiny.

The influence of Pythagoras on Western thought has been of extraordinary longevity and range, extending from antiquity through the Renaissance and into the modern period in a continuous, if at times subterranean, stream. In the centuries immediately following the dispersal of the original Pythagorean brotherhood, the teaching survived through figures such as Archytas and Philolaus and was absorbed into Platonic philosophy. In the 1st century BCE through the 3rd century CE, a Neo-Pythagorean revival sought to reconstruct and develop the original teaching. Figures such as the Roman senator and scholar Nigidius Figulus, the 1st-century CE philosophers Moderatus of Gades and Numenius of Apamea, and the wandering sage Apollonius of Tyana (himself regarded as a Pythagorean divine man) elaborated a reformed Pythagoreanism that increasingly resembled what would become Neoplatonism. The Neoplatonists themselves — Plotinus, Porphyry, and above all Iamblichus — regarded Pythagoras as the supreme authority and Plato as essentially his greatest expositor, with Iamblichus claiming that all genuine philosophy derived ultimately from Pythagorean wisdom.

The Pythagorean legacy in the Western esoteric tradition is equally profound. The principle that numbers and geometrical forms are not merely abstract quantities but sacred symbols expressing the structure of divine reality was transmitted through Neoplatonism to Jewish Kabbalah — the practice of gematria (assigning numerical values to Hebrew letters and divine names) reflects a fundamentally Pythagorean approach to sacred arithmetic — and to Christian theological numerology. Music theory from Boethius through the medieval quadrivium — in which arithmetic, geometry, music, and astronomy constituted the four mathematical disciplines — was grounded in Pythagorean harmonic theory, and Johannes Kepler's Harmonices Mundi (1619) represents a magnificent late flowering of the Pythagorean conviction that planetary motions embody musical harmonies. In the Renaissance, Pythagoras was one of the supreme prisci theologi — the ancient theologians who had received divine wisdom before Plato — and Johannes Reuchlin's De Arte Cabalistica (1517) presented an influential synthesis of Pythagorean number philosophy and Jewish Kabbalah.

In the modern esoteric tradition, Pythagorean number symbolism has remained a living force. Numerology — the interpretation of the hidden significance of numbers in relation to human lives and events — draws directly on the Pythagorean conviction that numbers express the deepest patterns of reality. Sacred geometry, as practised in Freemasonry and in various modern esoteric movements, preserves the Pythagorean understanding of geometrical forms as expressions of divine order. The Pythagorean theorem itself, which bears his name though it was certainly known before him, became a central symbol of Freemasonic initiation, representing the rational structure of the cosmos. More broadly, the Pythagorean legacy endures in the vision — fundamental to modern science as well as to esotericism — that the universe is, at its deepest level, mathematical in structure, and that in understanding mathematics we are not merely performing abstract calculation but penetrating to the hidden order of things. Pythagoras stands, for both the scientific and the mystical traditions, as the patron of the philosophical ideal that mathematics and mysticism are not opposites but complementary expressions of a single sacred science.