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Pythagoras is often remembered as the namesake behind the Pythagorean theorem, but an overlooked aspect of his legacy is the intensely secretive and communal lifestyle he required of his followers. Early Pythagorean communities functioned more like religious brotherhoods or even mystery cults than open philosophical circles, demanding years of silent study, strict dietary laws, and communal sharing of property. The foundation of Pythagoreanism was not just mathematics, but a comprehensive way of life that blended science, mysticism, and social engineering.
Pythagoras was born around 570 BC on the Greek island of Samos, the son of Mnesarchus, who is variously described as a gem-engraver or a wealthy merchant. Samos at the time was a thriving cultural center in the eastern Aegean, known for its advanced engineering feats such as the Tunnel of Eupalinos, and its exposure to ideas from the Near East brought by traders. Pythagoras grew up during the flowering of Ionian natural philosophy, making him a contemporary of figures like Anaximander and Anaximenes from neighboring Miletus. His mother, Pythaïs, was said by some ancient sources to be a descendant of Ancaeus, the mythical founder of Samos.
Accounts from Herodotus and Isocrates agree on his Samian birth, but details of his early education remain uncertain. Later legends report that he traveled widely, learning from the priests of Egypt, the Magi of Persia, and possibly even sages in India. Some sources claim he learned arithmetic from Phoenicians and astronomy from the Chaldeans. By the time he was forty, around 530 BC, Pythagoras left Samos, possibly due to political disagreements with the tyrant Polycrates or because of burdensome public duties.
His destination was Croton, a wealthy Greek colony in southern Italy, then part of Magna Graecia. On arrival, Pythagoras quickly gained influence among the local elite, serving as advisor and moral reformer. Biographers describe his rhetoric as so persuasive that the people of Croton supposedly abandoned luxurious habits in favor of the ascetic regime he proposed. Pythagoras established a school—or more accurately, a closed community—where initiates undertook a five-year period of silent study before they were admitted to the inner circle. Members shared all property communally and lived according to strict regulations, including a vegetarian diet and a deep sense of loyalty to each other.
The organization of Croton’s Pythagoreans was hierarchical. Early sources distinguish between the akousmatikoi, who “listened” mainly to religious and ritual teachings, and the mathematikoi, who were allowed access to deeper mathematical and scientific studies after their initiation period. Even the Platonic Academy, established much later outside Athens, was organized in part on the Pythagorean model of a cenobitic, semi-monastic institution set apart from the city.
Pythagoras’s own family was deeply involved in this movement. Suda writes that he had four children: Telauges, Mnesarchus, Myia, and Arignote. His wife, Theano of Croton, is noted as a distinguished philosopher and is said by some traditions to have taken over leadership of the school after his death. The wrestler Milo of Croton, famed for his strength, was also closely associated with Pythagoras and is credited in some stories with saving his life.
The core of Pythagorean philosophy extended far beyond mathematics. The most securely attributed doctrine is metempsychosis—the transmigration of souls. According to this belief, every soul is immortal and, after death, is reborn in a new body. This teaching is referenced by contemporaries such as Xenophanes, who satirically described Pythagoras intervening on behalf of a beaten dog, professing to recognize the soul of a departed friend. Other accounts, such as those by Heraclides Ponticus, claim Pythagoras remembered four previous incarnations, including the mythical Aethalides, Euphorbus of the Trojan War, Hermotimus, and Pyrrhus the fisherman.
Pythagorean numerology, another cornerstone of the system, held that the universe could be explained by whole numbers and their relationships. The tetractys, a triangular figure of ten dots arranged in four rows, was considered the perfect number and a symbol of utmost mystical importance. Later Pythagoreans would swear oaths by the tetractys. Numbers themselves were endowed with moral and cosmological significance. For example, the number four was associated with justice because it was the first square number resulting from an even multiplied by itself.
Pythagoras and his followers are credited with profound discoveries in mathematics and music. In geometry, they proved the theorem that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, now called the Pythagorean theorem. In music, Pythagoras discovered that harmonious intervals could be expressed as simple ratios between the lengths of strings: the octave as a 1:2 ratio, the fifth as 2:3, and the fourth as 3:4. These insights led to the system of Pythagorean tuning and the belief that the cosmos itself was structured according to mathematical harmony—a doctrine known as the musica universalis.
Pythagorean cosmology departed radically from the geocentric view of the time. Philolaus, a later Pythagorean, proposed that the Earth and other planets orbited a “central fire” rather than being fixed at the center of the universe. He even introduced the notion of a “Counter-Earth,” an invisible planet orbiting on the opposite side of the central fire. While this was not based on empirical observations, it represented a profound philosophical shift, placing mathematical order at the heart of cosmology.
The Pythagorean community also enforced strict rules on daily life. They practiced vegetarianism, justifying it on ethical and spiritual grounds. Pythagoreans believed that eating meat impeded the soul’s purity and hindered spiritual ascent. The prohibition on beans, still a subject of speculation, may have originated in Athenian ideas linking beans with Hades or as a symbol of the cycle of reincarnation. Pythagoreans also advanced arguments for the ethical treatment of animals, insisting that any creature capable of suffering should not be harmed unnecessarily.
Women played a significant role in the Pythagorean movement. Theano of Croton, Pythagoras’s wife, is recognized as a philosopher in her own right. Iamblichus, writing much later, listed seventeen women among 235 named Pythagoreans. Surviving texts from women such as Perictione and Phintys address topics from the harmony of womanly virtues to the right of women to philosophize. Perictione, writing in Ionic, outlined virtues for women that echoed the terms Plato would later use in the Republic.
Political tensions eventually led to the destruction of the Pythagorean community in Croton. Around 510 BC, after Croton’s victory over the neighboring colony of Sybaris, some citizens advocated for a democratic constitution. The Pythagoreans rejected these reforms, leading to resentment among the excluded elite. Cylon and Ninon, the leaders of the democratic faction, incited an attack on a Pythagorean meeting. During the assault, their meeting place was set on fire. Many members perished; only the younger and more agile escaped. Accounts differ on whether Pythagoras himself was present, but one tradition holds he fled to Metapontum, where he and his followers eventually died of starvation after seeking sanctuary and being denied.
Following these attacks, Pythagorean communities faced further persecution throughout Magna Graecia. By around 400 BC, most Pythagoreans had left Italy, though the ideas persisted and found fertile ground elsewhere. Philolaus of Croton and Archytas of Tarentum became key figures in the transmission of Pythagorean doctrines.
The influence of Pythagoras extended far beyond his life and immediate circle. Pythagorean ideas on numbers, harmony, and the transmigration of souls profoundly shaped Plato’s dialogues, particularly the Timaeus and the Republic. The Platonic Academy, founded almost a century later, was organized along Pythagorean lines. The Pythagorean cosmology, especially as interpreted by Philolaus, introduced the model of a cosmos governed by mathematical laws—an idea that resurfaced in the scientific revolutions of Copernicus, Kepler, and Newton two millennia later.
In the 1st century BC, Pythagoreanism was revived as Neopythagoreanism, a movement blending Pythagorean, Platonic, Aristotelian, and Stoic doctrines. Figures like Moderatus of Gades and Nicomachus of Gerasa became leading teachers, and Apollonius of Tyana was regarded as the last great Neopythagorean sage. The tradition continued to influence early Christianity, as seen in texts like the Sentences of Sextus, which were widely adopted by monastic orders.
The reach of Pythagorean numerology and philosophy extended into the Middle Ages and the Renaissance. In the 13th century, Fibonacci explored Pythagorean triples in his Book of Squares and showed how square numbers arise from the sum of consecutive odd numbers, echoing methods attributed to Pythagoras. The concept of the tetractys—ten as the perfect number representing the sum of the first four natural numbers—became a central symbol in Western numerology and cosmology. The lasting influence of Pythagoras is evident in the fact that as late as the 12th century, Pythagorean numerological concepts had become a universal language in medieval Europe, hidden in the fabric of theology, music, and mathematics.