Pythagoras

Early Life and Travels

Pythagoras was born around 570 BCE on the island of Samos in the eastern Aegean. Ancient sources attribute to him extensive travels: to Egypt, where he reportedly studied with priests and was initiated into their mysteries; to Babylon, where he may have encountered Mesopotamian mathematics and astronomy; and possibly to Phoenicia and even India, though these later attributions grow increasingly legendary. What is reasonably certain is that Pythagoras absorbed a wide range of intellectual and religious traditions before establishing his own school.

The Move to Croton

Around 530 BCE, reportedly fleeing the tyranny of Polycrates on Samos, Pythagoras emigrated to Croton in Magna Graecia (southern Italy). There he founded a community that was simultaneously a philosophical school, a religious brotherhood, and a political association. Members followed strict rules of conduct, including dietary restrictions (most famously, the prohibition on eating beans, though the reason remains debated), communal property, silence for initiates (the akousmatikoi or 'listeners'), and secrecy about the group's teachings.

Mathematics and the Harmony of Numbers

The core Pythagorean insight was that number (arithmos) is the principle of all things. This conviction reportedly originated in the discovery that musical harmony is governed by simple numerical ratios: the octave corresponds to the ratio 2:1, the fifth to 3:2, the fourth to 4:3. If something as qualitative and seemingly subjective as musical beauty could be reduced to exact mathematical relationships, the Pythagoreans reasoned, then perhaps the entire cosmos is structured by number.

This led to a program of research that sought mathematical order in astronomy (the 'harmony of the spheres' — the idea that the planets produce music through their orbital motions), geometry (the famous Pythagorean theorem, relating the sides of a right triangle: a² + b² = c²), arithmetic (the study of odd and even numbers, perfect numbers, figurate numbers), and cosmology.

The Pythagorean Theorem and the Crisis of Incommensurability

While the relationship between the sides of a right triangle was known empirically in Babylon and Egypt, the Pythagorean school is credited with developing the first deductive proof. Ironically, the very theorem that bears Pythagoras' name led to a devastating crisis: the discovery of incommensurable magnitudes (irrational numbers). The diagonal of a unit square has length √2, which cannot be expressed as a ratio of whole numbers. This shattered the Pythagorean doctrine that all things are numbers (interpreted as ratios of integers) and, according to legend, the member who revealed this secret (possibly Hippasus) was expelled or drowned.

Cosmology and the Central Fire

Later Pythagoreans developed a distinctive cosmology. Philolaus of Croton proposed that the earth, sun, moon, planets, and a counter-earth all orbit a central fire (not the sun), making the Pythagoreans among the first to displace the earth from the center of the cosmos. This system was driven by mathematical considerations — the desire to have exactly ten celestial bodies orbiting the center, ten being the sacred number (the tetractys).

Metempsychosis and Ethics

Pythagoras taught the transmigration of souls (metempsychosis) — the doctrine that the soul is immortal and passes through successive incarnations in human and animal bodies. This belief, which connects Pythagorean thought to Orphic religious traditions, had profound ethical implications: it grounded vegetarianism and the prohibition against animal sacrifice, and it made the purification and perfection of the soul the central aim of life. Philosophy and mathematics were understood as spiritual disciplines — means of liberating the soul from the cycle of rebirth.

Legacy

Pythagoras wrote nothing himself. His teachings were transmitted orally and developed by successive generations of followers, making it difficult to distinguish Pythagoras' own doctrines from later Pythagorean elaborations. His influence, however, was immense. Plato absorbed Pythagorean ideas deeply — the metaphysical role of mathematics in the Timaeus, the immortality and transmigration of the soul in the Phaedo and Republic, and the general conviction that reality is intelligible through reason rather than sense perception all bear Pythagorean stamps. Through Plato, Pythagorean ideas entered the mainstream of Western philosophy and eventually shaped the scientific revolution, where the conviction that nature is written in the language of mathematics — from Galileo to modern physics — echoes the original Pythagorean insight.

Pythagoras died around 495 BCE, reportedly during political upheaval that led to the persecution and dispersal of the Pythagorean communities in southern Italy.