Pythagoras

Pythagoras was born on the Greek island of Samos in the eastern Aegean Sea. Ancient sources suggest his father was Mnesarchus, a gem engraver or merchant, though details of his early life are uncertain and often mixed with legend. Samos was a prosperous island with strong connections to Egypt and the Near East, exposing young Pythagoras to diverse cultural and intellectual influences. Later accounts describe him as a beautiful child with exceptional abilities who would grow to become one of history's most influential mathematicians and philosophers, though separating historical fact from legend in his biography remains challenging.

According to ancient accounts, Pythagoras embarked on extensive travels to study with priests and scholars in Egypt and Babylon, though modern historians debate the extent of these journeys. These travels allegedly exposed him to Egyptian geometry, Babylonian astronomy and mathematics, and various mystical and religious traditions. Whether historical or legendary, these accounts reflect the ancient view of Pythagoras as a seeker of universal wisdom who synthesized knowledge from multiple traditions. His later teachings would indeed show influences from Egyptian religious practices and Babylonian mathematical knowledge.

Pythagoras left Samos (possibly fleeing the tyrant Polycrates) and settled in Croton, a Greek colony in southern Italy. Here he established a philosophical and religious school or society that would become famous throughout the ancient world. The Pythagorean community was both a philosophical school and a way of life, with strict rules including vegetarianism, communal property, and various prohibitions. Members were divided into two groups: the mathematikoi (learners) who lived in the community and studied Pythagoras's teachings directly, and the akousmatikoi (listeners) who lived in their own houses and attended daytime lectures.

Pythagoras is credited with discovering or proving the theorem that bears his name: in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). While Babylonian mathematicians knew this relationship empirically centuries earlier, Pythagoras or his followers may have provided the first formal proof. The theorem became fundamental to geometry and mathematics. However, the Pythagoreans kept much of their knowledge secret, considering mathematical truths sacred, so the exact nature of Pythagoras's personal contributions versus those of his followers remains debated by scholars.

Pythagoras discovered that musical harmonies could be expressed through simple mathematical ratios. According to legend, he noticed that blacksmiths' hammers of different weights produced harmonious sounds when struck together. He experimented with vibrating strings and found that strings of equal tension and thickness produce harmonious tones when their lengths are in simple ratios: 2:1 (octave), 3:2 (perfect fifth), and 4:3 (perfect fourth). This discovery that harmony could be reduced to numbers profoundly influenced Pythagorean philosophy and led to the doctrine that 'all is number'—that mathematical relationships underlie all reality. This insight influenced Western music theory for two millennia.

Building on his musical discoveries, Pythagoras developed the concept of the 'harmony of the spheres'—the idea that celestial bodies (sun, moon, and planets) produce harmonious sounds through their movements, though humans cannot hear them. He proposed that the universe itself was constructed according to mathematical principles and musical harmonies. This cosmological vision influenced both ancient and medieval astronomy and represents an early attempt to understand the universe through mathematical laws. The idea that mathematics describes the physical world became a cornerstone of Western science, though the specific theory of celestial music was eventually disproven.

Pythagoras taught the doctrine of metempsychosis, or transmigration of souls—the belief that the soul is immortal and, after death, reincarnates in other bodies, whether human or animal. This belief, possibly influenced by Egyptian or Indian thought, led to Pythagorean practices such as vegetarianism and various purification rituals. He reportedly claimed to remember his own previous incarnations, including being Euphorbus, a warrior in the Trojan War. This religious and philosophical doctrine profoundly influenced later Greek philosophy, particularly Plato, and represented one of the earliest systematic attempts in Western thought to address questions of the soul, death, and the afterlife.

The Pythagorean society gained significant political influence in Croton and other cities in Magna Graecia. Pythagoreans became involved in local governance, generally supporting aristocratic interests. The society's emphasis on order, harmony, and rule by the wise appealed to aristocratic classes. However, this political involvement would eventually lead to conflict. The Pythagorean influence on government, combined with the secretive nature of the society and its strict rules, created resentment among those excluded from power. Democratic factions began to view the Pythagoreans as an aristocratic conspiracy threatening popular rule.

A democratic revolt against aristocratic rule in Croton led to violent attacks on the Pythagorean society. According to various accounts, Pythagorean meeting houses were burned, and many members were killed. Pythagoras himself fled Croton, seeking refuge in other Greek cities in southern Italy. The exact details vary in different sources, but the persecution scattered the Pythagorean community, though the school continued in various forms. Some sources suggest Pythagoras fled to Metapontum, another Greek colony in southern Italy, where he would spend his final years.

Pythagoras died in Metapontum, though accounts of his death vary. Some sources claim he died of starvation after taking refuge in a temple, refusing to eat beans (which Pythagoreans avoided, though the reason is debated). Others suggest he was killed during the persecution of Pythagoreans. Despite his death, his influence continued through his followers, who preserved and developed his teachings. The Pythagorean tradition influenced Plato profoundly, and through Plato affected all subsequent Western philosophy and science. Pythagoras's vision of a mathematical cosmos laid groundwork for modern science, though his religious and mystical ideas were eventually separated from his mathematical insights. His theorem remains one of the most famous in mathematics, taught to students worldwide over 2,500 years after his death.