Pythagoras
Quotes & Wisdom
Pythagoras: The Philosopher Who Heard the Music of the Universe
Twenty-five centuries before quantum physics revealed that reality is fundamentally mathematical, a Greek philosopher from the island of Samos declared that "all is number." Pythagoras, born around 570 BCE, founded a secretive brotherhood in southern Italy that was part religious cult, part mathematical research institute, and part commune. His followers discovered the mathematical ratios underlying musical harmony, explored the properties of numbers with almost mystical reverence, and may have been the first to prove the famous theorem that bears his name. Pythagoras left no writings - his teachings were transmitted orally and guarded by strict vows of secrecy - yet his influence runs through Western mathematics, philosophy, music theory, and science like an underground river surfacing everywhere.
Context & Background
Pythagoras was born around 570 BCE on the island of Samos, a prosperous trading hub off the coast of Asia Minor in the eastern Aegean Sea. His father, Mnesarchus, was a merchant - possibly a gem engraver - who traveled widely, exposing the young Pythagoras to the cultures and intellectual traditions of the Mediterranean world. Ancient sources, writing centuries after his death, describe a precocious child who learned to play the lyre, studied poetry, and could recite Homer from memory.
The Greece of Pythagoras's youth was experiencing one of the most remarkable intellectual awakenings in human history. The Ionian philosophers - Thales, Anaximander, Anaximenes - were developing the first attempts to explain the natural world through reason rather than mythology. Instead of attributing floods to the anger of Poseidon or lightning to the wrath of Zeus, they sought natural causes and underlying principles. This revolution in thinking - the birth of philosophy and proto-science - was the intellectual atmosphere in which Pythagoras grew up.
According to ancient tradition, Pythagoras traveled extensively in his youth. He reportedly studied with the priests of Egypt, where he may have encountered geometry and astronomy; with the Babylonians, who possessed sophisticated mathematical knowledge; and with the philosopher Thales in Miletus, who urged him to travel to Egypt for further learning. How much of this is historical fact and how much is legend crafted by later admirers is impossible to determine, since Pythagoras wrote nothing and the first accounts of his life appeared over a century after his death.
Around 530 BCE, Pythagoras left Samos - possibly to escape the tyranny of Polycrates - and settled in Croton (modern Crotone), a Greek colony in southern Italy. It was here that he founded the community that would make him famous.
The community Pythagoras established at Croton was unlike anything in the ancient world. It was simultaneously a philosophical school, a religious order, and a political faction. Members were divided into two groups: the mathematikoi (learners), who lived permanently within the community, shared all property in common, followed strict dietary rules (including vegetarianism), and studied Pythagoras's teachings directly; and the akousmatikoi (listeners), who lived outside and attended lectures but were not bound by the full set of rules.
The Pythagoreans observed strict secrecy about their inner teachings. They attributed all discoveries to the master himself, which makes it virtually impossible to distinguish Pythagoras's personal contributions from those of his followers. They followed unusual taboos - including, famously, a prohibition against eating beans - and believed in the transmigration of souls (metempsychosis), the doctrine that the soul passes through successive incarnations in different bodies.
What made the Pythagoreans truly revolutionary was their conviction that the fundamental nature of reality is mathematical. "All is number" was their central doctrine. Where other philosophers proposed water, air, or fire as the primary substance of the universe, Pythagoras proposed something far more abstract: number and mathematical relationship.
Pythagoras's most celebrated discovery was the mathematical basis of musical harmony. According to tradition, he noticed that the sound produced by a blacksmith's hammers varied with their weight, and he investigated the relationship systematically. He found that the most pleasing musical intervals - the octave, the fifth, the fourth - corresponded to simple ratios of whole numbers. A string half the length of another produces a note one octave higher (ratio 2:1). A string two-thirds the length produces a fifth (3:2). A string three-quarters the length produces a fourth (4:3).
This was an extraordinary revelation. It demonstrated that aesthetic beauty - the harmony that pleases the ear - has a precise mathematical structure. The universe is not chaotic but ordered, and that order is expressible in numbers. Pythagoras extended this insight into a cosmic principle: the heavenly bodies, he believed, move according to mathematical proportions and produce a celestial music - the "music of the spheres" - that human ears cannot hear but that the soul can apprehend through the study of mathematics.
The idea that the universe is governed by mathematical laws, and that understanding these laws gives access to the deepest truths about reality, is the founding insight of Western science. When Galileo Galilei wrote that the book of nature "is written in the language of mathematics" and when Isaac Newton described the laws of gravitation in mathematical equations, they were working within a tradition that Pythagoras inaugurated.
The theorem that bears Pythagoras's name - that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides - was known to the Babylonians a thousand years before Pythagoras was born. What Pythagoras or his followers may have contributed was the first rigorous proof, though even this is debated by historians. What is certain is that the Pythagorean school placed the theorem at the center of their mathematical investigations.
The theorem also led to a deeply troubling discovery. If both sides of a right triangle have a length of one, the hypotenuse has a length equal to the square root of two. And the square root of two, as a Pythagorean named Hippasus reportedly demonstrated, cannot be expressed as a ratio of whole numbers. It is what we now call an irrational number.
This was a crisis for Pythagorean philosophy. If "all is number" meant all is expressible as ratios of whole numbers, then the square root of two was a crack in the foundation of reality itself. According to legend, Hippasus was drowned at sea for revealing the secret - whether by the gods or by his outraged fellow Pythagoreans depends on which ancient source you trust. The story may be apocryphal, but the mathematical crisis was real and had to wait centuries for adequate resolution.
Pythagoras was as much a religious figure as a mathematical one. His doctrine of the transmigration of souls - the belief that the soul is reborn in successive bodies, human and animal - linked him to the Orphic mystery traditions and anticipated aspects of Plato's philosophy. He reportedly claimed to remember his own past lives and to recognize the soul of a deceased friend in the howling of a beaten dog.
He was also a political figure. The Pythagorean community at Croton became involved in local politics, and their elitist, secretive ways provoked hostility. Around 509 BCE, a popular uprising against Pythagorean influence led to the burning of their meeting places and the scattering of the community. Pythagoras may have fled to Metapontum, where he reportedly died around 495 BCE - though the circumstances of his death, like so much of his life, are uncertain.
The influence of Pythagoras on Plato was profound. Plato's theory of Forms - the idea that mathematical and abstract objects are more real than physical things - is deeply Pythagorean. The inscription reportedly above the entrance to Plato's Academy, "Let no one ignorant of geometry enter here," could serve as a Pythagorean motto. Through Plato, and through the mathematical tradition more broadly, Pythagoras's conviction that reality is fundamentally mathematical has shaped Western thought from Euclid to Einstein - a legacy remarkable for a man who left behind not a single written word.