Most people remember Pythagoras for a triangle theorem from school. To the ancient world he was closer to a holy man. Born on the Greek island of Samos in the sixth century BCE, he settled at Croton in southern Italy and gathered a community that studied mathematics, music, astronomy and the right way to live. None of his own writings survive, so nearly everything we know comes from followers writing long after his death.
A way of life, not just a school
Later writers describe the Pythagorean community as a kind of brotherhood. Members are said to have shared property, followed strict dietary rules and kept silent for years while they listened to the master from behind a screen. Ancient sources divide the followers into two groups: the mathematikoi, who learned the full teaching, and the akousmatikoi, “listeners,” who memorized sayings. The word philosopher, “lover of wisdom,” is traditionally credited to Pythagoras himself, who is said to have refused the title of sage and called himself only a lover of wisdom.
Number as the key to the universe
The Pythagoreans taught that number underlies everything. Tradition credits them with finding that musical harmony follows simple ratios, such as 2 to 1 for the octave and 3 to 2 for the fifth, and they saw the same order in the planets, the idea behind the phrase “music of the spheres.” Their most sacred emblem was the tetractys, ten dots arranged in a triangle of four rows. It adds up as 1 + 2 + 3 + 4 = 10, and it contains the ratios of the main musical intervals. Later writers say the rows stood for the point, the line, the surface and the solid.
The end of the brotherhood
The community did not last. Around 500 BCE a political uprising in southern Italy is said to have burned the Pythagorean meeting houses, and Pythagoras fled to Metapontum, where tradition says he died. His followers scattered, and the teaching survived through the schools of Plato and the later Neopythagoreans.
From the tetrahedron to Kepler
Plato linked four of the regular solids to the elements, and the tetrahedron, the pyramid with four triangular faces, stood for fire. In 1596 the astronomer Johannes Kepler tried to explain the spacing of the planets by nesting the five regular solids inside one another in his Mysterium Cosmographicum. That is the Pythagorean dream of a geometric universe still at work in the early scientific revolution.
Pythagoras and Freemasonry
That mix of mathematics, secrecy and initiation is why Pythagoras turns up so often in the history of secret societies. In Freemasonry his theorem, called the 47th Proposition of Euclid, became a Masonic emblem, and in many American lodges it appears on the Past Master’s jewel. Historians are cautious about any direct line from his school to the lodges, but the image of the philosopher-initiate shaped Western esotericism from Renaissance Hermeticism to modern sacred geometry.
The painting
Pythagoras holds a pyramid-shaped solid, with the tetractys hanging in the sky above him and his theorem drawn on a cloth beside a lyre and a globe. It was painted by J. Augustus Knapp for Manly P. Hall’s The Secret Teachings of All Ages (1928).
Little-known facts
- The theorem is older than Pythagoras. Babylonian clay tablets from around 1800 BCE, such as the one known as Plimpton 322, list right-triangle number triples more than a thousand years before him.
- Critics in antiquity mocked his supposed golden thigh and his ban on eating beans. One story says he was killed because he refused to flee through a bean field, a tale historians doubt.
- Later writers report that members swore their oaths by the tetractys.
- A famous legend says a follower named Hippasus was drowned for revealing that some lengths cannot be written as ratios of whole numbers. Ancient sources disagree about it, and it may be only a story.
- Iamblichus lists 218 men and 17 women among the famous Pythagoreans, which is why the school is often cited as an early community open to women.
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