📐

Pythagoras

Ancient Greek Philosopher and Mathematician, Proposer of the Doctrine "All Is Number"

Remembered for a Single Line · Small Roles, Famous Names

Number TheoryThe Transmigration of SoulsThe Pythagorean School

Who they are

Pythagoras (c. 570–495 BC) was an ancient Greek philosopher and mathematician who founded at Croton in southern Italy a secret brotherhood combining philosophical research, religious belief, and a discipline of life, holding that "all is number" — that the order and harmony of the universe, and even whether music is pleasing to the ear, can in essence be explained by numerical ratios (by tradition he discovered a precise mathematical correspondence between the ratios of string lengths and the harmony of intervals). He also believed the soul immortal and subject to transmigration, a belief that made him an early advocate of vegetarianism (fearing to eat by mistake an animal carrying a transmigrated soul). The "Pythagorean theorem" named for him, though earlier applied in the Babylonian and Chinese mathematical traditions, received from the Pythagorean school the earliest known systematic attempt at mathematical proof, and its core conviction of "understanding the order of the universe through mathematical relations" also profoundly shaped Plato’s later philosophical conception of the relation between mathematics and the world of Forms.

Primary sourcesDiogenes Laertius, Lives of the Eminent PhilosophersIamblichus, Life of Pythagoras

Key stories

The Discovery of Intervals in the Blacksmith’s Shop

Legend says Pythagoras, passing a blacksmith’s shop, noticed that hammers of different weights striking the anvil gave off sounds of different pitch, and that among the pitches there was a kind of regular harmonious relation; from this he inferred a deep connection between the sense of musical harmony and numerical ratio, and through experiments measuring the correspondence of string-length ratios to the harmony of intervals reached such important findings as "the octave corresponds to a 2:1 string-length ratio," laying the foundation of the "mathematical harmony" tradition of Western music theory.

The Mysterious Bean Taboo

The Pythagorean brotherhood had a rather odd rule — the prohibition of eating fava beans; ancient sources vary on the specific reason, some linking it to the belief in transmigration, while some modern scholars conjecture it may relate to the prevalence of "favism" (a hereditary condition causing hemolytic anemia from eating fava beans) among the local population; the exact cause of this rule is still an unsolved puzzle of interest to scholars.

Version differences

The "Pythagorean theorem" was already applied in the earlier Babylonian and Chinese mathematical traditions; the Pythagorean school’s contribution lies more in giving the earliest known systematic attempt at mathematical proof.

Relationships

Ally

💡Plato　The stance in Plato’s theory of Forms that "mathematical truth is eternal and unchanging" was deeply influenced by the Pythagorean school

Echoes today

Below are how modern works borrow or reinterpret this name or story — not the original material. The two differ, so keep them apart.

The "Pythagorean theorem" (mathematics education)One of the most basic and famous geometric theorems in secondary-school mathematics education worldwide, named for him.

Appears in

The Pre-Socratics: From Myth to ReasonPythagoras Discovers That "All Is Number"The Pre-Socratics: From Myth to ReasonXenophanes Criticizes Anthropomorphic Conceptions of the Gods

⏳ Who lived at the same time as Pythagoras? →🔗 Who taught whom →

← Back to Figures