Pythagoras Founds a Brotherhood Built on Number
A secretive Greek society treats whole numbers as the key to the universe, then is undone by the one number that refuses to be a ratio
Quick facts
- Pythagoras's dates
- c. 570 BCE to c. 490 BCE
- Society founded at
- Croton, southern Italy
- Membership tiers
- Mathematikoi (inner), akousmatics (outer)
- Contradicting discovery
- Irrationality of the square root of 2
What happened
Pythagoras, born around 570 BCE and dead by around 490 BCE, left no writings of his own, and the secrecy code followed by the society he founded at Croton in southern Italy means historians today treat him as a genuinely mysterious figure, with early biographers attributing divine powers to him that make separating fact from legend difficult. The Pythagorean society had two tiers of membership: an inner circle called the mathematikoi, who lived communally, held no personal possessions, and were vegetarians taught directly by Pythagoras, and an outer circle called the akousmatics, who kept their own homes and property. Both men and women were permitted to join. The society held that whole numbers and their ratios were the key to understanding the universe, a belief the discovery of irrational numbers, certainly attributed to the Pythagoreans though unlikely to be due to Pythagoras himself, directly contradicted, since a number like the square root of 2 cannot be written as any ratio of whole numbers at all.
Why it matters
The Pythagoreans are the first documented group to treat mathematics as a path to philosophical and even religious truth rather than only a practical tool, a stance that shaped how later Greek mathematicians, especially Plato, thought about numbers. The irrational-number discovery that broke their own worldview from the inside also marks one of the first moments in history when a mathematical proof forced people to abandon a belief they were emotionally and philosophically committed to.
How we know
No writing by Pythagoras himself survives, and the Pythagorean code of secrecy means everything known about the society comes from later Greek authors summarizing or reporting on a tradition several generations removed from Pythagoras's own lifetime, which is why historians describe him as a legendary as much as a historical figure.
Sources
- MacTutor History of Mathematics, University of St Andrews. Pythagoras · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
- MacTutor History of Mathematics, University of St Andrews. Pythagoras's theorem in Babylonian mathematics · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
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Related timelines
- Ancient Greece → · See the Ancient Greece timeline for the wider Archaic-period world Pythagoras worked in, including the Greek colonization of southern Italy and Sicily that put Croton on the map.