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Pythagoras and the Pythagoreans
c. 570–495 BC· Philosopher· Reality, mind & God
DebatedScholars disagree about what happened, what it means, or who said it.
A Greek sage who led a religious brotherhood in southern Italy and taught that reality is built on number.
See it on the Philosophy map →The idea
Born on Samos, he settled around 530 BC in Croton, Italy, heading a community with strict rules: shared property, silence, no beans, belief in reincarnation. Idea: the universe is ordered by number. Reasoning: musical harmony follows simple ratios; a string half as long sounds an octave higher (2:1). If music is number, perhaps everything is. Main objection: Aristotle asked how abstract numbers could make up physical, weighty things.
Why it matters
The conviction that nature is written in mathematics runs from him through Plato to Galileo and modern physics.
Legacy and sources
He wrote nothing. Accounts come from followers and biographies written centuries later by Porphyry and Iamblichus; Philolaus (c. 470–385 BC) is the earliest Pythagorean whose words survive.
Still debated
What he taught versus later followers is unclear. The 'Pythagorean theorem' was known in Babylon over a thousand years earlier; whether he proved it is doubtful.
Connections (2)
▸Pythagoras and the Pythagoreans inspired PlatoMostly agreed
The connection
Plato took from the Pythagoreans the belief that mathematics reveals the hidden order of reality, that the soul is immortal and reborn, and that philosophy is a disciplined way of life. His Timaeus builds the elements from geometric triangles, and his Republic makes years of mathematics required training for rulers.
When and how
Around 388 BC Plato visited southern Italy and befriended Archytas of Tarentum, a leading Pythagorean statesman and mathematician.
How sure are we?
Aristotle (Metaphysics I.6) says Plato followed the Pythagoreans in most things; Pythagorean themes run through the Phaedo, Republic and Timaeus.
Debates and open questions
Pythagoras left no writings, so separating his own ideas from later Pythagoreans, and from Plato's reworking of them, is very hard.
▸Pythagoras and the Pythagoreans answered "number" to What is ultimately real?Mostly agreed
The connection
Where the Milesians named a stuff, Pythagoras named a structure: number and ratio. Because musical harmonies and shapes follow numerical rules, Pythagoreans claimed all things are, or imitate, numbers. This shifted the question from matter to form, a step Plato took further.
When and how
Croton, southern Italy, from about 530 BC, developed by later Pythagoreans such as Philolaus in the 5th century BC.
How sure are we?
Aristotle's Metaphysics reports that the Pythagoreans held 'the principles of mathematics are the principles of all things.'
Debates and open questions
Whether this was Pythagoras' own view or that of later followers like Philolaus is unclear.