Mathematics

Pythagoras

Greek mystic-mathematician · ~570–495 BC

Number as the hidden order of the cosmos - and the theorem that bears his name.

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Lessons

The Theorem and the Brotherhood

The theorem that bears Pythagoras’s name, and the strange brotherhood that first proved it - a community where mathematics, music, and mysticism were one, and where to discover a truth was a religious act.

All Is Number

The boldest idea of the Pythagoreans - that number is not merely a tool for counting but the very substance and structure of reality, the hidden order from which all things are made.

The Numbers Hidden in Music

The Pythagorean discovery that musical harmony is governed by simple whole-number ratios - the first time an invisible mathematical law was found behind a sensible quality, and the seed of mathematical physics.

The Crisis of the Irrational

How the diagonal of a simple square produced a number that no ratio of whole numbers could express - shattering the Pythagorean faith that all is whole-number ratio, and forcing mathematics to confront the irrational.

The Soul, the Cosmos, and the Way of Life

The other half of Pythagoras - the religious teacher who taught that the soul is immortal and reborn across bodies, that the cosmos is an ordered harmony, and that a disciplined life of study could purify the soul and a…

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