Definition:Pythagoreans

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Definition

The Pythagoreans were a semi-mystical cult which dated from around $500$ B.C.E., founded by Pythagoras of Samos.

Can claim to be the world's first university.

It is feasible to suggest that their initial work in the field of geometry may have formed the basis of at least the first two books of Euclid's The Elements.


For specious socio-political reasons based on the fact that their puritanical philosophy was at odds with the contemporary way of thinking, in $460$ B.C.E. their cult was attacked and destroyed.

Its survivors scattered, many of them fleeing to Thebes in Upper Egypt.


Quadrivium

The quadrivium was the medieval name of the required course of study of the Pythagoreans, which had been adopted by the educational establishments in Europe.

The required bodies of knowledge were divided into discrete and continuous:

Thus:

Arithmetic: study of the absolute discrete
Music: study of the relative discrete
Geometry: study of the stable continuous
Astronomy: study of the moving continuous.


Trivium

The trivium was the medieval name of the supplementary course of study of the Pythagoreans, adopted by the educational establishments in Europe.

These supplementary bodies of knowledge were:

Grammar
Rhetoric
Logic.


Notable Quotes

Number rules the universe.
-- Quoted in 1937: Eric Temple Bell: Men of Mathematics: They Say: What Say They? : Let Them Say


Everything is number.
-- Quoted in 1992: George F. Simmons: Calculus Gems: Chapter $\text {A}.2$: Pythagoras (ca. $580$ – $500$ B.C.)


Critical View

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but, saturated with it, they fancied that the principles of mathematics were the principles of all things.
-- Aristotle in Metaphysics (Book $\text I$, Chapter $5$, ca. $300$ B.C.E.)


Sources