Pythagoras: the teaching

With the Pythagoreans conceptual thinking entered a world view shaped by myth. What the teaching covered and why master and pupils can hardly be told apart.

The influence of the Pythagorean teaching reaches into our own time. It is said that through the Pythagoreans rational, conceptual thinking entered a world view that until then had been ruled by myth. For Nicholas of Cusa (Cusanus), the fifteenth-century theologian, philosopher and churchman, Pythagoras was the first philosopher in name and in fact.

The word philosophy, “love of wisdom”, is said to go back to him. He called himself not a wise man but one who loves wisdom.

Coloured woodcut: half-length portrait of a bearded man in a fur cap, above it the label Pytagoras phus — Pythagoras as a late medieval scholar in the Nuremberg Chronicle (1493), woodcut from the workshop of Michael Wolgemut and Wilhelm Pleydenwurff. “phus” stands for *philosophus*. The chronicle used many woodblocks for several people, so this is no portrait.

Master or pupils?

Which ideas really come from Pythagoras himself and which were only developed by his successors can no longer be determined, apart from a very few basic thoughts. Aristotle already almost never speaks of the teachings of Pythagoras, but of those of the Pythagoreans. The pupils traditionally credited their discoveries to the master.

What the teaching covered

How far the teaching reached can be guessed from a summary in Iamblichus, for all due caution about his reliability. In essence he says: Pythagoras was rightly held in high esteem. Through him the Greeks gained a correct idea of the gods, heroes and daimons, of the world, of the movements of spheres and stars with their eclipses, eccentricities and epicycles, of heaven and earth and everything visible and hidden between them. Through him science and spiritual vision took root, everything that makes the soul see and purifies the mind so that it recognises the true first causes of the universe.

Iamblichus goes on to list what was owed to Pythagoras:

the best constitution and concord among the people
common property among friends
worship of the gods and duties towards the dead
legislation and education
the art of silence
sparing other living beings
self-control, prudence and sharpness of mind

From this one can read the roles in which Pythagoras was seen. He was priest, philosopher, statesman and natural scientist, and as natural scientist at once mathematician, astronomer and physician. The next parts follow these roles.

All is number

What united the Pythagoreans despite all their differences Aristotle sums up in a famous sentence: they held the principles of numbers to be the principles of all things. In numbers they saw more resemblances to what is and comes to be than in fire, earth or water, and because they also found the ratios of harmony in numbers, the whole heaven seemed to them to be harmony and number (see Number and sound).

Aristotle reports this not without criticism. The Pythagoreans, he writes, forced the phenomena into their scheme and filled in where something was missing. Because ten seemed perfect to them, there had to be ten heavenly bodies, and since only nine were seen, they invented a counter-earth that no one ever sees. This is the oldest recorded example of a danger this website considers again and again: bending the world to fit the number instead of testing the number against the world (see Chance and pattern).

Two circles of pupils

The Pythagoreans distinguished between akousmatikoi, the “listeners”, who followed rules and sayings, and mathematikoi, the “learners”, who were initiated into the reasons. This division explains why much of the inner circle remained secret. More in Part 8: The Pythagorean brotherhood.

From the akousmatikoi sayings have come down to us that were framed as questions and answers. Iamblichus names some of them: “What is the wisest? Number. What is the second wisest? He who gave things their names.” And: “What is the oracle of Delphi? The tetractys, for it is the harmony in which the Sirens sing.” To these came rules of life whose reason was not explained, such as not eating beans or not walking on the highway. Already in antiquity they were read as parables, the highway, for instance, as the opinion of the crowd.

Shaman or scientist?

Who Pythagoras really was is disputed in scholarship to this day. In 1962 Walter Burkert saw him above all as a religious teacher, almost a shaman, whose fame as a mathematician arose only later. Leonid Zhmud argues, on the contrary, that the early Pythagoreans really did practise mathematics and natural science. Probably there is truth in both, and precisely that makes him so significant for this website: in him number and religion, knowledge and initiation were not yet separated (see Pythagoras: the priest and Pythagoras: the naturalist).

Sources and further reading

Sources

Iamblichus, On the Pythagorean Life, around 300 AD, 81 to 89 (acusmatici and mathematici)
Aristotle, Metaphysics A 5, 985b to 986b
Iamblichus, On the Pythagorean Life 82 to 86 (the akousmata)
Aristotle, Metaphysics A 5, 986a (the counter-earth)