Pythagoras Bust

As mentioned last time, Anaximander had a student named Pythagoras (570 – 495 BCE) who is said to have met Thales, who told Pythagoras to go to Egypt to learn about mathematics, science and the cosmos.  Pythagoras is best known today for the Pythagorean theorem of mathematics, triangular like much of the work of Thales as well as the pyramids of Egypt.  Pythagoras is the most famous of the ‘presocratic’ philosophers, those who taught before Socrates, Plato and Aristotle.

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Plato Marble Statue

While the Milesians had a school by association, Pythagoras is the first Greek thinker to found a school which for hundreds of years was known as the Pythagoreans.  Pythagoras is also the first to call himself a ‘philosopher’, a lover of wisdom, and he had a great influence on Plato, the most famous and influential of Greek philosophers.  Plato, like Pythagoras, founded a major movement of Platonism (known today as Neoplatonism), and it was from several prominent Neoplatonists (particularly Porphyry and Iamblichus) that we know of Pythagoras and his teachings.  These Neoplatonists believed that both Pythagoras and Plato were sent by the gods to humanity.  While the Pythagoreans only lasted a few hundred years, the Neoplatonists brought much Pythagoreanism along with Platonism into the Islamic golden age and the Italian Renaissance.

pythagoras statue on Samos

Pythagoras was born on the island of Samos, off the Turkish coast of ancient Ionia and not far from Miletus.  He traveled before settling in Croton, a Greek colony in what is today southern Italy.  Pythagoras gathered many students and these Pythagoreans became involved in politics, playing a significant part in the aristocratic rule of Croton.  Like Plato, Aristotle and other Greek thinkers, Pythagoras believed in aristocracy through meritocracy, that those who rose in achievement and education should rule society.  Later, the Pythagoreans were persecuted and chased off the island.  Their meeting place was set on fire and many of their members died in the flames.

Pythia priestess of Delphi

Pythagoras, like Plato, was revered by later followers as a divine being, and much mythology was added to his biography.  He was said to have been the son of Apollo (a name which the Pythagoreans interpreted to mean ‘Not’ (A) ‘Many’ (poly), a supreme oneness like that of Anaximander’s apeiron and Xenophanes’ god we will examine next).  Like Apollo and the sun, Pythagoras was said to glow with a sagely aura.  The Oracle of Apollo at Delphi, the place Anaximander places as the center and navel of the earth and cosmos and the place Socrates went to inquire about his own worth, was the home of the Pythia, the priestesses who huffed incense and/or geological gasses to predict the future in enigmatic riddles.  The name ‘Pythagoras’ means ‘Apollo-Priestess Professor’, one who professes the greatness of Apollo’s Oracle to others (as in the Agora, the public square), one who speaks for Apollo like the priestesses, or one who speaks/professes on an equal level with the priestesses.  One Delphic priestess named Themistoclea is said to have taught Pythagoras about ethics.

Indian cobra head

Pythagoras had many legends told about him.  Other than glowing like the sun itself, he was said to have a golden thigh that he showed off once at the Olympic games (it is not written which thigh was golden or why he did not have two), that he could predict the future several generations, that he could translocate (be in two or more places at once, similarly said of some Indian gurus), that a river once welcomed him by calling his name, and, best of all, that he killed a poisoned snake by biting it (an ancient version of the “Bigfoot keeps a picture he took of Chuck Norris” bit).

Shiva meditating

Pythagoras is said to have traveled extensively and according to Diogenes Laertius studied with the Egyptians, the Babylonians, the Phoenicians, the Persians, the Judeans, the Indians, and others (note that he mentions the Indians).  While this is the most extensive list of instructive cultures for a thinker so far, as mentioned previously it is difficult to know whether Pythagoras reached all of these places or if he is made to look worldly afterwards.

Xenophanes said Pythagoras believed in the transmigration of souls, and that Pythagoras once stopped a man from beating a dog saying he heard the voice of his dead friend in the dog’s cries.  Heraclitus affirms this too, ridiculing Pythagoras for being the wisest of men, yet believing that in one previous life he had been a sardine, and in another a cucumber.  Heraclitus seems to be using Pythagoras to show us that the wisest are still foolish, only relatively wise themselves.  Like Thales, Pythagoras thought all things were full of souls and/or gods, which required the ethical treatment of all life.


It is difficult to know about teachings of Pythagoras and the practices of the Pythagoreans as they believed in keeping secrets.  In the ancient world knowledge was often kept secret for its own protection, as we will see Plato advocate in his Republic.  The most important teachings are spoken to those one trusts and lived in practice, not written down for unknown people to misinterpret.  Pythagoras was not known to have committed any of his teachings to writing.  Not only was divulging teachings outside community forbidden, new members were tested as to how long they could keep silent, refraining from saying anything to anybody.  The community was divided into the new ‘listeners’ who were instructed in general teachings and the inner circle of ‘learners’ who actively pursued truth and shared their findings only with this group.  Some sources say these were two separate schools, one dogmatic and the other progressive, while others say these were two levels in one and the same school/society.

pythagorean teaching

There were many female Pythagoreans in the community, though all the major Pythagorean texts left to us are written by men and it is unclear what status women would have had.  Some say the Pythagoreans shared all things in common, which is Plato’s ideal of the Republic.  This could include property or relationships and child rearing.

beans on the vine

The Pythagoreans were believed to be vegetarian, though it could be that only some types of meat were prohibited.  The Pythagoreans didn’t eat beans, as they were believed to be embryonic souls at an early stage of transmigration (possibly because beans resemble testicles).  Diogenes Laertius says that when the Crotons burned down Pythagoras’ school, Pythagoras tried to escape but found he could not without trampling bean plants, and so he allowed himself to be caught and killed.  All other sources say he escaped, and make no mention of beans being harmed in the burning of the school.

Gaffurio Pythagoras Music

For Pythagoras, the cosmos is ruled by order, specifically mathematics and music.  The story goes that as Pythagoras was passing a blacksmith’s workshop, he heard the various hammer blows harmonizing with each other.  On closer inspection, he discovered that the hammers created different tones proportionately to their size, so a hammer harmonized naturally with another half its size.  While this story is thought to be false, he could have discovered the same in numerous ancient cultures by measuring string lengths of various instruments.

The Harmony of the Spheres (also Music of the Spheres), the mathematical rotations of the planets was seen as a silent symphony.  It was mentioned with the epic poets that larger choral productions involved many singers and instruments along with choreography.  Pythagoras thought this was how the cosmos worked as well as the soul, which was itself like the stars a harmony of numbers and proportions.  Mathematics is unchanging (2 + 3 = 5), unlike the body but like the mind, which is ideal and immortal.  This prefigures Plato who also believed that the ideal and numerical are the supreme causal forces of the physical and material.


Numerology is the study of sacred numbers, back when mathematics and physics were not specialized apart from the religious traditions (like alchemy to modern chemistry).  The Tetractys is a ten point pyramid, ten being the perfect number.  A sacred symbol to the Pythagoreans, they were said to swear oaths in front of it and that it was revealed to Pythagoras by the divine (likely Apollo’s Oracle at Delphi).  All proceeds out of the great One, the supreme All that Islamic and Christian Neo-Platonists later equated with monotheism.  The Tetractys series does not simply unfold into a two dimensional pyramid, but a three dimensional pyramid as well (one dimensional point, two dimensional line, two dimensional triangle, three dimensional pyramid).  The pyramid is the shape of fire and light, fire being pointed on top and light shining down through clouds appearing as a pyramid.  The Pythagoreans believed that the world originated out of a singular point (like modern Big Bang Theory), which gave birth to numbers, from which came points, from which came lines, from which came planes, from which came solids, from which came the elements.

platonic pythagorean elements shapes

Unlike the Milesians, Pythagoras made numbers and proportions the primary element, his arche.  Pythagoras taught that earth is made of cubes, fire from pyramids, air from the octahedron (eight-sided double pyramid), water from the icosahedron (twenty-sided) and the sphere of the cosmos from the dodecahedron (twelve-sided).  The numbers, lines, sides, and things of the cosmos are separated and delineated from each other by void, which is inscribed by the breath of the cosmos.  This void, like the cosmos itself, is not infinite but finite, limited in proportion.


Aristotle argued against the Pythagoreans saying that, unlike the Milesians, the Pythagoreans base their cosmos on things not perceivable in nature.  We do not see math or unchanging numerals when we look into the world.  It should be mentioned, however, that Aristotle did believe that the heavens are driven by absolute forces and that this comes down and is mixed up and chaotic here on earth unlike its perfect circling in the heavens.

pythagorean harmony

The musical intervals of fourth, fifth and octave were thought to be sacred.  Plato followed Pythagoras in this, and these ‘ratios’ are the basis of our word ‘rational’ (as well as ‘irrational’).  The ‘rational’ is that which is correctly proportional.  Musicians were well aware in earlier cultures that plucking half of a string gives one an octave, three fourths gives one a fourth and two thirds gives one a fifth.

Here is a place for Nietzsche’s criticism of Plato and idealism: the true is what is most beautiful to us, and with Pythagoras and Plato the beautiful musical intervals and symmetric constructions of mathematics are revered as the truly real that gives rise to the physical and apparent.  Asymmetric organic fractal patterns were seen as abhorrent and nonsensical even though Mandelbrot showed how they are the beauty of nature through fractal geometry while working at IBM in the 1960s.  Just like many modern physicists, Aristotle tells us the Pythagoreans assumed the cosmos is governed by a few universal mathematical principles.  Why must the cosmos correspond to simple mathematics, when even math is not entirely systematic according to Godel’s incompleteness theorem?

pythagorean square sum triangle

When thinking of a square number, such as those involved in the Pythagorean theorem, it would have been understood by Pythagoras as a square of dots (ex: 9 is a square grid of three rows of three dots each).  Pythagoreans would only be able to square whole numbers or numbers that could be expressed in simple ratios (ex: the square of two thirds is four ninths).

Oppositions, central to human thought, were important to the Pythagoreans, and their set of ten opposites is similar to other systems found across cultures (some are identical to Daoism).  Limit, odd, one, right, male, rest, straight, light, good, and square were paired against unlimited, even, many, left, female, moving, bent, dark, evil, and oblong.  Note that first is limit/unlimited, from which comes odd/even, from which comes one/many, akin to the generation of the cosmos.  Square and oblong refer to numbers, which are formed in rows of dots as a square or as close to a square as possible.


Particular numbers were associated with important things.  One was associated with mind and essence, as mind is the union and essence of the human individual and of the cosmos.  Four was associated with justice, as it is the first number which is an even number times an even number (2 x 2).  Five was associated with marriage and union, as it is even added to odd (2 + 3), female added to male.  Seven was associated with fulfillment, as children were thought to become adolescents at seven and then adults at fourteen.

While specifics of Pythagoras’ teachings are unknown, it seems he taught moderation and abstaining from excessive pleasures to thrive in mind and body.  Similar to Indian asceticism, the soul must be ordered and thus purified.  Like Buddhists, Pythagoreans believed that the soul/mind/self is reincarnated until it achieves release into union with the soul of the cosmos, the universal soul.  Unlike Buddhists, Pythagoreans see this as a release from the limitless into union with order, not a release into the limitless which the Pythagoreans believed to be largely outside the cosmos.

egyptian wall birds

Heraclitus says the Egyptians taught a three-thousand year cycle that takes the soul through all orders of animal life before it is again reborn as a human being.  It is not clear whether Pythagoras adhered to this, but Herodotus says several Greeks did without mentioning names.  Pythagoras saw that the human individual was bound by cycles like the cosmos, and so individuals should strive to adhere to balanced cycles that build one up rather than destructive cycles that tear one apart.


Similar also to Egyptian and Indian doctrines, Pythagorean dietary restrictions aimed at incurring the least amount of punishment and karmic demerit.  Some plants such as beans were thought to incarnate human souls and so were prohibited, but other plants, honey and nuts were acceptable.  It may be that later Neo-Pythagoreans lifted the ban on certain meats or got rid of the dietary restrictions entirely.  Diogenes Laertius mocks Pythagoras with several humorous poems, in one saying that like Pythagoras, he also does not eat living food, but prefers his meat roasted and salted.

white rooster

Other prohibitions for Pythagoras included not touching white roosters (as they are sacred), not picking up food off the ground (ancient 0 second rule), not eating on the day of an acquaintance’s death, not stirring fire with a knife (as it might offend Apollo), not urinating while facing the sun (again, it’s rude to Apollo), and making your bed every day.

Some of these prohibitions are symbolic of ethical teachings.  The Maxims of Pythagoras were sayings that are concealed through metaphor from those outside the Pythagorean community but easily understood once explained.

“Do not poke the fire with a sword” meant “Do not provoke the angry”.

“Suffer no swallows around your house” meant “Do not associate with the chatty”.

“Do not unload people, but load them up” meant “Encourage work and virtue”.

pythagoras statue with toga

“Do not sleep at noon” meant “Stay aware and alert”.

“Do not cut wood on the road” meant “Do not use or do privately what should be public”.

“Sit down when you worship” means “Take your time doing what needs to be done”.

“Eat not in the chariot” meant “Focus on the task at hand”

“Stop not at the threshold” meant “Be decisive and take a side”.

“Avoid the weasel” meant “Avoid the deceitful”.

“Sleep not on a grave” meant “Work rather than rely on inheritance”.

“Threaten not the stars” meant “Do not threaten superiors”.

“Do not place a candle against the wall” meant “Do not waste time on the hopelessly ignorant”.

“Do not speak in the dark” meant “Do not talk about what you don’t know”.

pythagorean Y

Another symbol used was the Pythagorean Y, in ancient Greek the capitalized letter ‘epsilon’.  One forks into two, the right and left paths.  The right path is tough, but it ends in virtue, peace and immortality.  The left path is easy, but ends in hardship and destruction.  This applied equally to the cosmos and the human individual.  Virtuous things and people prosper and become permanent, like the cosmos itself.

Pythagoreanism was a big influence on later secret mystical societies of the Middle East and Europe such as the Rosicrucians and the Freemasons.  Pythagoreans, like Masons, were said to wear symbols by which they could recognize each other.  Like Masons, many New Age groups take Pythagorean teachings as the sacred wisdom of ancient Egypt, sometimes adding aliens into the mix as the builders of the pyramids and teachers of the Egyptians.