More Than A Theorem: Pythagoras and his Brotherhood

More Than A Theorem:
Pythagoras and his Brotherhood

by Samuel Scarborough


Everyone whom has taken geometry has heard of Pythagoras and his famous Theorem. The Pythagorean Theorem states:

That the square of the hypotenuse of a right triangle equals the sum of the squares of the sides forming the right angle.1)

The following drawing often represents this idea with a diagram of right triangles:

The famous theorem is often expressed by the equation of:

a2 + b2 = c2

This is of course not the only thing that Pythagoras is remembered for. There are a great deal of other contributions that he and his Brotherhood made to Western Civilization or to Western Metaphysical and Magickal thought. We are going to explore the life of Pythagoras and many of his contributions that have come down to us, and also show his influence on others whom have made their influence felt on the Western Mystery Traditions.

The Life of Pythagoras

Very little accurate information concerning much of the life of Pythagoras has come down the centuries to us. Part of this comes from the fact that in all of his teachings, he never committed anything to writing and forbid his students and disciples from writing his teachings down. What we do know of his life comes from three separate lives written about Pythagoras in late antiquity, by Diogenes Laertius, Porphyry, and Iamblichus (died circa 330 C.E.), in order of age.2) It is from these documents that we learn anything about the life of Pythagoras before his arrival in Kroton (Croton), in Magna Graecia (southern Italy and Sicily) around 530 B.C.E., but if this documents are to be believed, then Pythagoras had a most interesting life before he appears in any other historical documents. Each of these documents gives a better account of the life of Pythagoras the further from Pythagoras'; own time it is.3)

What all three of these classical accounts of Pythagoras' life do agree on is where he was born and who was his father. The exact year of his birth is in question though, but tradition has it at 569 B.C.E.4) He was born on Samos, near Asia Minor, and his parents were Pythias5), mother, and Mnesarchus6), father. Mnesarchus was said to not to have been Greek, but a Phoenician, originally from the city of Tyre. Pythagoras' father was a fairly successful merchant according to these accounts; in others he is a stonecutter.7)

Nothing at all is known of his childhood on Samos. One of Pythagoras' first mentors was Pherecydes of Syros who taught at Delos.8) He was an excellent student, who while still young made a name for himself in the other centers of learning in Ionia (Asia Minor).

Shortly after the death of his father, and sometime around being eighteen years of age, the tyrant Polycrates came to power on Samos. Polycrates was a rather brutal and strict tyrant, and Pythagoras seeing that learning would be limited under Polycrates' rule, left Samos. He used his father's contacts in Polycrates' court to secure a letter of introduction to the Egyptian pharaoh Amasis.9) The connection between Polycrates and Amasis is due to their having fought against the Persians.

Though before heading off to Egypt, Pythagoras headed to Syros spending time with Pherecydes. From Syros, he traveled to Miletus, which is on the coast of Asia Minor to study at the schools of Thales and Anaximander. Pythagoras' studies with Thales and Anaximander helped to found the basis of his questions into the nature of the world around him. It is believed that Thales took Pythagoras as a personal student and further encouraged him to go to Memphis in Egypt and study with the priests there.10)

The story goes that from Miletus, Pythagoras traveled in the direction of Egypt, stopping at local centers of learning along the way. Supposedly he was initiated into the mysteries and rites of the Phoenician gods Baal and Ashtara in the cities of Bylos and Tyre. From the Phoenicians he learnt how to interpret dreams, how to use incense in ritual, and an understanding of the principals of ritual.11)

After leaving the lands of the Phoenicians, mostly present day Lebanon, he continued into Egypt. In Egypt he traveled to Heliopolis and the court of Amasis. Amasis admired the Greek culture and had made several extravagant gifts to some of the major Greek sanctuaries, including the Temple of Apollo at Delphi. Here, in Heliopolis, Pythagoras presented the pharaoh with his letter of introduction. Amasis was awed by the bearing and knowledge of the young Pythagoras. He granted Pythagoras with the needed documents to be properly admitted into the priest schools of Egypt.12)

At that time there were four major centers of learning in Egypt; Heliopolis, Memphis, Hermopolis, and Thebes. Since Pythagoras was already in Heliopolis, he went to the priest there first, but they refused to train him, as he was not Egyptian. From Heliopolis, he traveled to Memphis, south of Heliopolis. It was rumored that the temples in Memphis held the more ancient knowledge of the kingdom. The priests in Memphis used the same argument to get rid of Pythagoras and sent him to Thebes.

It was apparently in Thebes that the priest decided to teach Pythagoras. Though before initiating him into any of their mysteries they forced him to perform severe and menial work. He was also, according to Iamblichus, given a strict program of study, temple service, fasting, and other ascetic hardships, which far exceeded what any other dedicant endured. They did this with the intent of getting Pythagoras to abandon his plan to learn the mysteries of Egypt. Pythagoras did not quit, but through his work and dedication earned the respect of the priests in Thebes. They initiated him into their mysteries, and lived among them studying the sciences of Egypt.

After learning all that he could in Thebes, Pythagoras traveled to the other centers of learning throughout Egypt. He managed to earn the respect of the priests and scholars that he met throughout the land. He was the first Greek to become fluent in the Egyptian spoken language, the written language, the herbalism, medicine, geometry, and mathematics of Egypt. At that time no other foreigner of Egypt had ever learn so much of Egyptian culture.13)

Pythagoras stayed in Egypt for twenty-three years before leaving. He did not leave on his own though. During that year, the armies of Cambyses of Persia conquered Egypt. The royal house was executed; the priesthood captured, and was sent to Babylon. It was here that again, his knowledge and willingness to accept new ideas and situation that helped Pythagoras. The priests in Babylon learned much from him about Egypt, while he learned from them.

Pythagoras spent twelve years in Babylon learning the mysteries of the Persians. He was initiated into the Persian mysteries of Ahura Mazda, perfected his knowledge of mathematics, harmony and rhythm, and mastered the art of astronomy. He was at this time fifty-six years old when he returned to Samos, now part of the Persian Empire.

Pythagoras attracted the attention of some of the people on Samos and acquired a few students. One of these was Eurymenes, an athlete of Samos who was of small stature, but through the training regimen that Pythagoras set for him was able to become an Olympic champion. This regimen apparently differed from the normal training regimen that Greek athletes undertook, which consisted of training and eating only cheese and figs. It has been thought that Pythagoras encouraged Eurymenes to eat meat to build up his strength, and to visualize the perfection of skill that he used.14)

He left Samos to tour the various shrines and oracles of the Greek world, first going to the sanctuary of Apollo on Delos. From there he traveled to the oracles at Samothrace, Imbrus, Eleusis, Thebes, and ultimately to Delphi. Apparently he learned at Delphi that the roots of the worship of Pythian Apollo had its beginnings on the island of Crete and set out for Crete.

In Crete, Pythagoras was initiated into the cult of Morgos, which partook in orgiastic musical rites related to the birth and death of Zeus on the island of Crete. Iamblichus describes how Pythagoras was purified by the application of meteoric stones in a ritual that required him to lie face down at dawn beside the sea, and that at night he lie beside a river crowned with a wreath of black lambs wool. After this, Pythagoras entered a cave on Mount Dicte where the infant Zeus had been hidden to prevent Kronos (Chronos) from eating him. Here he remained in solitude for twenty-seven days until he came forth and worshiped with the other initiates.15)

From Crete, Pythagoras traveled to Sparta. There he studied their government and ways of life. He was impressed with the lifestyle of the Spartans, which gave him the idea for an ordered philosophical community. He then returned to Samos and established his first school, called the Semicircle.16)

While on Samos, his reputation was such that he could not devote the time he wanted to learning and pursuit of knowledge as the people constantly asked his advice on how to govern. Coupled with the fact that the Samians, people of Samos, were not serious students, he decided to leave his home yet again. This time he set out for Kroton (Croton), a republic in Magna Graecia on the southern coast of Italy. He arrived here around 530 B.C.E. not long after the defeat of Kroton (Croton) by the Locri at the Sagas River.17)

Iamblichus reports that when Pythagoras arrived at Kroton (Croton), a crowd gathered before he even set foot on shore. Many rumors where spreading about him in the city, anything from he was Apollo, another of the Olympian gods, or a powerful guardian spirit sent by them.18) Pythagoras addressed the crowd when he got ashore, but what he said is not recorded, partly at his request. Whatever he told the people of Kroton, they respected him and his wishes, and because of his speech nearly two thousand of the inhabitants, both men and women, of the city decided to be his students.

Pythagoras set up a community near Kroton that had two types of students or members. These were those that lived full time at the community and those that only came for lectures on a regular basis. The reason for the latter was that many people of Kroton and the other cities in the southern Italian region of Magna Graecia had responsibilities to their communities and cities.19) Strictly speaking those students that lived full time at the community were called Pythagoreans, while those that came only for the lectures were known as Pythagorists. To the outsider, this distinction was rarely understood. Especially since the members of both groups were referred to as homakooi (those who come together to listen)20), it can be seen how this distinction would confuse an outsider.

The community began to have a strong effect on Kroton. The Thousand, the ruling body of Kroton, listened to the advice of Pythagoras. One of the main beliefs of Pythagoras and the Pythagoreans/Pythagorists concerning government was that the people entrusted the government to them, and that this government should not be exploited for selfish purposes.21) In other words that the governing body should see itself as equal to the populace that it governed, rather than being an elite body. Only in this way would the city of Kroton and its people prosper.

Apparently, this line of thinking was very popular in the region, as over the years the cities of Sybaris, Catanes, Rhegium, Himaera, Agrigentum and Tauromenium changed from more repressive governments to the more liberal one espoused by the Pythagoreans. Pythagoreans and Pythagorists in these other cities helped pass laws, which help them to be more prosperous overall and models of peace.22)

It seems that the people of Kroton were content with the state of things in just their city, where the teaching of Pythagoras and his students influenced the ruling oligarchy, but the influence of the city had spread beyond their walls and borders. It now expanded by controlling or colonizing other areas of Magna Graecia in southern Italy. These included Caulonia and Terina, and after defeating its rival city Sybaris in 510 B.C.E., the territorial expansion and increased wealth caused a shift in the political influence of the traditional ruling families of Kroton.23) One particular instance that turned the new powers against the Pythagoreans was that after the defeat of Sybaris, the land was not divided up by lot, but remained to those whom were already in power. This started to cause popular sentiment to sway against the Pythagoreans.

Kylon, an aristocrat of Kroton whom had been rejected by Pythagoras and the community to be taught by Pythagoras, turned the general resistance into hostility. Kylon took this as a personal insult.24) Kylon plotted to seize control of the local government of Kroton or to insinuate himself and his closest accomplices into positions of power.

Kylon used the popular movement within the area to form an assembly of the people, to open the public offices to all citizens, and to elect representatives that the Thousand, the traditional ruling body, would be held accountable. The Pythagoreans opposed all these actions.25)

Kylon and his accomplices saw their opportunity to move ahead with their plans when Pythagoras left Kroton to travel to Delos to visit his old mentor Pherecydes whom was on his deathbed. Kylon and one of his followers, Ninon used the opportunity to attack the Pythagoreans. Kylon inflamed the people with a highly provocative speech against the Pythagoreans, while Ninon countered that he had been initiated into the mysteries of the Pythagoreans and had proof that Pythagoras and the Pythagoreans were plotting against the people of Kroton. He used sections of a book called, The Sacred Discourse, supposedly written by Pythagoras as evidence.26) One of the passages that was used to enrage the people of Kroton was supposed to be the following:

It was better to be a bull for one day than a cow for life.27)

John Milton in Paradise Lost later echoed this sentiment when he has the rebellious archangel Lucifer utter the famous, “It is better to rule in Hell, than to be a slave in Heaven.” Ninon's evidence and quotes from this book so enraged the people of Kroton that the Pythagoreans lives were in danger. Demo cedes, a famous physician and Pythagorean was driven from the Thousand. Days later, a group of Pythagoreans were attacked at the house of Milon, the great Olympian wrestler, and the house was burnt to the ground by the angry mob. Only two of the gathered Pythagoreans escaped with their lives.28)

This incident corresponds to reports made by the historian Polybius that state that in the middle of the century Pythagorean synedria (meeting places) were burnt down in Magna Graecia and that leading citizens and men lost their lives in each city.29) This seems to imply that the opposition to the influence of Pythagoras and the Pythagoreans had spread to all those cities in the region that had been influenced by Kroton and the Pythagoreans.

As the story goes, Pythagoras returned to Kroton during the height of the tensions against him and his followers. After several more attacks against his followers in and around Kroton and he surrounding communities, the Pythagoreans withdrew from the public eye. As the state of affairs grew worse, Kylon and his followers brought in judges from several of the other cities of Magna Graecia including Tarentum, Metapontum and Caulonia to render verdicts against the Pythagoreans. They drove the Pythagoreans into exile from Kroton, and they also drove out those citizens whom would not swear loyalty to the existing government. Kylon then had all the lands of the exiles seized and redistributed.30)

Pythagoras escaped Kroton by boat, sailing nearly fifty miles to the south to Caulonia. From Caulonia, he traveled overland to Locri, but the Locrians heard of his approach and turned him away at their borders. Pythagoras then traveled to Tarentum by ship, but met the same fate in Tarentum as at Locri. Again he left and headed to Metapontum. The same fate seemed to be happening to his followers because after the upheaval reported by Polybius, there are Pythagorean refuges in Greece proper, such as the noted Pythagorean Philolaus in Thebes.31)

Pythagoras managed to get into the city of Metapontum and take refuge, but when people learned he was in their city they rose up against him. He fled into the Temple of the Muses in Metapontum where he was given sanctuary. He remained in the temple for forty days without food and died there of starvation.32) Tradition holds that Pythagoras was buried in Metapontum.

The Teachings of the Pythagoreans

The teachings of Pythagoras have come down to us in very small fragments, and not directly form Pythagoras himself as he commanded that none of his knowledge be committed to writing, but rather to memory. What we do know of the teachings of Pythagoras and the Pythagoreans comes to us from a variety of sources after the death of Pythagoras. We do know that Pythagoras placed a great deal of his teaching on mathematics and numbers in general. One source of this is from Aristotle (384-322 B.C.E.), the famous philosopher who wrote in his Metaphysics:

Pythagoreans applied themselves to mathematics, and were the first to develop this science; and through studying it, they came to believe that its principles are the principals of everything. And since numbers ar by nature first among these principals, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analogues of what is and comes into being – such and such property being Justice, and such and such Soul or Mind, another Opportunity, and similarly, more or less with all the rest – and since they saw further that the properties and ratios of the musical scales are based on numbers, and since it seemed clear that all other things in nature were modeled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of number to be the elements of everything, and the whole universe to be a proportion or number.33)

Much of the importance of numbers in Pythagoras' philosophy, a word which Pythagoras himself was the first to use to describe himself as philo sophos (lover of wisdom)[34), came from the importance of sacred numbers in the Orphic Mysteries, and from his studies in Egypt and later in Babylon and Persia. For the Pythagoreans, the number ten was the most sacred number, and they had a representation of both the number ten and the other primal numbers, numbers one through nine that led up to ten, in a sacred symbol. We know that the Pythagoreans had a sacred symbol that they could identify each other by and that held a great deal of their teachings. This symbol was a pattern of ten dots known as the tetraktys (this is from tetra, which means four), and the symbol was made up of four levels that formed into a triangle with a base of four dots, followed by a level of three dot, followed by two dot, and finally a single dot at the top level of the symbol. This sacred symbol to the Pythagoreans was expressed by the following arrangement of dots in the triangular pattern:

. .
. . .
. . . .

The glyph of the tetraktys may have had its origins in an arrangement of pebbles used to study mathematics, as well as in first letter of the Greek word dekad (meaning ten) was a triangle, the letter delta in the alphabet. This letter was also used in the Herodianic, numerical system to represent the number ten.35) There developed a study of the mystical properties of the numbers in the decad, called arithmology. This study dealt with the attributes and magickal powers of the numbers, relating them to animate and inanimate objects, as well as, to certain gods and goddesses.36) The system is discussed in Plato's Timaeus, where it survived along with three other books dedicated to the subject to the modern age. I give the examples of each number of the decad below using the arithmology.

The meaning of the tetraktys once it is broken down by each individual line and dot has a rather striking similarity to the later Tree of Life used in the Kabbalah. The concepts attached to the tetraktys are as follows:

Monad: Was of course One, and represented many metaphysical principals and concepts; it was known as eidos, the source of limit and form; the eudaimonia, the demiurge, the creator; happiness; harmony, order and friendship. It was equated to Apollo, the god of reason, and to Hyperion, the central flame, and both the sun as the center of the universe and the mind as the center of all within the human body. It also represented Unity and Perfection.

Dyad: Is of the number Two. For the Pythagoreans, this number represented the first stage towards the route of creation. The dyad represented polarization, opposition, divergence, inequality, and mutability. It is often called tolma (daring), as it breaks away from the perfection and unity of Monad.37)

There are surviving lists of opposite qualities that exist in the works of later writers from the classic period that reflect the teachings of Pythagoras and his students. One such list from Aristotle's Metaphysics goes like this:

Limit Unlimited
Odd Even
One Plurality
Right Left
Male Female
At rest In motion
Straight Crooked
Light Darkness
Good Evil
Square Oblong

Triad: The next number is the number Three. The Pythagoreans saw three as the first true number. It was a whole, representing a beginning, middle, and end.38) The number represents the principal of everything that is whole and perfect, three dimensions, and the three-part soul.39)

The number also implies Past, Present, and Future. Embodies wisdom and foresight, because people that consider all three parts of time will choose a correct course of action. Knowledge was also represented by the triad, as were the powers of prophecy and fate. To correlate the triad to the acts of prophecy, the oracles of the ancient world would stare into bowls upheld by a tripod before delivering their prediction. The most famous was the Oracle a Delphi.40)

Tetrad: This is the number Four. Four represented completion. For the Pythagoreans, everything both natural and numerical was completed in the progression of One to Four. To express this they showed that there were four seasons, four elements (earth, air, fire, and water), four vital musical intervals, and four kinds of planetary movement. Four portrayed righteousness and stability.41)

The philosopher Plato (427-347 B.C.E) later used the number four to relate that there were four faculties of man – intelligence, reason, perception, and imagination.42) The Pythagoreans considered the four mathematical sciences of arithmetic, music, geometry and astronomy the foundations of true knowledge. Thus the tetrad represented Justice to Pythagoras and his students.

In the minds of the Pythagoreans, the number four represented completion of all things in the following progression of 1 + 2 + 3 + 4 = 10. This is how they arrived at the glyph of the tetraktys. The tetraktys then became the model for the kosmos (universe or cosmos), and the human psyche.43)

Pentad: The number Five was represented by the pentad. It is a combination of odd and even, represented by the numbers Two and Three added together. Five also represented marriage, the union of male and female reconciliation and harmony. Five was sacred to Aphrodite.

The Pythagoreans saw the pentad as comprehensive of the natural phenomena of the universe. Often this was worded as the universe was seeded by the monad, gains movement through the dyad, then gains life through the pentad and is encircled by the decad.44)

Hexad: The hexad is the number Six. To the Pythagoreans it is the first perfect number. By adding together the numbers of One, Two, and Three (1 + 2 + 3 = 6) to arrive at the number Six the hexad is created. The number represents the states of health and balance. It also represented wholeness, peace, and sacrifice.45) The number six was also associated with androgyny.

Heptad: The heptad is the number Seven. This number cannot be generated by any operation of math with any of the numbers that make up the decad. The concepts that are represented by the heptad are joy, love, and opportunity.46) The number also represented virginity and was considered to be sacred to the virgin goddess Athena.47) Also, since seven cannot be divided, except by itself, it represented an acropolis (fortress).

Octad: The octad or the number Eight was significant to the Pythagoreans because it was the first cube (2 x 2 x 2). They linked eight to safety, steadfastness and everything that was balanced in the universe.48) The Pythagoreans often called the octad, “Embracer of Harmonies”, because it is the source of musical ratio.

Ennead: The number Nine, which was also called horizon, because it marked the line between the decad (10) and the numbers that led up to it. The Pythagoreans saw nine as a number of completion49), this was due to the nine months of pregnancy and that there were nine Muses.

Decad: The decad or the number Ten was the most sacred of all numbers to the Pythagoreans. It was said that Pythagoras used the word dechada (receptacle) as a pun to describe this number.50) This number contained all things in a single structure and influence. It was the sum of the divine influences that held the universe together, and was all the manifest laws of nature. It was also seen as the universe, heaven, God, and fate.

Further correspondences by the Neopythagorean school of thought appear in works by Nicomachus of Gerasa (circa 100 C.E.), particularly his Introduction to Arithmetic, which formed the basis of the fourth century C.E. text called the Theology of Arithmetic, which is commonly attributed to Iamblichus.51) These correspondences and attributions are as follows:

Monad: Zeus, Prometheus, and chaos
Dyad: the Muse Erato (Love), Isis, Rhea, justice, and nature
Triad: Hekate, prudence, and the three phases of the moon.
Tetrad: Herakles (Hercules), the four elements, justice, and the four seasons.
Pentad: Nemesis, providence, Aphrodite, Pallas, justice, aethyr or quintessence, the fifth element (Spirit).
Hexad: Kosmos (Cosmos) or universe, the Muse Thaleia (Abundance), and harmony.
Heptad: Athena, virginity, and chance.
Octad: Changeable nature, and the Muse Euterpe (Delight).
Ennead: Oceanus, Prometheus, Hephaestus, Hera, and Hyperion.

After the basis of Pythagoras’ thought on number, he is credited to an intense study of music. Pythagoras saw music as not merely as a form of entertainment, but as harmonia (harmony), the principle that brings order to chaos and discord.52) For the Pythagoreans, music, like numbers held a dual structure, not only a useful and practical one, but one nature that allowed people to see the structure and nature of the universe.

Pythagoras determined mathematically the eight tones that make of the scale, the forerunner to the modern do, re, mi, fa, so, la, ti, do. Originally it was used to tune the lyre, and this particular scale came to be known as the “Eight-stringed Lyre of Pythagoras”.53)

The way that he was supposed to have reached this particular theory is rather interesting. It goes like this:

Pythagoras happened to pass by a blacksmith's shop, where he heard the sound of hammers striking a piece of iron on an anvil. He noticed that the sounds made by the hammers were all different. But, with on exception, they were all in harmony with each other.

He went into the blacksmith's shop and carefully observed the work. To begin with, thinking the difference in tone might me due to the strength of the workers, he had them exchange hammers. The difference in tone did not stay with the men but rather followed the hammers. He observed further that this phenomenon arose not from the force of the stroke, nor the shape of the hammer, nor the changes in the beaten iron.

He then turned his attention to the weight of the hammers, which was six, eight, nine, and twelve pounds, and discovered that the harmony of the tones was produced in precise relationship to their weights.54)

What he found was that hammers had different ratios that produced this harmony. The six and twelve pound hammers had a ration of 1:2, and produced the interval of an octave. The eight and twelve pound hammers had a ration of 2:3, and produced the tone of a fifth, while nine and twelve pound hammers had a ratio of 3:4, and produced the interval known as the fourth.55)

He further noticed that these three ratios had a connection to the numbers one (monad), two (dyad), three (triad), and four (tetrad), which when taken together formed the tetraktys, his model of the kosmos (cosmos). Seeing this connection to the universe, he theorized that he could mathematically describe the harmony of the celestial spheres in conditions of the world around him.

To prove his theory, he experimented with various instruments. He tested pipes of varying length, the triangle, pans of various sizes, and the monochord, an instrument with a single string. Of all these different instruments, he found that if divided proportionally in the same ratios as he had found with the hammers of the blacksmith's shop, that he produced the same musical results and intervals.

Another concept within the Greek or Hellenistic world that Pythagoras had an impact was the view of the soul. Many of the Ionic, mainland Greece, philosophers did not believe that man had a soul, but Pythagoras disagreed with them. Not only did he say that man had a soul but also taught that the soul transmigrated, had a kinship with all living things, and reincarnated. Also, Pythagoras thought that the soul was immortal and potentially divine.56) The traditional Greek approach was that immortality was a quality of the gods and beyond man.

Where he came up with this theory is not known. Many think that he learned about souls (the ba and or the ka) in Egypt, but it appears that the Egyptians did not have a concept of reincarnation57), at least not one that we have seen yet. There has been a theory that he actually went to India on his travels, but there is no evidence that Pythagoras ever visited there. There is one other source in classical times that had the belief of the prospect of purification and escape from the cycle of reincarnation, from the burden of bodily form, and is the Orphic Mysteries that originated in Thrace.58) As a matter of fact there appears to be a great deal of influence on Pythagoras from the Orphic Mysteries, both had a reverence of numbers, but Pythagoras carried much further, and both were vegetarians.59)

The Pythagorean concepts of the soul are further developed extensively in Plato's Phaedo, but are also developed in his works Republic and Phaedrus.60) This influence on later thinkers helps to expand the knowledge of the classical world, and would later lead to the philosophies of Neopythagoreanism and Neoplatonism.

With his concepts and beliefs in numbers and math, it is only natural that Pythagoras and the Pythagoreans used numbers as a divinatory tool. He is often considered the father of modern numerology, and was supposed to have initiated at least one-person art of divination by numbers61), Abaris, the Hyperborean, an area thought to be Scythia or the steppes of Russia.62) The modern idea of reducing a number to a single digit of between one and nine is called Pythagorean Reduction.63) An example of this is found in numerology when you add up the letters of a name or date whose sum is grater than nine. In the following example, I will use my last name and break it down using the basic techniques of numerology, and reduce it using the Pythagorean Reduction technique:


1 + 3 + 1 + 9 + 2 + 6 + 9 + 6 + 3 + 7 + 8 = 55

5 + 5 = 10

1 + 0 = 1

In this case the letters of my last name add up to fifty-five. By adding the numbers of this sum (55) together, i.e. five plus five, we get a sum that is between the numerical value of one and nine.

The next radical departure that Pythagoras took was in the area of cosmology. The fundamental Greek idea of how the universe and solar system work was that the heavenly bodies, i.e. the Sun, moon, and planets, revolved around the Earth, which was stationary. For Pythagoras and the Pythagoreans, there were two models of the kosmos (cosmos).

The first of these models held that there was a central fire (Sun) that the Earth revolves creating its own day and night. After the Earth, then come the moon and planets, and finally the outer fixed stars.64) Because there were nine celestial bodies that revolved around the central flame, the classic seven planets, Earth, and the fixed stars, they added another body to the heavens, the counter-earth, which was opposite of the Sun. Brought the number of celestial bodies of spheres to ten and equal to the decad.

The second model of the universe viewed it as having twelve concentric rings. In the outermost ring were the fixed stars. After this ring came the seven planets in descending order, Saturn, Jupiter, Mars, Venus, Mercury, the Sun, and the Moon. Under the Moon are the rings for the elements Fire, Air, and Water. All of this circled the Earth, which itself revolved at the center of the universe.65)

These concepts were hotly argued about for centuries, and the Pythagorean models were not taken seriously by most philosophers or scientists at all. It was not until Nicolaus Copernicus reasserted the heliocentric theory of the Pythagoreans that it became more widely accepted.66)

Influence of the Teachings of Pythagoras and the Pythagoreans

The teachings and concepts of the Pythagoreans can be seen in the works of Plato, like the Republic, Phaedrus, and Phaedo, where he expounds on the basic teachings of Pythagoras and the other Pythagoreans. Such concepts as the soul being immortal and close to divinity, numbers, and arithmetic are all dealt with in Plato's work. Aristotle follows his mentor's lead by including much of the number philosophy of Pythagoras in his Metaphysics. These works greatly influenced classical Greece and the later ancient world.

In Rome, Pythagoras' influence was also felt. A statue was erected to Pythagoras during the Samnite War (298 – 290 B.C.E.), according to Pliny.67) This is one of the earliest references to Pythagoras in Rome. The writer Varro, who died in 27 B.C.E. was reported to have been buried “in the Pythagorean manner” in a clay coffin with leaves of myrtle, olive and black poplar.68) And the writer Cato had a reference to Pythagoras in the early second century work, De agricultura (On Agriculture) in which he names a species of cabbage as brassica Pythagorea.69)

By the first century C.E. we start seeing the rise of the Neopythagorean philosophy. People like Nicomachus of Alexandria and Numenius from Syria helped to reestablish the Pythagorean concepts in the world. It was the works of these men, as well as the works of Plato and Aristotle, that helped forge for Plotinus (205-270 C.E.) the school of thought know as Neoplatonism.70) It is this philosophy that has influenced much of the modern era's thinking as regarding magic, numerology, astrology, astronomy, and other areas of thought.


Though there is no actual work out there that can be said to have been written by Pythagoras or even his closest students from the sixth century B.C.E. we have people like Plato and Aristotle whom knew Pythagoreans to rely upon for an idea as to what those teaching might have been. Through these, and later through the writings of the Neopythagoreans and the Neoplatonics we are further influenced by the at that time, the sixth century B.C.E through the early common era, was revolutionary ideas concerning the soul, the role of numbers, and the universe.

What would have happened had not someone like Copernicus not been interested in the works of what some of the Pythagoreans were supposed to have believed? Would we still think that we were the center of the Universe? I would like to think that we all have been influenced by the works of Pythagoras and the other Pythagoreans beyond that of the theorem that bears his name.


Barry, Kieren. The Greek Qabalah – Alphabetic Mysticism and Numerology in the Ancient Word. York Beach, Me.: Samuel Weiser, Inc., 1999.

Budge, E. A. Wallis. Egyptian Magic. New York, N. Y.: Dover Publications, Inc., 1971.

Cavendish, Richard. The Black Arts. New York, N. Y.: G. P. Putnam’s Sons, 1967.

D’Olivet, Fabre. The Golden Verses of Pythagoras. Nayan Louise Redfield, translator. Cutchogue, NY: Solar Press, 1995.

Godwin, David. Light In Extension – Greek Magic form Modern to Homeric Times. St. Paul, Minn.: Llewellyn Publications, 1992.

Greer, John Michael. The New Encyclopedia of the Occult. St. Paul, Minn.: Llewellyn Publications, 2003.

Kahn, Charles H. Pythagoras and the Pythagoreans: A Brief History. Indianapolis/Cambridge: Hackett Publishing Company, 2001.

Levi, Eliphas. Transcendental Magic. A. E. Waite, translator. York Beach, Maine: Samuel Weiser, Inc., 1992.

Strohmeier, John, & Westbrook, Peter. Divine Harmony. Berkeley, California: Berkeley Hill Books, 2003.

Whitcomb, Bill. The Magician’s Companion. St. Paul, Minn.: Llewellyn Publications, 1997.

Strohmeier & Westbrook, Divine Harmony, p.68.
Kahn, Pythagoras and the Pythagoreans, p.5.
ibid, p.5.
Strohmeier & Westbrook, Divine Harmony, p. 23.
ibid, p. 21.
ibid, p. 21. Kahn, Pythagoras and the Pythagoreans, p. 6.
Barry, The Greek Qabalah, p. 27.
Strohmeier & Westbrook, Divine Harmony, p. 24.
ibid, p. 26.
ibid, p. 28.
11) , 35) , 46)
ibid, p. 29.
ibid, p.32.
ibid, p. 33.
ibid, p. 38.
ibid, p. 39.
ibid, p. 40.
Kahn, Pythagoras and the Pythagoreans, p.6.
Strohmeier & Westbrook, Divine Harmony, p. 41.
ibid, p. 45.
Kahn, Pythagoras and the Pythagoreans, p. 8.
Strohmeier & Westbrook, Divine Harmony, p. 110.
ibid, p. 111.
23) , 24)
ibid, p. 124.
ibid, p. 125.
ibid, 126.
27) , 28)
ibid, p. 126.
29) , 31)
Kahn, Pythagoras and the Pythagoreans, p. 7.
Strohmeier & Westbrook, Divine Harmony, pp.126-128.
Strohmeier & Westbrook, Divine Harmony, p. 128.
Barry, The Greek Qabalah, pp. 27-28.
ibid, p. 32.
ibid, p. 30.
Strohmeier & Westbrook, Divine Harmony, p. 71.
38) , 45) , 49)
Barry, The Greek Qabalah, p. 29.
Strohmeier & Westbrook, Divine Harmony, p. 72.
ibid, p. 72.
Barry, The Greek Qabalah, p.29.
Strohmeier & Westbrook, Divine Harmony, p. 73.
ibid, p. 73.
ibid, p. 74.
Strohmeier & Westbrook, Divine Harmony, p. 75.
ibid, p. 75.
Strohmeier & Westbrook, Divine Harmony, p. 76.
Barry, The Greek Qabalah, p. 31.
Strohmeier & Westbrook, Divine Harmony, p. 78.
ibid, p. 85.
ibid, p. 82.
ibid, p. 84.
56) , 60)
Kahn, Pythagoras and the Pythagoreans, p. 4.
57) , 59)
Godwin, Light In Extension, p. 49.
Kahn, Pythagoras and the Pythagoreans, p. 4
Cavendish, The Black Arts, p. 66.
Strohmeier & Westbrook, Divine Harmony, p. 101.
Cavendish, The Black Arts, pp. 52-53.
Strohmeier & Westbrook, Divine Harmony, p. 88.
ibid, pp. 89-90.
Barry, The Greek Qabalah, p. 41.
Kahn, Pythagoras and the Pythagoreans, p. 86.
68) , 69)
ibid, p. 88.
ibid, p.122-130.

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