When people hear the name Pythagoras today, they typically think of math class. They think, specifically of the Pythagorean theorem, which tells us that there is a geometrical relation between the three sides of a right triangle. Some may take it further and associate the name with more than one mathematical discovery, such as the existence of irrational numbers, numbers that stretch on into infinite, unrepeating decimals, like pi, or with the categorization of numbers as prime and perfect. Some may even have a sense of him as a man, a great philosopher and mathematician, an Ionian polymath from the Greek island of Samos, founder of a movement of rational thinkers who, in practicing Pythagoreanism, moved away from notions of divine influence and magic toward a more scientific view of the world, whose phenomena can be observed and described and whose laws can be demonstrated. These may also credit him with the discovery of musical harmony. But all of these may be surprised to learn that very little is known about Pythagoras for certain, that sources about him come from long after his death, and that he may not have actually been or done any of these things. Rather, there is strong reason to think of Pythagoras as nothing more than the leader of a cult. And I don’t mean that in the more ancient and traditional sense of a systematic religious belief or the formal veneration of someone, as we have spoken before about the cult of Demeter and Persephone, as practiced in the Eleusinian Mysteries, or of the cult of some Catholic saint or another. No, I mean it in the modern sense, that he was a cult leader, that he seems to have been a charismatic figure who taught unorthodox and even spurious doctrines and who gathered a significant following of adherents who believed him to be a sage. This certainly does not jibe with the notion that he and his followers spearheaded a more rational worldview based upon reason and deduction, and such a notion of Pythagoras further erodes when it is learned that the tenets of Pythagoreanism were not only centered on sound mathematical proofs. That does seem to have been an aspect of the beliefs his cult developed, but he also promulgated a decidedly mystical belief system also relating to numbers. Indeed, Pythagoreanism and its number mysticism would eventually develop into a form of magic, its practitioners believed to be capable of mystical divination. For Pythagoras was the originator of what would eventually become known as numerology.

For those of you who may be new to the podcast, I occasionally write a post on the history of magic or at least of magical beliefs, which I label as volumes of my Encyclopedia Grimoria. The most recent entry in this series was my episode on the magical lore about King Solomon, who is said to have originated certain forms of magic, such as the ritual binding of demons to do his will. A couple years before that, I completed an episode on the legendary Hermes Trismegistus, who was said to have invented alchemy. In this volume, I trace the origin of another form of magic, numerology. Some may not think of numerology as a form of magic, but in that it assigns mystical significance to otherwise natural phenomena, and then applies that mystical significance to fortunetelling and divination, it is as much a magical practice as is astrology, which I traced back, according to the lore of magic, to Zoroaster, the figure said to have invented all magic, the name of whose adherents, the magi, is where we get the word for magic. I spoke about all of this in my very first volume of the Encyclopedia Grimoria. In all of those volumes, it became increasingly clear that the legends about these magical figures were entirely unreliable, appearing much later, typically in that hotbed of syncretism and mythmaking, Hellenistic Egypt. In the case of Pythagoras, he too exists mostly in legend and myth. None of his own writings have survived. He is only known by later hagiographical and satirical writings about him—thus we know only how he was later aggrandized and lampooned. Certainly he did not invent mathematics, which was developed in Mesopotamia and Egypt before his time. Stories about his travels to the East are dubious as well, so that he may not have even been the person who brought mathematics to Greece. And there is plenty of reason to doubt whether he himself discovered anything of mathematical importance, since much of his teachings seem to be relatively standard cult teachings, about communal living and dietary restrictions and even mystical notions about the human soul. He was an early proponent of metempsychosis, the idea of the transmigration of souls, but he was not the first to have imagined it. However, whether it was Pythagoras himself or his followers, Pythagoreans can be credited with the first development of number mysticism, of assigning occult significance and qualities to numbers, a practice that evolved inevitably, through the practical application of these mystical qualities assigned to numbers, directly into numerology, or arithmancy, as it was originally called, and that name alone should indicate that it was believed to be a form of magic. And at the same time there evolved gematria, also used by Pythagoreans, which is all tied up with other mystical arts, such as kabbalism and even, as we saw in the previous episode, the modern divinatory practices involved in the Bible code. It is perhaps strange that the name of a mystic and cult leader is so closely related with modern mathematics, but we should remember also that modern chemistry originated in the practices of alchemy, diverging on a more scientific path over time. We find the same is true here, in that after Pythagoras, the principles of mathematics developed parallel to and separate from the mystical notions that Pythagoreans attached to numbers.

A 17th century engraving imagining Pythagoras.

Much like Jesus Christ, there is ample evidence that Pythagoras did exist, but little reliable information about him. We have only suspect traditions about his deeds and teachings, most recorded long after his death. Contemporaries who wrote about him certainly did not view him in a favorable light. The philosopher Heraclitus of Ephesus thought him a charlatan, calling him “the chief of swindlers,” and suggesting that his “wisdom” amounted to “artful knavery.” These, of course, are the sorts of things that might be said about a cult leader today, and most of Pythagoras’s actual teachings, as they have been transmitted to us by later writers, seem very much the sorts of ascetic controls that cult leaders place on their followers. It is claimed that new initiates were forbidden from speaking for years. He placed restrictions on clothing, specifically wool, and most especially on diet. He was a vegetarian, but more than that, it is claimed that he forbade the consumption of beans. The fact that contemporary sources about his teachings and practices are contradictory and many of the claims about him did not appear for several hundreds of years, until the Hellenistic period when his supposed doctrines were revived, makes it unclear whether he actually enforced any such restrictions. And the clearly mythical tales that also appeared make it apparent that stories about him cannot be trusted. It is said that he stopped someone from beating a dog, saying that his friend’s soul resided in the animal. That’s perfectly plausible, I suppose, given the doctrines of metempsychosis associated with him. Less believable are the stories about killing a poisonous snake that bit him by biting it himself. Impossible are the accounts of his bilocation, being in two places at one time, and ridiculous is the story that once, when he crossed a river, the river spoke aloud, greeting him with the words, “Hail Pythagoras.” Aristotle wrote that he had a golden thigh, and opposing traditions said that he was either Apollo’s son or that he even claimed to be Apollo himself. But wouldn’t it be just like a cult leader to say he’s a god? As for the notion that Pythagoras made mathematical discoveries, this too appears false. Take the Pythagorean theorem that bears his name; scholars have traced knowledge of this theorem back a thousand years before his time, to Mesopotamia, where it was widely used in Old Babylonian arithmetic. Some have then argued that Pythagoras himself brought these concepts back to Greece from his travels, but even those travels are in question, as competing traditions have him learning mathematics from Egyptian priests, from Magi in Persia or even from Zoroaster himself, from Jewish sages, from Phoenicians or Chaldeans, or even from Zeus himself in the Cave of Ida. Still other traditions had it that he arrived at his mathematical knowledge through the interpretation of his own dreams. It should be noted that some scholars do credit him as a great mathematician, and they even assert that he could have arrived at extant mathematical theorems independently. I, however, take the view expressed by Underwood Dudley, in my principal source Numerology, or What Pythagoras Wrought, that he was less a mathematician and more a mystic and cult leader. Still, it is apparent that mathematics was practiced among the followers of Pythagoras, that in fact they were central to their arcane philosophy, and the simplest explanation of any discoveries being attributed to Pythagoras is that one or more of his followers stumbled upon some proposition or mathematical truth, leading to ideas that Pythagoras encouraged and spread. Case in point, the discovery of irrational numbers is often attributed not to Pythagoras himself but to a particular Pythagorean, Hippasus of Metapontum. Eventually, Pythagoras himself gets credited with the discoveries of any Pythagorean.

One of the major discoveries thus attributed to Pythagoras himself is that of musical harmony. As the tale goes, he was walking by a smithery and was pleased by the uniform sounds of their hammers striking the anvils. However, the clang of one hammer was dissonant, so Pythagoras is said to have borrowed these hammers and conducted an elaborate experiment, involving the careful weighing of the hammers, attaching each to strings that he would pluck to produce musical notes, and the slow addition of weight to the dissonant hammer in order to bring the notes into harmony. The whole story smacks of legend. It seems unlikely that Pythagoras might convince all four blacksmiths to loan him the tools of their trade, which they surely needed to complete their work, so that he could conduct a time-consuming experiment. But regardless of whether it was really Pythagoras himself or one of his cultists who discovered harmonics simply by experimenting with a stringed instrument, which had long existed, is immaterial. What’s important is that Pythagoreanism produced music theory, and this in turn was applied to both astronomy and mathematics. In the realm of astronomy, Pythagoras seems to have taught or promoted a doctrine about the Music of the Spheres, musica universalis, that the planets resonated a kind of music. Many were the astronomical notions also dubiously attributed to Pythagoras—that he identified the evening and morning stars, which were actually identified by Babylonians more than a millennium earlier, that he was the first to identify the Earth as spherical, but scholars question this as well, as first mention of the notion didn’t appear until more than a hundred years after his death, and the first attribution of the concept to Pythagoras did not appear for several hundred years, during a time when many dubious legends about the man were appearing. What is certainly true, though, is that Pythagoras, or his adherents, do seem to have been the first to associate harmony with number, which may explain their association of harmony with the planets, since the movement of heavenly bodies had long been thought of in mathematical terms. They also discovered connections between harmonics and geometry, which led to mathematical discoveries about numbers themselves, that they could be classified as Abundant, deficient, or perfect based on the sums of their factors. I’ll spare you the mathematical details, as what’s important here is that this is where Pythagorean number mysticism originates, whether extrapolated by the Pythagoreans who discovered harmony or by others or perhaps even by Pythagoras himself, looking to turn mathematical notions into a mystical doctrine. Beyond these characteristics of numbers, they began attributing others to them. Numbers are odd or even; this we understand easily enough, as the notion is still prominent today, but Pythagoreans saw numbers as being associated with the left or the right, with light or darkness, with being in rest or in motion, being crooked or straight, male or female, good or evil.

20th century depiction of Pythagoras and his followers, many of whom were women.

As a final illustration of how little is known with certainty about Pythagoras, even his death is in question. Tradition has it that he died with many of his followers during a politically motivated attack on their meeting place in Croton. This attack may have been motivated by Pythagoras’s failure to support a recent democratic initiative, or it may have been fomented by a certain individual who had been denied initiation into the cult, or a combination of both. It also might have been none of these, as there are no reliable accounts of the attack. Some are contradictory and may actually be describing later anti-Pythagorean attacks. Interestingly, some sources say Pythagoras wasn’t even there, or that he escaped. One story even has it that, as their meeting place burned around them, his followers lay down on the ground to create a safe path for him to get out of the building. Even the stories about his escape do not agree, however, as one claims he and other escaped followers, being denied sanctuary elsewhere, died of starvation, while another has it that after escaping, Pythagoras killed himself out of guilt, and a third claims that he escaped but ran smack into a beanfield, and since he held beans in such high esteem, apparently, he couldn’t bring himself to cross it and was thus cut down by his enemies regardless. After the suppression of his cult, the study of mathematics in Greece continued, carried on by surviving Pythagoreans and others who had never been associated with the cult. Their doctrines of number mysticism too persevered, but they disappeared for a time, not to be revived until the 1st century CE, by Neopythagoreans, a Hellenistic school of philosophy that would take Pythagorean notions about numbers to extremes. Perhaps the most famous Neopythoagorean was Apollonius of Tyana, not for his Pythagorean ideas but rather because he was long compared with Jesus Christ, such that Christ mythicists love him. Of course, those responsible for actually transmitting the legends of Pythagoras and the notions of Pythagorean number mysticism were those who left behind written works, such as Nicomachus of Gerasa, who wrote two works that now only exist as fragments, one a Life of Pythagoras and another called the Theology of Arithmetic that recorded the mystical qualities Pythagoreans believed numbers to have. Afterward, centuries later, came Neoplatonist Iamblichus, whose work of the same name further preserved and developed Pythagorean and Neopythagorean notions about numbers, though much of it appears to have been taken from the work of Nicomachus and other existing works, with the only original material resembling marginalia, like annotations that may not have even been written by Iamblichus himself.

Neopythagoreans attributed not only mystical properties to numbers, but entire personalities, transforming integers into characters like the gods of mythology. Indeed, they invented a kind of pantheon of numbers, with the number one being the supreme entity, called the monad. The monad was not even considered by them a number, since numbers must either be even or odd, which is determined by how it can be divided, and the monad cannot be divided. Since any number multiplied by the monad remains itself, which means that the monad is in all numbers, in all things and thus the origin of them. Almost as important was the dyad, or the number two, which also was differentiated from numbers in that every other number can be divided in more than one way, whereas the dyad can only be divided by itself, and results in two monads. Then the number three, the triad, had further mystical significance for them in that it has a beginning, middle, and end. And so on each numeral took on such characteristics, and then was further imbued with associations, the dyad being associated with sex and the moon, for example. Four, the tetrad, was the number of knowledge and of the world, representing the four elements and four seasons, and five, the pentad, being in the center of the nine digits (for there was no zero yet), represents balance, equality, and thus justice. So we see the mystical notions of Pythagoreans, who ironically are even today frequently praised as being scientifically minded and resistant to superstition and irrationality, evolving into an esoteric cosmology and theology. Indeed, we see Neopythagoreanism’s enormous influence on religion through Gnostic thought, which crept into early Judaic and Christian traditions in the first century CE, in which the supreme Godhead was called the Monad. Elements of Pythagorean number mysticism had already been introduced into Jewish tradition by Philo of Alexandria, and into early Christian tradition by Clement of Alexandria, and with the addition of a related practice, gematria, it would further evolve into what we today know as numerology.

Gematria too was not original to the Pythagoreans or to Greeks, having been in use in ancient Babylon as well. The first known reference to the process of assigning number values to letters was in an 8th century BCE inscription about Assyrian king Sargon II, which declares that he had a certain wall constructed a certain length so that it corresponded with the numerical value of his name. Among the Greeks, the first use of letters to represent numbers came from Miletus and was thus known as the Milesian system. We see a definite move toward modern notions of gematria among the Pythagoreans, though, in that they used the Milesian system to practice isopsephy, taking the individual numbers associated with individual letters of names and words, adding them together and producing a sum that represents the thing the word or name refers to, which sum can then be used to draw correlations with other words and things whose names produce the same number. The isopsephic values of one through nine were assigned to the first nine letters of the Greek alphabet, followed by ten through ninety by tens for the next nine, and 100 through 900 by hundreds for the rest. This is exactly the sort of system that would be in gematric alphabets, which would be developed not only for Greek, but also for Hebrew, and eventually for English as well. Gematria was especially popular in Hebrew, in rabbinic literature, early Christian writings, and Gnostic teachings. More and more sophisticated uses of gematria would be developed in the Middle Ages in Kabbalistic literature, and some of these would remain in diluted form in modern English language gematria, which often involves adding together not only the numbers of letters, but then adding each numeral of the sum together until reaching one essential single digit that represents the word or name. Over the centuries of its use to interpret scriptures, gematria would become more and more associated with prophecy, which was, after all, mostly a matter of scriptural interpretation. Thus we see a clear line of descent from the number mysticism of Pythagoreans evolving through gematria into the realm of numerology. Perhaps the best known example of gematria used in prophecy can be found in the Book of Revelation, chapter 13, verse 18, which states, “let anyone with understanding calculate the number of the beast, for it is the number for a person. Its number is six hundred sixty-six.” Not only does this famous verse about the Number of the Beast state outright that it’s the number of a person, or man in other translations, or even the number of his name in others, making it manifestly a gematric value, but also the word translated as “calculate” or “count” in other translations actually derives from the same root as isopsephy, the ancient Greek word for gematria.

For those who want to hear more about the Number of the Beast and the potential meanings of this Bible verse, and how it has been misconstrued and misapplied by end times conspiracists throughout history, I encourage you to check out my episode from 2021, False Prophecy: The Mark of the Beast – 666. The point I want to emphasize here is that this longstanding Christian tradition of interpreting and reinterpreting Revelation to guess who the foretold Beast might be through the use of gematria essentially represents the practice of a form of magic or sorcery in the context of a religion that forbids it. There is a laundry list of verses in both the Hebrew Bible and the New Testament that explicitly prohibit practices of divination, fortune telling, and the interpretation of omens. “But is it really a form of magic?” some may protest. Prophecy is a cornerstone of these religions, so how could it be wrong to interpret it? Well that is certainly an odd contradiction, in my eyes, that a deity would forbid the prediction of the future, excluding certain acceptable examples of it. It seems to me that “interpretation of omens” is an exact description of what people are doing when they interpret prophecy through the arcane numerological practices of gematria. But I suppose that those who apply gematria to such ends can rest assured that they aren’t actually doing anything magical or supernatural, that they aren’t really divining anything, since it’s all nonsense, especially today. There are so very many gematric alphabets—some that change from single digits to tens and hundreds, some that don’t; some that start by assigning the number one to the letter A, but others starting with zero, or three or eight; some that skip multiple numbers between each letter, using all sorts of calculations so that by the time you get to Z it might be in the twenties, or the 100s, or it could be any unusual number, 276, 529, 852, or even in the many thousands, because remember that later you’ll add the digits together and reduced them to smaller numbers—with so many competing and alternative systems for calculation, you can literally make the numbers say anything, very much as we saw with the Bible Code. And considering the mathematical Law of Small Numbers, which says that there simply aren’t enough small numbers to be certain whether a seeming pattern has occurred coincidentally, it is rather meaningless to go around freaking out about some such name being reducible to sixes. I’m not a mathematician, but with if you can set up any sort of number application and calculation system that suits your ends, then it seems there is a 1 in 9 chance that any word or name can be made to output a six. Take my own name. I only need to drop it to Nathan Lloyd, rather than Nathaniel, which is what I go by really, and then use a gematria system assigning the number 45 to A, 46 to B, and so on, and I’ve Beasted myself, creating a gematric name value of 666.

Art in a 17th century manuscript of the New Testament depicting the placement of the Mark of the Beast in Greek, χξς' (666), in peoples' forehead

As we saw with the Bible Code, reading into numbers in this way, you can see find whatever it is you’re looking for. It seems to be a form of pareidolia, perceiving some meaningful image in what are really random phenomena, like seeing faces in things. One need not use a computer program to become lost in obsessive searching of the bible for hidden codes. Take the case of 19th century Russian literary critic Ivan Panin, who while reading the Gospel of John began to wonder about the presence of a certain article, the word “the,” where he felt it didn’t belong. Instead of disregarding it as an aberration of translation, which it most certainly was, he resorted to gematria, and taking the sums of words and phrases, he kept finding sevens. But just as I indicated with sixes, it is not unusual to find any one number coincidentally, and when looking for many instances of the same number, one tends to use the gematric systems and methods of calculation that will help you reach that number. It is a self-fulfilling prophecy, and that way lies madness. Ivan Panin labored over his calculations twelve hours a day for fifty years, producing a massive 40,000-page manifesto as a monument to his folly and wasted life. We saw it too in Shakespeare conspiracism and denialism, as when anti-Stratfordians got it in their heads that someone else wrote the works, the beauty and profundity of the work was ruined for them, and thereafter all they saw in them were hints about the true authors and the conspiracy of obscuring the authorship. Conspiracist thought is very similar to pareidolia this way, in that the conspiracist sees patterns that aren’t really there. And otherwise legitimate Shakespeare scholars too have resorted to gematria to divine some hidden and deeper meaning from his texts, such as Alistair Fowler, who claimed that a secret numerical code embedded in the Sonnets and decipherable using gematria showed that Shakespeare wasn’t really writing poetry about love and longing, pain and despair, but was rather more interested in creating word puzzles that constructed geometrical patterns with numbers, which rather does the Bard a disservice, if you ask me, reducing him and his work to meaningless triangles. To offer one final example, take the case of my own uncle, whom Patreon contributors will know, from an exclusive minisode last year, is a conspiracy theorist and fringe radio host with a focus on bible prophecy. He sees triple sixes everywhere…because, of course, sixes are everywhere. Specifically, in 1997, he produced a VHS tape called Secret Sixes, in which he compiled clips from major Hollywood movies that he claimed secretly inserted the number of the Beast into their scenes. His examples would be a movie that had a series of scenes in which, say, someone walked down a hall and the number six was seen on a door, and in the next scene a clockface was shown with the number six, and finally, in a later scene, a car’s license plate is shown with the number six on it. There you have it – 666. But this only shows the extreme madness that Pythagorean thought and gematria, especially when combined with religious belief, have engendered. There were sixes in those scenes because of course there were. There were also other numbers on those doors and on that license plate, and on a clockface, every digit can be seen.

From the days of Pythagoras to today, the form of magic known as numerology has slowly developed. It began not with real mathematics, which again did not originate in the Pythagorean cult. It started with number mysticism, developed through its application to religious thought and prophecy by gematria and became only more and more associated with the mystical and the magical in the Middle Ages and the Renaissance. But it would not reach its final form until the early 20th century, when a woman began writing about Pythagoras and expanding on his ideas under the name Mrs. L. Dow Balliett, suggesting that every number had a certain vibration at a certain frequency, and that, therefore, every person, who could be reduced to a number discernible in their name, also vibrated uniquely. From Balliett came the notion that parents did not choose the names of their children, no, their names were preordained, or chosen by the children themselves before their birth to represent their core being and their fate. If this sounds very woo-woo, that’s because it is, extremely. Now everywhere online you’ll find the coining of the term Numerology incorrectly credited to a “Dr. Julian Stenton,” or “Stanton,” or “Seton,” but this, it turns out, after much searching, was actually Dr. Julia Seton, who was close friends with Balliett. It was with these two women that the modern style of numerology was born, the “Science of Names and Numbers,” which has turned out to be such a wild and bizarre New Age philosophy and practice. Using gematria and number mysticism, they sell their services as self-help gurus, life coaches, unlicensed therapists, and fortune tellers. They are dyed-in-wool scammers, and they also dabble in pseudohistory. The American Institute of Man, for example, a short-lived neo-neo-Pythagorean “research organization” with a focus on numerology, published some claims about history that are interesting to say the least. It begins with their biography of Pythagoras, who of course they credit with the invention of mathematics, but instead of an end to the cult in its suppression, like claims about the Knights Templar, they imagine Pythagoreans escaped, spread overseas long before Columbus, and founded far flung civilizations. Pythagoreans, they claimed, came to ancient Britain and became the Druids, and thus created Stonehenge. They discovered Iceland and the Americas, and they went east to Persia and India, and in expeditions beyond, they discovered South America and made it all the way to Easter Island, where they carved the stone heads there. And what was their proof of all this? Well, it’s all in the numbers, of course. Take the measurements of the statues, for example, and reduce them by numerological methods and, well, you can get them to provide whatever proof it is you might be seeking. For as Pythagoras claimed, “All is Number.”

While no image survives of Mrs. L. Dow Balliett, the modern inventor of Numerology, this photograph of her partner and friend, Julia Seton, survives.

Until next time, I’ll leave you with these two alliterative quotations from the mathematician who first outlined the Law of Small Numbers I mentioned earlier. According to Richard Guy, there just aren’t enough small numbers, which leads to false perception of patterns, or as he says, “superficial similarities spawn spurious statements” and “capricious coincidences cause careless conjectures.” And doesn’t that just perfectly describe a lot of the topics I discuss on the podcast?

All Is Number: Pythagoras and Numerology (An Encyclopedia Grimoria Volume)

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