I have a confession. I am not good at math. Not in a charming, self-deprecating way, but in the way where someone starts reading out numbers, and my mind quietly leaves the room. So when my reading on the Western Mystery Tradition brought me to Nicomachus of Gerasa, a man best known for writing an arithmetic textbook, I’ll admit I started dozing off before I’d even cracked the book open.
This turned out to be one of the most challenging parts of my recent occult studies, and not, if I’m honest, one of the most rewarding. Still, what Nicomachus offers isn’t really about calculation. It’s about what number is, where it comes from, and why a magician might care.
I’ve been tracing a thread from Pythagoras through Empedocles, Plato, and the Corpus Hermeticum. Pythagoras gave the tradition its sacred numbers, but almost nothing he taught survives in his own words. Much of what later centuries believed about Pythagorean number came through Nicomachus, writing some six hundred years after him. If Pythagoras planted the seed, Nicomachus is a large part of how it reached us.
Who was Nicomachus?
Nicomachus lived in the late first and early second centuries CE in Gerasa, a prosperous city in the Roman East now Jerash in Jordan. We know remarkably little about him. The only personal detail in all his surviving writing is a passing remark that he hopes to finish a longer book once he has “leisure and a rest from my journeyings.” He was a traveller, then, and a teacher.
He belonged to the Neopythagorean revival, a movement that reclaimed Pythagoras as a divine sage and wonder-worker. It’s the same world that produced Apollonius of Tyana and Numenius of Apamea, and the same cross-cultural ferment that gave us the Hermetica. Greek philosophy, Egyptian temple religion and Near Eastern traditions were all reading one another.
Two of his works survive. The Introduction to Arithmetic became one of the most widely used textbooks in history, studied for well over a thousand years. The Manual of Harmonics is a short handbook on the mathematics of music. Two more are lost: a Life of Pythagoras, which fed into the later biographies by Porphyry and Iamblichus, and the Theologumena Arithmeticae, the “theology of arithmetic”, which we know only through fragments and later summaries. That last one is where the gods come in, and we’ll get there.
First, it’s worth pausing on the Life of Pythagoras. When I wrote about Pythagoras, I was drawing on a picture of him partly shaped by Nicomachus himself. The lineage isn’t a straight line handed down intact. Each generation remakes its ancestors.
Number in the mind of the gods
For Nicomachus, numbers aren’t human inventions for counting sheep. They existed before the world did. In the Introduction to Arithmetic, he describes the cosmos as ordered according to a pattern “fixed, like a preliminary sketch, by the domination of number preëxistent in the mind of the world-creating God, number conceptual only and immaterial in every way, but at the same time the true and the eternal essence.” Time, motion, the heavens and the stars were all made with reference to it, “as to an artistic plan.”
This is Plato’s Demiurge from the Timaeus, the divine Craftsman who looks to an eternal pattern as he shapes the world. Nicomachus tells us what the pattern is made of. It’s number. That’s why he insists arithmetic must be studied first: it is “origin and root and, as it were, mother” to all the other sciences, because it existed in the creator’s mind before anything else.
Here’s what helped it click for me. Nicomachus separates two kinds of number. There is the divine number in the mind of the creator, purely conceptual and eternal. And there is what he calls “scientific” number, the kind that measures material things and tracks their movements. The numbers I zone out at, the ones on invoices and in spreadsheets, are scientific number. What Nicomachus invites us to contemplate is the other kind: number as the shape of divine thought.
That helped change my perspective. I didn’t have to become good at arithmetic. I had to learn to look at numbers the way I’d look at a tarot card: as an image carrying a quality, a relationship, and a presence.
Harmony from opposites
“Everything that is harmoniously constituted,” Nicomachus writes, “is knit together out of opposites.” But not just any opposites. Things that don’t exist can’t be harmonised, he says, nor can things that are identical, nor things so different they have no relationship at all. Harmony needs things that are real, different, and connected.
The most basic pair in number is odd and even. Odd numbers can’t be split into equal halves; there’s always one left in the middle. Even numbers divide cleanly. For Nicomachus, these two are “reciprocally woven into harmony with each other, inseparably and uniformly, by a wonderful and divine Nature.” Every number after them is some weaving of the two.
Readers of my Empedocles post will hear an echo here. Empedocles gave us Love and Strife, two forces whose push and pull make a world. Nicomachus gives us odd and even, two principles whose weaving makes number, and through number, everything.
There’s a catch, though. The oldest Pythagorean tradition, which Aristotle records, set out a table of opposites: limit and unlimited, odd and even, one and many, right and left, male and female, light and dark, good and bad. Odd sits on the side of limit, male, light and good. Even sits with unlimited, female, dark and bad. Later writers in Nicomachus’s circle followed this, calling odd numbers male and even numbers female.
In the Empedocles post I praised Love and Strife precisely because they offer a polarity not built on gender. I can’t do that here. The Pythagorean scheme carries the old habit of mapping the feminine onto the material, the unbounded and the lesser. I don’t think we need to keep that mapping. What I find worth keeping is the idea underneath it: that difference, held in right relationship, makes harmony possible. Interestingly, the tradition also called the monad, the source of all number, “male-female”. The One holds both before anything divides.
Perfect numbers and the shape of virtue
Nicomachus turns arithmetic into a moral teaching.
I’ll keep the maths to one example, I promise. Six can be shared out evenly in three ways: six ones, three twos, or two threes. Now add up those sizes: one, two and three. You get six again. The pieces make exactly the whole, with nothing left over and nothing missing. Most numbers don’t do this. Their pieces add up to more than the number itself, which Nicomachus calls superabundant, or to less, which he calls deficient. Too much, too little, or just right. Six is the first perfect number.
Nicomachus doesn’t leave it there. He describes superabundant numbers as being like a monster with too many limbs: ten tongues, a hundred hands, three rows of teeth, like Scylla in the Odyssey. Deficient numbers are like a creature missing something, such as the one-eyed Cyclops. And then he makes the connection explicit. Evil, disease, and disproportion, he says, can exist only as excess or deficiency. In the space between, in equality, are found “virtues, wealth, moderation, propriety, beauty, and the like, to which the aforesaid form of number, the perfect, is most akin.”
He borrows the idea of virtue as a mean from Aristotle, but he gives it a striking image. And he goes further. Perfect numbers are rare: only four were known to him, 6, 28, 496 and 8,128. Superabundant and deficient numbers are everywhere, scattered without pattern. “Even as fair and excellent things are few and easily enumerated, while ugly and evil ones are widespread,” so it is with numbers.
I find this a useful lens for magical work. A working can be overstuffed, with too many correspondences, too many intentions, too many moving parts, until the whole collapses under its own limbs. Or it can be thin, missing something essential. The question Nicomachus teaches us to ask is simple: are the parts in right relation to the whole?
The theology of numbers
The Introduction to Arithmetic is mostly technical. The devotional heart of Nicomachus’s thought lived in his lost Theologumena Arithmeticae, which worked through the numbers one to ten and linked each to its qualities and its gods. Much of it survives through a later anonymous compilation, The Theology of Arithmetic, once attributed to Iamblichus, together with a summary by the Byzantine scholar Photius.
This side of the tradition speaks to me most. Number here isn’t only cosmic architecture. It’s divine presence. A few examples:
Five is Justice. This was Nicomachus’s most elaborate argument in the work. Five sits at the centre of the decad, dividing ten into two equal halves, and Justice is what divides fairly and gives each their due.
Six is Aphrodite. Six is the first perfect number, and it was associated with the soul. It’s made by multiplying the first even number, 2, by the first odd number, 3, so Nicomachus called it the marriage number above all, and named it Aphrodite. When I wrote about Aphrodite in Empedocles, she was the craftswoman who blends the elements into form. Here she is again: the number in which opposites join and the parts and the whole come into balance.
Seven is Athena. Within the decad, seven is the only number that neither generates another number nor is generated by one. Multiply it by anything, and you leave the decad; no two smaller numbers multiply to make it. Like the goddess born from the head of Zeus without a mother, who never bore children, seven stands alone. It was also called “chance” and “due season”, the kairos, through its link with the moon and the cycles of time.
Other numbers carried other names. Eight, the first cube, was linked to Rhea. Nine was the “horizon” and “ocean”, the boundary after which the numbers begin to repeat. And the decad, ten, held them all.
You don’t need to accept every one of these associations. Some of them feel forced even to me. But they model a way of seeing in which a number is something you can stand in relationship with, much as you would a god.
Number made audible
In the Introduction, Nicomachus divides the mathematical arts into four. Arithmetic studies number in itself. Music studies number in relationship, as ratio. Geometry studies magnitude at rest, and astronomy studies magnitude in motion. Music, in other words, is what number sounds like when two numbers meet.
The Manual of Harmonics is where he explores this. It’s a short handbook, written for a non-specialist: a woman he addresses as “most noble and august lady, since it is you that bid me.” We don’t know who she was. But it comforts me that Nicomachus’s own reader had asked for something accessible.
The Manual contains the earliest full telling of a famous legend. Pythagoras walks past a smithy, hears the hammers ringing in consonant intervals, and discovers that the octave, the fifth and the fourth correspond to the simple ratios 2:1, 3:2 and 4:3. It’s a lovely story. It’s also physically impossible as told, since hammers of different weights don’t produce those intervals that way. It tells us less about what Pythagoras did than about how Nicomachus wanted him remembered: as someone who heard the divine order in an ordinary workshop.
Nicomachus also links the notes of the scale to the planets. It’s an early systematic step towards the music of the spheres, the idea that the heavens move in harmonic proportion, which I touched on in the Pythagoras post. That idea would echo through Renaissance magic and into planetary hymns and correspondences.
Working with the Nicomachean current
These practices are for people like me, who do not think in equations. None of them needs a calculator.
Contemplate a number a day
Spend ten days with the numbers one to ten, taking one a day. Rather than thinking about how much the number is, sit with what it does and what it is like. Ask:
- What does this number do in the world?
- What relationship or quality does it hold?
- Where do I see it in nature, in my body, in my life?
Two might be breath in and breath out, self and other, day and night. Three might be beginning, middle and end. Keep notes. You’ll soon find your own associations sitting alongside the ancient ones.
Honour the numbers of the gods
If you work with Aphrodite, Athena or any deity linked to a number, bring that number into your devotion. Six candles or six offerings for Aphrodite, reflecting the joining of opposites. Seven for Athena, perhaps on the seventh day of the lunar month, a meditation on standing whole and self-contained. The point isn’t magic by numbers. It’s letting the number become a doorway into the god’s nature.
Ask whether the work is perfect
Before a ritual, look at its parts the way Nicomachus looked at 6. Is anything superabundant: an extra intention, a correspondence added because you could, a step that doesn’t serve the whole? Is anything deficient: a missing element, an unacknowledged need? Aim for a working whose parts add up to exactly what it is.
The same question works as an evening reflection. Where today did I overreach? Where did I fall short? Where was I in right measure?
Listen for ratio
You don’t need to read music for this. Sing or hum a note, then a note an octave above it. Notice how they feel like the same note at two heights. Then try a fifth. Let your ear learn what proportion feels like before your mind tries to explain it. If you work with chant, notice which intervals feel settled and which feel unresolved, and use them deliberately.
Where this leads
Nicomachus’s influence ran along two channels, and both still shape magical practice today.
The first ran through the Neoplatonists. Iamblichus, the philosopher who argued that the soul needs ritual, not just contemplation, to return to the divine, wrote a commentary on the Introduction to Arithmetic. For Iamblichus, Pythagorean number was part of the theurgist’s training, a way of aligning the soul with the order of the gods.
The second ran through the schoolroom. In the early sixth century, Boethius adapted the Introduction into Latin. His four mathematical arts, the ones Nicomachus had laid out, became the quadrivium, the core of medieval education alongside grammar, rhetoric and logic. For close to a thousand years, educated Europeans learned arithmetic through a version of Nicomachus. When Renaissance magicians reached for the symbolism of numbers, they reached for something their culture had absorbed in the classroom.
A textbook carried a theology. Generations of students learned perfect and deficient numbers without knowing they were learning something Nicomachus believed was the shape of the creator’s mind. The sacred travelled hidden inside the ordinary.
And for someone who once switched off at the sight of a times table, I’m grateful. Nicomachus taught me that number can be approached the way we approach any mystery: slowly, with attention, and with the expectation that something is looking back.
Recommended reading
Introduction to Arithmetic, translated by Martin Luther D’Ooge, with studies by Frank Egleston Robbins and Louis Charles Karpinski (1926). The standard English translation, now in the public domain. The long introduction is excellent on the lost Theologumena, and the translation itself is more readable than you might fear.
The Manual of Harmonics of Nicomachus the Pythagorean, translated by Flora R. Levin (Phanes Press, 1994). A clear translation with commentary, ideal if the music side draws you.
The Theology of Arithmetic, translated by Robin Waterfield (Phanes Press, 1988). The surviving compilation on the numbers one to ten and their gods, drawing heavily on Nicomachus. This is the one for devotional work.