The Theology of Arithmetic/Introduction

The Theology o f A rithm etic is a curious, but valuable work. It is

preserved for us in the corpus of works of the eminent Neoplatonist

Iamblichus, but it is almost certainly not the arithmological

treatise he promised to write (On N icom achus’ Introduction to

Arithm etic, 125.15 ff.): the author of our treatise is unknown.

This is, as far as I know, the first translation of the text out of its

original Greek, let alone into a modern language. There are two

main reasons for the neglect of the work. In the first place,

Neoplatonism in general, and Neopythagoreanism in particular,

are not popular studies in today's universities. Secondly, the text

itself is undeniably scrappy.

The treatise is, in fact, a compilation and reads like a student's

written-up notes. Whole sections are taken from the Theology o f

A rithm etic of the famous and influential mathematician and

philosopher Nicomachus of Gerasa, and from the On the D ecad of

Iamblichus' teacher, Anatolius, Bishop of Laodicea. These two

sources, which occupy the majority of our treatise, are linked by

text whose origin is at best conjectural, but some of which could

very well be lecture notes—perhaps even from lectures delivered by

Iamblichus. At any rate, the treatise may tentatively be dated to the

middle of the fourth century A.D.

The value of the treatise is threefold. First, from an academic

point of view, given the author's eclecticism, he has preserved, or

he reflects, work which would otherwise be lost to us: that of

Nicomachus is especially important (Anatolius' book is independently

preserved), but there is also, for instance, a long fragment of

Speusippus, Plato's successor as head of the Academy in Athens.

The second, and related merit of the book is simply that we have

little extended evidence of the vast tradition of arithmology (as

distinct from the hard science of mathematics) among the Greeks;

The Theology o f A rithm etic is a welcome, if sometimes obscure,

addition to the slender corpus of such texts.

The third chief merit of the treatise is harder to explain. Pythagoras

of Samos lived towards the end of the sixth century B.C. Our knowledge of his work and that of his successors is usually

tantalizingly scanty, but enough is preserved to be sure that, while

in exoteric areas such as mathematics there was considerable

development, the esoteric and religious side of their work remained

firmly based on the same principles and fully deserves to be called

the Pythagorean tradition, which lasted for at least a thousand

years. At any rate, to anyone familiar with the fragments of

Pythagoreanism and Neopythagoreanism, it is immediately clear

that a great deal of what The Theology o f Arithm etic says could

equally well have been said, and in many cases was, by a Pythagorean

of the fifth or fourth centuries B.C.

I shall say a little more about this Pythagorean arithmological

tradition shortly; here I need only say the following about it. Like

Kabbalists, they recognized ten principles of all things. These ten

principles are equated with, or described as, the first cycle of ten

numbers. Thus our treatise simply takes each of the numbers from

one to ten, and spends a few pages describing its qualities and giving

reasons for those qualities. These qualities are primarily mathematical,

and then by extension allegorical. So, for instance, the

number one is present in all numbers and makes them what they

are. This is a straightforward mathematical proposition; an extension

is to call the number one Intellect, Artificer, Prometheus.

This approach has often been called superstitious mumbo-

jumbo, but it is really only a different theological approach to ones

with which we are more familiar. Mathematics is the most abstract

language known to mankind; to base a theology upon it is to

attempt to describe the abstract laws, as distinct from their applications,

which govern God's universe. The outstanding nature of

The Theology o f Arithm etic, and its third chief merit, is that at one

level it is unexceptionable, and fairly simple, Greek mathematics

(since the complexity of mathematics lies in proving theorems, not

merely in using the terminology, axioms or conclusions)—but the

simplest mathematical statement is simultaneously imbued with

religious import. The text makes it clear that for the Pythagoreans mathematics was more than a science: God manifests in the

mathematical laws which govern everything, and the understanding

of those laws, and even simply doing mathematics, could bring

one closer to God.

In the Western world, arithmology is inevitably associated with

the name of Pythagoras and his followers. It should not, however,

be forgotten that long after the demise of the Pythagorean schools

number mysticism was still flourishing among Jewish and Christian

mystics. The study and use of gematria by Jewish Kabbalists

is relatively well known; more often forgotten is the fact that even

such seminal Christian writers as John of Ruysbroeck (1293-1381)

were perfectly prepared to see numbers as authoritative symbols

and paradigms of divine principles.2

Among the Greeks, arithmology enjoyed a long history, as has

already been remarked. It was practiced and studied concurrently

with the science of mathematics, and by the same practitioners. As

far as we can tell, no sooner had the Greeks been prompted

(probably by contact with the Middle East) to elevate mathematics

out of the market-place and into a pure science, than they also

began to perceive philosophical and religious connotations to what

they were doing. It is not too misleading a generalization to say that

the Greek philosophers were impressed by the apparent orderliness

of the universe and that this was for them the chief argument for

some Intelligence being behind the universe. The Pythagoreans

simply attributed this orderliness to the presence of number:

numbers contain and manifest the laws of God's universe. Since all

numbers after ten are repetitions of the first cycle, the first decad

of numbers alone manifest these principles.

In passing, it should be noted that the idea that the laws which

govern the universe are numerical is not in itself at all silly. It is not

just that we are happy with formulae such as E=mc2: these are

perhaps different in that they are supported by scientific proof.

More significant is the fact that we are still happy to accept more