The Theology of Arithmetic
Definition
A late-antique Pythagorean treatise traditionally attributed to Iamblichus (c. 245-325 CE), surviving in Greek as Theologoumena Arithmeticae. The text presents the cosmological and divine meanings of the first ten numbers, drawing on earlier Pythagorean material now lost.
Literal meaning
Greek Theologoumena Arithmeticae. The attribution to Iamblichus is contested; some modern scholars assign the surviving text to Anatolius of Laodicea (third century CE) or to a later compiler working in the Iamblichian tradition. The standard English translation is by Robin Waterfield (Phanes Press 1988).
Esoteric meaning
The text systematizes the Pythagorean conviction that the first ten integers are not abstract counters but cosmological principles, each carrying a distinct character and a distinct set of correspondences. The Monad is the source from which all multiplicity emerges; the Dyad is the principle of difference and otherness; the Triad is the first true number, the principle of mediation; the Tetrad is the first square, the principle of structure and the four elements; the Pentad is the principle of life and the marriage of male (3) and female (2); the Hexad is the perfect number that contains its own factors; the Heptad is the principle of the virgin and the ungenerated; the Ogdoad is the cube of harmony; the Ennead is the boundary that completes the decad; the Decad is the perfect whole that contains all the principles.
Extended meaning
The work draws on the lost works of the Pythagorean Philolaus, on Speusippus and Xenocrates of the early Academy, and on the Neopythagorean revival represented by Nicomachus of Gerasa's Arithmetica Theologumena. The text was preserved through Byzantine and Renaissance transmission and informed the cosmological number-theology of Renaissance Pythagoreans including Marsilio Ficino and Pico della Mirandola. Modern scholarly attention is found in Dominic O'Meara, Pythagoras Revived: Mathematics and Philosophy in Late Antiquity (Oxford UP 1989).
Comparative tradition
Vedic Sankhya number-philosophy and the Brihadāranyaka Upaniṣad numbered emanations. Kabbalistic Sefirot, the ten cosmic emanations of the Bahir and the Zohar. Chinese Yijing numerology of the eight trigrams and sixty-four hexagrams. The numbered-emanation cosmology recurs across the major contemplative traditions.