Podcast episode

Episode 142: Run the Numbers: The Theology of Arithmetic

We discuss a little gem of a work from late antiquity, the ‘Theology of Arithmetic’. This book is a late-antique arithmological handbook, collecting all manner of lore to do with each of the arithmological numbers from the Monad to the Decad in sequence. In the course of discussing the book (its sources, its intellectual background, and the possibility that it is by Iamblichus like the manuscripts say it is) we expand a little bit on:

  • How arithmologists in the ancient Greek tradition think about number,
  • The kinds of esoteric hermeneutics opened up when numbers have meanings beyond simply their ‘amount’,
  • The esoteric iconography of the Tetraktys in western esotericism,
  • And similar useful matters.

Works Cited in this Episode:


  • Anatolius On the Decad: this difficult-to-find work was first published in French translation in Johan Ludwig Heiberg. Anatolius d’Alexandrie sur les dix premiers nombres. Annales internationales d’histoire: congrès de Paris 1900, 5e Section: histoire des sciences:12– 31, 1901, now conveniently available online. It survives in a single manuscript, cod. Monac. gr. 384 (fol. 57v-59r).
  • Aristotle on the Pythagoreans positing numbers as the archai (principles) of all things: Metaph. 987b 24. See Walter Burkert. Lore and Science in Ancient Pythagoreanism. Harvard University Press, Cambridge, MA, 1972. Translated by Edward L. Minar, p. 31 n. 15 for loads more sources on this Pythagorean doctrine.
  • Iamblichus promises an arithmological treatise: On Nicomachus’ Introduction to Arithmetic 125.15 ff.
  • On the Pythagorean Life: see John M. Dillon and Jackson P. Hershbell, editors. Iamblichus: On the Pythagorean Way of Life. Scholars Press, Atlanta, GA, 1991.
  • Nicomachus of Gerasa Introduction to Arithmetic: see M.L. D’Ooge, F. E. Robbins, and L.L. Karpinski. Nicomachus of Gerasa: Introduction to Arithmetic. Macmillan, New York, NY/London, 1926.


  • John Dillon suggests that Plotinus’ Forms are best conceptualised as ‘… a system of quasi-mathematical formulæ, which project themselves on matter to produce the multiplicity of the physical world’ in Plotinus at Work on Platonism. Greece and Rome, 39(2 (Second Series)): 189–204, Oct. 1992, p. 197.
  • Waterfield 1988a: see below.

Recommended Reading:

  • Juan Acevedo. Alphanumeric Cosmology from Greek into Arabic. Mohr Siebeck, Tübingen, 2020.
  • José Sabás Medrano Calderón. La teología de la aritmética de Pseudo-Jámblico. Estudio introductorio, revisión del texto y traducción. PhD thesis, Universidád Nacional Autónoma de México, 2015.
  • V. De Falco, editor. Iamblichi theologumena arithmeticae. Teubner, Leipzig, 1922.
  • Joel Kalvesmaki. The Theology of Arithmetic: Number Symbolism in Platonism and Early Christianity. Number 59 in Hellenic Studies Series. Center for Hellenic Studies, Washington, DC, 2013.
  • Thomas O’Loughlin. The Mysticism of Number in the Medieval Period Before Eriugena. In John J. Cleary, editor, The Perennial Tradition of Neoplatonism, pages 397– 416. Leuven University Press, Leuven, 1997.
  • F. E. Robbins. The Tradition of Greek Arithmology. Classical Philology, (16):97–123, 1921.
  • Robin Waterfield, editor. The Theology of Arithmetic. Phanes Press, Grand Rapids, MI, 1988a.
  • Idem. Emendations of [Iamblichus], Theologoumena Arithmeticae (De Falco). Classical Quarterly, 38(1):215–27, 1988b.
  • Leonid Zhmud. From Number Symbolism to Arithmology. In L. Schimmelpfennig, editor, Zahlen- und Buchstabensysteme im Dienste religiöser Bildung, pages 25–45. Seraphim, Tübingen, 2019.
  • Idem. The anonymous arithmologicus and its Philosophical Background. In C. Macris, T. Dorandi, and Luc Brisson, editors, Pythagoras Redivivus: Studies on the Texts Attributed to Pythagoras and the Pythagoreans, pages 341–79. 2021.
Pythagoras by J.A. Knapp, from Manly P. Hall’s The Secret Teachings of All Ages (1928). Note the signs of pre-socratic kabbalah, from the Yod-Tetraktys to the tree of life diagram at lower left!


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