Theon of Smyrna

Theon of Smyrna, a Platonist of the early second century, wrote the work whose title declares the whole program of Pythagorean Platonism: Mathematics Useful for Reading Plato. Its premise is that the dialogues cannot be understood without the mathematical sciences — that when Plato speaks of means and proportions, of the soul-numbers of the Timaeus, of the nuptial number of the Republic, or of the music of the heavens, he presupposes an exact science that the reader must recover.

The surviving treatise covers arithmetic and music and part of astronomy: the kinds of number, figurate and tetraktic numbers, the theory of ratios and the musical consonances, and the order and motions of the planets. Theon writes as a compiler, openly preserving the teachings of earlier Pythagoreans — including precious testimony on the several kinds of tetraktys — and it is precisely this fidelity that makes him so valuable a witness.

With Nicomachus, Theon is a principal source of Thomas Taylor's Theoretic Arithmetic, and a standing reminder that in this tradition mathematics was never separate from theology: the same ladder leads from counting to the monad, and from reading Plato to seeing what Plato saw.