A number of passages in the Timaeus make a connection that strikes us as odd, even bizarre perhaps. Who nowadays thinks that the study of geometry or number theory has anything to do with being a good person? Yet these passages emphasize the importance for human virtue and happiness of mathematical studies, especially the study of the ratios of numbers and the geometry of solids in motion, the harmonies and revolutions of the world or of the god. We are told, for example, that by learning to know and compute these rightly we shall bring our souls into order and consonance and control their irrational components. We may recall also that in Republic VII a lengthy mathematical curriculum is proposed for the training of virtuous rulers, and Plato continues to insist in Laws XII that it is necessary for the god-fearing man and that "he who is unable to master these [mathematical] sciences will never be a sufficient magistrate of the whole community" (967d4-968a4, cp. 817e6ff.) This line of thought is summed up in the Timaeus as follows:
Now there is but one way of caring for anything, namely to give it the nourishment and motions proper to it. The motions akin to the divine part in us are the thoughts and revolutions of the universe; these, therefore, every man should follow and correcting those circuits in the head that were deranged at birth, by learning to know the harmonies and revolutions of the world, he should bring the intelligent part, according to its pristine nature, into the likeness of that which intelligence discerns, and thereby win the fulfilment of the best life set by the gods before mankind both for this present time and for the time to come (Tim.90c5-d7, trans. Comford, cp. 47b5~e2, 44bl-c4, 42c5-d2)
My aim in this paper is to pave the way for a straightforward reading of such passages. However, I shall proceed by a "longer road" since I have not been able to discover any shortcuts. I must also confess that on the first part of this road I have encountered so many difficult curves and potholes that I do not yet have a great deal to say about later segments. Nevertheless, I hope to persuade you that it is a road worth traveling.
Kung, Joan, "How Learning Mathematics Helps Us Be Virtuous" (1985). The Society for Ancient Greek Philosophy Newsletter. 325.