Augustinian mathematics

In the Quotes on this blog, I have the following from David Knowles, in The Evolution of Medieval Thought:

Augustine took from the Neoplatonists that interest in number, which to the ordinary reader of his works seems an idiosyncrasy. … Plato, influenced by the Pythagoreans, tended towards the end of his life to see the ideal world—reality—as made up of mathematical concepts and symbols, which were therefore the metaphysical constituents of the visible universe. Plotinus adopted the conception, probably from the Neo-Pythagoreans, and Augustine in turn took it from the Neoplatonists. For him number is the intelligible formula which describes the qualities of being and the manner of change, so that all chage throughout the universe, which presents so much philosophical difficulty, can in a sense be “controlled” by numbers, just as an algebraic formula might express an electrical transformation or an engineering stress. Numbers are, in fact, a rationalization of the seminal reason of things. Numbers as used by Augustine had, of course, no scientific or mathematical basis, and it was easy, as Augustine found, to allegorize them, but the rational, or at least the pseudo-rational, foundation for what seems to many to be a strange aberration of a great genius can be seen to be one more legacy from Neoplatonism.

I asked for examples of Augustine’s use of numbers. I have now found one. If you know of others, please let me know.

In the Gospel of John, the most symbolic of the four gospels in the Christian Bible, it is recorded that, when Jesus appeared to his disciples after his resurrection and instructed them to cast their nets in a particular place, they caught 153 fish. This curiously precise number has invited reams of commentary. I am sure I have seen the claim somewhere that St Augustine thought is was special because it was the sum of the cubes of its digits: 1³+5³+3³ = 153. (This seems a little implausible because Augustine lived nearly a thousand years before the Indian–Arabic digits were introduced to Europe.)

Incidentally, this property of 153 (and three other numbers which are the sum of the cubes of their digits) is dismissed by G. H. Hardy in A Mathematician’s Apology as a mere curiosity, “recreational” rather than “real” mathematics. Hardy says, referring to this and the fact that there are two four-digit numbers which are divisible by their reversals,

These are odd facts, very suitable for puzzle columns and likely to amuse amateurs, but there is nothing in them which appeals much to the mathematician. The proofs are neither difficult nor interesting—merely a little tiresome. The theorems are not serious; and it is plain that one reason (though perhaps not the most important) is the extreme speciality of both the enuncuations and the proofs, which are not capable of any significant generalization.

Actually it seems that Augustine didn’t say that. Rather, 153 is special because it is the sum of the first 17 natural numbers; and 17 is important because it is the sum of 7 (the number of gifts of the Spirit) and 10 (the number of commandments), and so combines grace and law.

What would Hardy, a confirmed atheist, have made of that? After all, what better description of mathematics could you want than “a combination of grace and law”? Hardy’s own work certainly shows both aspects.