What metaphors are used in A Mathematician's Apology by G. H. Hardy?

Hardy employs a metaphor that equates theorems with geologic strata: the more difficult the theorem, the more layers it has, with each layer holding ideas that link to other ideas above and below it. An example of this can be found in Chapter 18, where Hardy explains why chess can never be "beautiful." In short, the very nature of chess demands that any given move can be answered with multiple countermoves—what Hardy refers to as "proof by enumeration of cases," which is the antithesis of beauty in a mathematician's eye. Rather than being a beautiful collection of mathematical theorems competing with one another, a chess game is, at its heart, a psychological battle between two intelligent beings.