John Allen Paulos, in an interesting essay on the co-option of mathematics into religious apologia, makes a useful explanation. To counter the idea that the elegance of mathematics is a reflection of the divine, he suggests otherwise — it is a reflection of the natural world.
The universe acts on us, we adapt to it, and the notions that we develop as a result, including the mathematical ones, are in a sense taught us by the universe. That great bugbear of creationists, evolution has selected those of our ancestors (both human and not) whose behavior and thought are consistent with the workings of the universe. The usefulness of mathematics is thus not so unreasonable.
Sad to say, the comments to the article are a bit depressing: the creationists descend and start yammering about transitional fossils and mangling Gould and that sort of thing, the usual foolishness we expect from them. It deserves better.