Geometry is so intelligible because (a) the figure is only given when we can specify a process by which we can make it and everything we subsequently learn about it arises from relating it to things we made and (b) the object is both as concrete as a sensible thing (look, a triangle) and as abstract as an intelligible one (let it stand for all triangles). It’s a science that is only appropriate for a being whose proper object is a mix of the sensible and intelligible, i.e. for human beings. Because of this, an idealized knower (e.g. God) only knows the truths of geometry by contemplating the contents of the human mind. Outside of our minds, there is nothing to know, and even if there were it would not be known in the best possible way.* Similar things can be said about the other maths, but my grasp of the ontology at work in these domains is more of a work in progress.
Maths are the closest we get to the act of creation, i.e. to being responsible for the existence of an objectively given universe.** But if this is our chief metaphor for creation, what literal truth can we cash it in for? We seem to get two competing ones:
1.) The purely intelligible universe. On this account, our takeaway from the metaphor is so far as anything is created it is intelligible. Being responsible for existence is inseparable from creating the objective and intelligible order. We see no contradiction, and in fact we see an unalienable harmony, between existence production and the objectivity of what is produced. We could not be more wrong in thinking that if a subject makes something exist that the product is relative and subjective. Such an account would make mathematics the most subjective and relative of all sciences, when in fact it is the paradigm of rationality, objectivity and science.
2.) The universe unintelligible to us. On this account out takeaway is that anything created is intelligible to the mind that makes it. Sure, the universe is perfectly intelligible… to God. But even a perfectly complete, Laplacian demon-TOE-understanding of physics is something that God could only know after he decided to take a peek into the contents of the human mind. In asking what God’s own view of the universe is we cannot do much more than say that it cannot include what admits of a formal contradiction. All of Medieval cosmology and metaphysics might be taken as an attempt to see how much truth we can distill out of this fact – but it won’t give us anything like what we get from science.
*And so we see the profound folly of seeing our science as an attempt to know with the mind of God. So far as something is what we now call “science” God only knows it by seeing it as part of the contents of our own mind (see infra).
**One of the better accounts of “science” is the attempt to understand everything the way we understand maths, i.e. define things according to the process that we make or identify them, try to reduce everything to an algebra of symbols and, of course, focus on the quantitative aspect of things.