Kant: How is Pure Mathematics Possible?

As I approach this entry, I'm not really sure what I want to write.
I guess I will start small, by trying to see if I comprehend Kant's theory about the Transcendental Problem: How is Pure Mathematics Possible?

He seems to say that Mathematics is the only "branch of knowledge" which is in itself a priori. That is, there is nothing before it, nothing empirical to prove it. Math is, and it works. We can delve into specifics about formulas, but the formulas themselves are only compounded within the actual branch of Mathematics which cannot be understood by any preceding factors. In the grand scheme of things, we just know that it works.

Kant continues by bringing up the first red flag with his statement, which regards the question, "How is it possible to inuit anything a priori?" (Kant, Immanuel. Prolegomena, 2). Because we perceive things via intuition which requires the presence of "a former or a present object to refer to [he says it]...could not be intuition" (Kant, Immanuel. Prolegomena 2). Taking that to be true, maybe intuition is not the issue. Maybe the epiphany that math is a priori yet not previously conceived by any object, yet it still works and functions as a solid and expanding branch of knowledge, is the manifestation of systems in our mind that are a priori. In this way we could solve the problem of intuition, by saying that systems in our mind exist by which mathematics was conceived.

Revisiting Hume, in class I brought up the idea that Hume should have been looking at the systems with which we sense forms and not the forms themselves. Maybe Kant could have taken Mathematics to be the outward manifestation of the a priori systems that Hume could have spoken about. Maybe math is how we perceive the world, considering that expands in to functional conceptions about time and space.