First, let me say a few words about the means by which I learned about and was able to participate in this discussion, namely Mars Hill. Mars Hill is a student organization at the U of M where we discuss various topics of academia, philosophy, and religion from a scholarly perspective. We welcome anyone interested in a good, deep discussion; topics this year have ranged from the nature of beauty to just war theory to what I'm about to write about.
Anyway, tonight our discussion came to the nature of math and science. What are they, and are they human creations or from God? For a former math major with considerable experience with the subject, it was a good topic for me. We started with science; the consensus was eventually that science is the rational study of the physical world, i.e. the creation. Then, on to the nature of math. My initial position was that mathematics is a series of statements derived from applied logic and exists separately. Others argued based on how we study math or what we do with it, but out speaker urged us to define it as "the study of ____". She defined it as the study of structure, which was new to me. The way I see it now, the mathematical truth is objective and not man-made, but mathematics is the study of how it all works and is man-made. Logic is the basic tool we use to study math.
Lastly, I apologize for my extremely abbreviated description of the discussion that doesn't do it justice. If anyone with a functioning memory who was there happens to read this, feel free to add on.