I have been asked if mathematics is part of science. The short answer is yes, the shorter answer is no. (Never ask a philosopher a simple question.) The problem is that language does not have the power this question presupposes, or we don't know the answer, or both.
Here's how I see it. Science is systematic knowledge of deep stuff. Hence mathematics is called the Queen of the Sciences, for two reasons actually. First, mathematics was the first of the systematic bodies of knowledge. Second, the use of mathematics is regarded by many as the hallmark of any true science.
But (and this is the big, big but), science is supposed to be about physical stuff, stuff that exists, and mathematics isn't about that at all. You can't put a number in a bag.
So this is one of the fundamental questions of philosophy, for which I could give you a nauseous number of citations, none of which I recommend reading. I think the true answer is that we have no idea, because we are still in somebody's Middle Ages. In what we call the Middle Ages they speculated about something called the `quantity of motion'. This led, via Galileo and Newton and many others, to what we now call physics. (Why can't we teach kids: What we don't know?)
To change the subject slightly, I find myself making notes to the effect that this turn of the Millennium marks the end of science (1600-2000, rip). Obviously overstated, but the issue of the practical and theoretical limits to knowledge looms before us. Chaos theory is my pet example, but there are others. Our traditional concept of science, a la Galileo and Newton, incorporates assumptions that are now known to be false. After all, concepts are in themselves theories of how the world works. The words we use have the meanings they do because we want to say what is true. So language changes with understanding.
That said, I believe that mathematics is indeed a science, because it is about something that is real. If there are trees then there are pairs of trees, so the number two is real. We did not invent two, we discovered it. (Aside: I have the same problem with the issue tree, by the way. People want to insist that I invented it, but I discovered it. It is how ideas really fit together. Not some concoction of mine.)
Perhaps the information age will make it easier for people to understand that what is real is much more than what you can put into a bag. What, after all, is information?