[lo_zamoyski]

It is absolutely a science, a formal science. What it isn't is an empirical science.

The "symbol pushing" is a methodological tool, and a very useful one that opened up the possibility of new expansive fields of mathematics.

(Of course, it is important to always distinguish between properties of the abstraction or the tool from the object of study.)

[weinzierl]

Well, we are talking about pure mathematics and there is not much Popperian scientific method in it.

[Warwolt]

Who cares? That's just semantics. If we define science as the systematic search for truths, then mathematics and logic are the paradigmic sciences. If we define it as only empirical search for truth then perhaps that excludes mathematics, but it's an entirely unintersting point, since it says nothing.