Earlier quoted context omitted.
I don't think math is the study of abstraction. It seems to me it's proving truths about formal systems. Abstraction has the same purpose in math as it does in programming, a tool to more effectively communicate ideas.
In addition to @sebatos response, I'd add that a formal system is nothing than an abstraction of some concrete problem.
I haven't really thought about it deeply, but I'm pretty sure this isn't true. It seems like mathematicians are often coming up with new proofs and formal systems and only later noticing that they're applicable to some real-world problem.