Math is a tool used in programming, programming isn't defined by math though (there are plenty of non-math activities that dominate the process). What is so hard about that?
Actually there's a deep equivalence theorem between mathematical statements and programs. Here are people doing ZFC as a program - http://en.metamath.org/
Yes, but that creative process isn't really doing math either (as defined by performing mathematical reasoning). The best we can say is that creative processes are involved in all disciplines.
Programming can involve math, math can involve programming, but neither is defined by the other.
