Most of programming involves figuring out what to do, not doing it.

The same is said of mathematics.

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.

You do realize that algorithms were invented in Euclid's day, right? Was he not doing math, or are algorithms no longer programming?

Even string processing is math (c.f. Godel).