When I have a programming problem I talk it over with someone who knows nothing about programming. Often times they ill provide the incite I need to solve the problem.
I think that mathematical skill is one of the most important (and underrated) strengths when it comes to programming. Possibly more-so than fluency with one's language of choice.
I don't think you necessarily need to know really advanced math, but you definitely need a solid grasp of stuff like trig. In games programming especially, it's all calculating angles and distances, and general problem solving of how to derive a number from a bunch of other numbers. So I agree that math is an important of programming logic.
After all, knowing the language inside out is useless if you can't figure out what you're actually trying to make your program do!