Is Being Really Good at Math a Power or a Skill?

There's a scene in the film "Stranger Than Fiction" in which the main character is having dinner with a friend and asks what the friend would do if he he knew he would die soon. In negotiating the terms of this hypothetical, the friend asks if he would have any super powers and the main character says, "You're really good at math," to which the friend responds, "That's not a power, that's a skill."

Is it?

What is the difference between a power and a skill? A power seems to be power over something. In this case, would it be having power over a problem to solve it? A skill on the other hand, is an ability to do something and that seems a better way to characterize being able to solve a class of problems. Score one for skill over power.

On the other hand, a skill seems to be something one could acquire by working at it whereas a power seems to be something one simply has. Hanno and I have had this discussion many times with respect to logic students. There are those who acquire the skills by working very hard at it and then there are those who are really good at logic who don't work hard. For those who are really good at logic, it seems more grammatically appropriate to use solve in a reflexive sense, it's not that they solve the problems, it's that the problems are solved to them. I'm one of these people. When I look at the problem, I don't labor over it, I look at it from different angles until it just resolves itself before my eyes. Those who are really good at something do seem to have a power rather than a skill. Or is it just that some acquire the skill more easily?

So, is being really good at math a power or a skill?