>When I was visiting with community college students in Arizona, one young man said to me, “I’m one of the people who’s not good at math.” It kills me when I hear that kind of thing. I think about how different things might have been if he had been told consistently “you’re very capable of learning this stuff.”

Couldn't agree more with this specific example. But you shouldn't ignore reality either. A man with no legs is not going to win the 100 meters at the Olympics. Understanding where your potential lies is important for deciding where to invest your effort. That doesn't mean he can't improve at all though.

Especially in things like math, there is a popular belief that you need some kind of 'math gene' to be decent at it. There is little evidence that there are math specific genes beyond general learning ability.

[Same genes 'drive maths and reading ability'] http://www.bbc.com/news/health-28211676

Sadly, in a lot of cases this will lead to a self-fulfilling prophecy where you will stop trying to improve your math skills because you weren't "made for it".

But that's really more a problem of a false belief that these things are set from birth. A blind belief in 'I can do anything i want despite the situation or environment i am in!' isn't going to help anyone. I would advise the runner with no legs to invest his precious time and resources in something other than trying to win the 100 meters at the Olympics.