A (female) mathematician friend of mine has often complained about the responses she often gets to her gender in her field; often she feels that others expect her to be incompetent until (and sometimes despite) being proven otherwise. The interesting thing is, she's seen other women internalize this, resulting in "impostor syndrome": effectively, no matter how well they do, they feel they don't really understand the material, that they only got as far as they did by fluke, and that it'll all come crashing down around them at any time. The interesting part is these women seem to do particularly well (barring nervous breakdowns) because they believe their abilities are not innate, and so they work much harder than they actually have to.

I think the same is true of men, albeit (based on this article) to a lesser extent. I coasted through most of my childhood on simply being smart, and it was only when I started forcing myself into difficult situations that I learned to actually develop abilities I didn't have automatically. This is why I'm skeptical about "gifted" programmes: they segregate children based on innate talents, rather than emphasizing hard work and dedication, and that seems to leave a lot of otherwise intelligent people unable to cope with day-to-day existence outside the world of academia.