I kinda know that I'm smart, but I remember being in a stage of life where I couldn't stand that someone else might think that I was dumb... especially if I felt they weren't very smart and so their opinion of me was based on their inability to realize I was smart.
(Gee, that sounds so stupid when I say it like that!)
I just didn't like to feel misrepresented, and I think I also only felt secure with my intelligence (I felt very socially inept, not very desirable, kind of a no one), so all I had going for me was that I was smart. Eventually when I started doing more creative things, I had to wrestle with similar feelings there as well -- not wanting to share, lest someone decide I wasn't very creative at all.
I still can feel that way sometimes but typically do not live like it: (1) I trust that reasonable people can make a reasonable assessment of me, enough that I don't need to convince them of anything, and (2) I guess I just feel better about myself and don't need to be viewed as super-smart or super-creative in order to be okay with who I am. I think this is also part of aging; the longer you're around, the more some things WILL decline (the brain slows down in terms of raw speed), plus you're gonna meet a lot more people and some of them WILL be better than you at things, and you just better have your self-value defined by things that time or other people cannot impact.
In the last year or so, I've even found myself okay (and willing) to ask people for advice when I've felt out of sorts... even if it makes me look less smart. Usually I want to resolve things on my own and seem very independent and self-capable; but less and less of my identity is being wrapped up in that projection. I think I realized that part of relationship building demands that I allow others to contribute to me, so they feel invested in me, and it actually makes me seem more real and human, without degrading their opinion of my intelligence; the autonomy thing, I think, is one reason why many of us struggle with alienation, loneliness, and whatever else. Gotta find a balance.