I feel that there is more to the simple ruling of brainy vs stupid. In fact I believe that there is no such thing, it's just that people choose to devote themselves to different uses of their brain.

Being intelligent has to be more than just academia.

For example, my girlfriend and I are very different in terms of our intellect, she has a masters degree which she achieved relatively easily, I could not do the same. She is knowledgable and has a good memory for facts. She is what's commonly termed; clever.

I on the other hand am not, I'm not stupid but I do not have the same mental capacity for facts, figures, and for memory of facts which I find uninteresting. 

However I am much better than her at looking inwardly, my girlfriend cannot see the value in looking at herself and wondering why?. She is not as good as me in social circles and doesn't realise when she speaks out of turn or offends someone, and has trouble with emotions.

I don't think there is a sex or hormone thing here, instead its a nature verses nurture thing and its done to just how our brains have become wired over the years. I feel I would have to drop something from my mental capacity to be able to get better at say; maths, and i would loose something such as; artistic ability.

I have found that as a general rule of thumb, If you come across a stereotypically clever person; they are not good in social situations, and people who are good in social situations are not good thinkers. Neither should be seen as stupid in one situation or the other however, their brains are just busy doing other things at the time.

Is it possible to not use all of your brain?

It might be, the brain may not always be running at maximum effeciency because its just full of rubbish sometimes.