I'm the same as soxfan, I am intimidated by beautiful girls. For me intelligent and mature girls are someone I can compete with anyway so it in no way intimidates me. I'm not a great looking guy so I feel like I don't deserve someone who I feel is out of my league. It might be the opposite for guys who feel attractive, but feel they lack book smarts.
I tend to be intimidated by a girl if she is extremely attractive, but I'm not intimidated by girls who are very smart or mature. I'm not sure why, maybe because I consider my strong points to be smarts and maturity, rather than good looks and that makes me feel like I could hold my own around smart girls but might be out of place with beautiful girls.
Anyway, when I'm intimidated by a girl I do tend to back off and avoid direct interaction where I could wind up being embarrassed.
I agree with these guys. I am intimidated if the girl is just beautiful cause its like she could probably have anyone she wants. But I'm not intimidated if she is smart. I like if she is smart and knows about some stuff that I may not know about.