I know that they are "just as human as we are", but I feel somewhat uncomfortable to talk nonchalantly with the top-notch math researchers and professors in my department because of their social position, their extremely superior knowledge and talent, and also because of their age.
Still, I feel that it is like a waste to have such interesting mind-expanding people around and not to interact properly and talk about maths when I meet them in the department (outside the lecture hall).
So my question is: according to your experience, what is the best (where best means: most polite, appropriate, acceptable, but also profitable) way to interact and make the most of the presence of such awesome professors? Can I discuss "lower" [mathematical and non-mathematical] subjects with them even though their actual (research) interests lie in much more abstruse topics?
Any suggestion (even in the form of a comment) is really appreciated.