I'm (27M) embarrassed/insecure about my girlfriend's (25F) intelligence. She knows it. SOS

I have a corporate lawyer in my close family. It's mind boggling how when we talk about certain subjects I feel like she doesn't understand things that are simple to me as quickly as I thought she would (like English language, for example), but she deals with complex laws and regulations on a daily basis and sometimes can even explain to me stuff that I couldn't grasp after reading pages after pages about it (which for me personally is a great way to measure a couple kinds of intelligence at once - how well can you explain to me something complex in a way that I can understand it.)
I'm told by a lot of people that I'm intelligent to the point of intimidation because I love to talk about things that I'm knowledgeable about. (And learned English pretty quickly pretty well, which seems to be seen as a sign of intelligence for those who do not speak foreign languages.) And yet sometimes people mock me, too. For instance the latest one, asking a colleague why there are stickers with crossed cigarette on all the dumpsters in front of our building, and where am I supposed to throw away the fags (turns out of course the stickers mean "non-smoking area", not "do not throw cigarettes here", obviously lol). Later I overheard a couple other colleagues from my team laughing about it (they thought I didn't hear them apparently).
Needless to say I'm not friends with these people and limit any interactions I need to have with them. And I feel good about it. I surround myself with friends on different intelligence/knowledge "levels" that don't mock anyone for not knowing things or having "brain farts". It's much better this way.

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