i’m applying to an ivy early (nov 1 deadline) and the school asks for a rec from a research mentor. i worked at a university this summer doing research. my mentor said at the end of the summer that he would be willing to write me a rec. i emailed him oct 1 to give him the specifics and kind of check in that he was still willing to do it, and he hasn’t responded. would it be rude to email him a reminder? thanks 
You should telephone him. What if he’s travelling or otherwise unavailable? You need to find out and go to Plan B if his promise can’t be fulfilled
Sometimes people get so many emails that one gets overlooked. It’s not rude to send a follow up inquiry - but if you have a Nov 1 deadline, then yes, you need to telephone.