How to pitch a research idea to a professor as an undergraduate? I have an idea which I'd like to work on with a professor at my university. In my initial email would it be arrogant to ask if he's interested in working with me on this particular topic (he's published some papers on closely related topics), or should I just say that I'm interested in generally doing research with him? I really do want to work on this particular idea but also don't want to come across as trying to tell him what to do.
A small point about language: in the U.S., in mathematics, it might be more tactful and less presumptious (also) to not ask about "work with me", but "advise me on" [the project you propose]. At least to my perception (=old guy) this leaves many more options for the precise relationship. E.g., experienced people can often and easily give helpful advice without really actively participating. At the same time, depending..., they might find interest in doing so. Or, at the same time, they might see that it's better to let you do it yourself... etc.