During an email conversation with my professor, I ended the email by writing
Let me know your thoughts.
I forgot to add a "Please" with it. It’s probably silly, but I am worried thinking is "Let me know your thoughts" polite enough?
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It might depend on the professor and your relationship. It could possibly seem a bit too informal to some who appreciate more deference: I would appreciate knowing your thoughts on this. ‘Let me know’ is not showing a lot of deference. It is more likely to be said by one’s superior. But this is nitpicking. I was married to a professor for a long time and let’s just say, many are an odd lot. Don’t worry.
Let me know your thoughts is slightly informal, and can be interpreted by some as having a tint of condescension. A decision maker, or an organiser of a project/programme etc. can say that to the others.
A safer expression for a student-teacher relationship is:
I would be grateful for any suggestions (you might have).
It depends on who you are talking to. In some contexts it sounds a bit stilted (too formal). In others it might sound condescending. If said said this to my partner, she might be somewhat offended for that reason: it sounds 'de haut en bas' (that is, as if I am talking down to her/him <literally 'from a height downwards'>). If you are leading a seminar, chairing a meeting or making a proposal to colleagues in a matter in which you are taking a lead, you could say 'let me have your thoughts'. I wouldn't, but that is just a matter of personal style.