Every few months I get an email about this topic, so here goes:
Is it appropriate to give your graduate adviser a gift when you graduate?
I can't speak for anyone else, but I personally do not want gifts from my students, even the students who became friends/colleagues by the time they graduated. I don't know about other departments/fields/countries, but gift-giving is not routine in my little academic niche.
Every once in a while a student gives me a gift; these are mostly new international students who may be used to a culture of gift-giving. I accept the gifts with polite thanks.
Every once in a while a graduating undergrad is inspired to give me a small geeky gift to thank me for some extra efforts I might have made on their behalf -- e.g. lots of letter-writing, advice, and/or research opportunities above and beyond what is typical etc. That's fine. It's not necessary but I appreciate the sentiment.
My best guess is that in many cases a gift is not expected. If gift-giving were a tradition in a department, I think most people would know about it and therefore students would not be wondering whether they should get something for their adviser. The best people to ask are probably recent graduates.
I don't want tangible gifts, but consider this: Last year my graduating PhD students sent me heartfelt thank you e-mail messages, and I very much appreciated those. The messages made me very happy and, although I delete a lot of my e-mail, I kept those.
Advisers: Which would you rather receive from a graduating student: a sincere and moving thank you note or an aliquot of your favorite food or beverage (chocolate, wine etc.)? (Note: in this poll, 'both' is not an option. You can of course be anonymous, so feel free to be venal.)
10 years ago