How should I thank mentors that I connect with via the Internet?

Question

I am an incoming undergraduate student, and I have reached out to people who are currently pursuing/once pursued the field that I'm interested in (it's physics if it matters), via the Internet. Most of them are willing to help me and have given me a lot of good advice. Thus, I really want to thank them for doing that while potentially improving their impressions of me. However, since I have never met most of them in person (even if we did, most of our communications still happen online), I have a hard time thinking of a way to express my gratitude. Here are some details of my situation:

1. I know very little about them as a person (their hobbies, preferences etc.). The conversations we had focused almost exclusively on their chosen fields - most of the time, they answer my questions and provide guidance.
2. People who have helped me are in various stages in their study/career right now. Specifically, undergraduate, Master's, PhD and postdoc. Thus, I think that they may prefer different types of gifts.
3. I've heard of people writing thank you letters to their mentors. However, I feel that doesn't apply to my situation since my relationship with my mentors doesn't have an explicit end. For example, the length of our relationship isn't defined by the length of a course or a program. Thus, I feel that writing them a letter that talks about our past interactions would be perceived as a signal that I no longer want to continue our relationships.
4. I tried to treat those who invited me to talk in person with drinks or meals (if they let me). I would like to hear your thoughts on whether or not it is a good way to express gratitude as food doesn't last very long. Should I keep doing that or even go out of my way to invite them when I travel to places where they live?
5. Alternatively, I am thinking of mailing them tangible gifts. But again, I am unsure about what to purchase yet.

Answer 1

A simple email is really all you need. Thank them for their help and update them on your recent progress, say by mentioning that you have been accepted to ...

Don't bother with gifts as they will embarrass many people and might be considered improper. The one exception I can think of is the situation in which you are from a different country or culture. Then a token tourist level souvenir from your country might be fine. Something like this if you are from Sweden (not the world's biggest, though). I find it harder to come up with anything appropriate if you are from the same culture/country, though. The gift should have personal value, rather than tangible value.

Later, when you finish a doctorate, say, and get a great job, you might think of something more elaborate.

But for people you have met and who have helped you, say a teacher, it is a good thing to go back after several years and thank them personally for their mentorship. Just a meeting in a hallway with the statement of thanks for their help and guidance is a deeply satisfying thing to do and to receive.