Way back when, when I went around interviewing for faculty jobs, there was one particular interview which I really enjoyed. Usually, you get to have a dizzying sequence of brief interviews with faculty members (no, this is not a tribute to David Foster Wallace), but in that one, unusually, I also got to meet with a delegation of graduate students. We had breakfast together and they asked me a few questions, and I got to see an aspect of the department you usually don’t get to see in an interview.
One question they asked stuck in my mind, maybe because I did not provide a good answer. Suppose you have a graduate student, just at the verge of discovering their own voice, maybe after completing their first project. They come to you with their first own idea, but the idea is not that great. It is not terrible, you cannot point out immediately any obvious flaws, but it doesn’t look like it is going to work out, and even if it does it may not be worth the effort. What do you do?
Shores of the Dirac Sea 