“The questions of the students are often the source of new research. They often ask profound questions that I’ve thought about at times and then given up on, so to speak, for a while. It wouldn’t do me any harm to think about them again and see if I can go any further now. The students may not be able to see the thing I want to answer, or the subtleties I want to think about, but they remind me of a problem by asking questions in the neighborhood of that problem. It’s not so easy to remind yourself of these things.”
Richard Feynman, from ‘Surely You’re Joking Mr. Feynman!’. Adventures of a Curious Character”, 1986.
I believe mentors and students interact in a positive feedback loop – students need energetic and inspiring mentors as much as mentors need to be constantly reminded of the meaningfulness of primordial scientific questions.