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Oct 12, 2023 at 2:43 comment added MarcoD Maybe the only piece of advice to the OP that I would add to this fantastic answer is to modify the perspective, not envisioning the professor-student relationship as a one-way transfer of information. The most gratifying human experiences are those in which there is a mutual exchange, we transfer some knowledge and we learn something. Working with exceptional students should be coveted as a win-win for both, for the professor to work with talented individuals in a field of interest and for the students to have an ally inside the institution who fights for them to get the deserved recognition.
Oct 10, 2023 at 20:06 comment added TOOGAM I have to +1 this because it is such a great answer that I didn't any longer feel free to write one up on my own. I would just add this: Some employers value a degree because it shows a person went through a lengthy experience, likely including some requirement to fulfill some expectations. If a student knows some thing(s) that you don't, that doesn't negate your ability to help with the overall school process. Some students may only want to be in school to learn from smarter people. Such short-term wants may not be the highest priorities that they need to focus on and fulfill.
Oct 10, 2023 at 15:29 comment added march Yes. For instance, it's extremely unlikely that a bright student knows how to write a good research proposal, or how to navigate the various grant systems, or what grants to apply for, etc. And while many bright students are good writers, many of them are not (in the sciences, at least, in my experience), and so an advisor can easily help them grow as a technical writer of publishable papers.
Oct 10, 2023 at 15:26 comment added GEdgar +1 "very very happily". I have advised very bright students, and not-so-bright ones. For me, it was much more work in the non-so-bright cases.
Oct 10, 2023 at 6:58 comment added xLeitix @Nelson Interestingly, the "superpower" of one of my previous students was that he literally could get to talking with basically anybody, in any context. I think his network was larger than mine no more than two years into his PhD.
Oct 10, 2023 at 0:35 comment added Nelson Experience counts, and so does reputation and people you know. Your student can't go up to a random professor and just pick their brains, but you probably can with some of them.
Oct 9, 2023 at 19:46 comment added Wolfgang Bangerth This is an excellent answer. Being a professor (or graduate student) is not only about being smart, but about so much more. You don't have to be better than a student in all of them to be a good adviser. In fact, perhaps seeing yourself as "team" with your student is a good perspective, where everyone brings to the table different skills (and different amounts of time -- something you can definitely not compete with your students with).
Oct 9, 2023 at 14:59 comment added Dave L Renfro (+1) especially for: any given student may outperform you in one or multiple of these dimensions, but it's unlikely that they are better than you in all of them
Oct 9, 2023 at 13:24 history answered xLeitix CC BY-SA 4.0