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This post asks for resources to handle the following situation: "I, suddenly, have students" and many wonderful answers have been provided. My question here is sort of a prequel: recently, a post-qualification second year graduate student $X$ expressed an interest in working with me.

What should I put $X$ through before agreeing to advise him or her?

I don't mean to ask about the part where I point $X$ to appropriate literature from my field and help $X$ to understand the textbooks and survey papers as needed: that I can do. But how should I measure $X$'s aptitude and gauge interest levels, etc? I don't want this to be a long and drawn out process for obvious reasons. The zoomed-out version of my question probably should be:

What do you look for in a graduate student before you agree to advise him or her?

If it turns out from the responses that this question is overly subjective and leads to wildly varying opinions, I can make the question community wiki.

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closed as not constructive by Benjamin Steinberg, Chris Gerig, Mariano Suárez-Alvarez, Suvrit, Ryan Budney Jul 3 '12 at 20:39

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

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Incidentally, now academia.stackexchange.com is in beta, your question will definitely look more in-topic there. –  Federico Poloni Jun 29 '12 at 20:09
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This question was clearly of general interest: 500+ views and 13 up votes in 9 hours, not to mention two useful and non-argumentative answers. This is important information not just for those starting their post-doctoral careers but also for first and second year grad students. I would like to thank the answerers for their help, and inform the closers that their views are shortsighted at best if they sincerely believe that a (possibly edited) version of this question is not useful to many research mathematicians and their potential students. –  Vidit Nanda Jun 30 '12 at 5:06
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I don't think it helps much to ask such a question at academia.stackexchange.com - any non-obvious advice would be very math-specific. –  Arend Bayer Jun 30 '12 at 12:30
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The fact that nobody's given an argumentative answer isn't evidence that nobody wants to. I've been tempted to give a mildly argumentative answer (that potential advisors should make sure students are well informed - what Tricia wrote is great - and try to find the right fit, but should not filter for aptitude in a US-style system, since everyone who has been admitted to grad school and remains in good standing needs and deserves an advisor). However, I don't think MO is the right venue or format for such a debate. –  Henry Cohn Jun 30 '12 at 13:22
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Speaking as one of the most active users at academia.stackexchange, this question would be very welcome there, @ABayer's comment notwithstanding. Nothing about advising students is "obvious" to everyone, in math or any other field. –  JeffE Jul 1 '12 at 0:55

4 Answers 4

up vote 28 down vote accepted

I usually suggest the student spend a couple weeks, or more if they want, taking a look at a little bit of material in my area and then come talk more with me, so that we can both get a sense of whether the area is a good fit for the student. Typically, I print out a survey paper in my area and suggest the student start reading part of it; and I also ask the student to try to do a couple of exercises from a book in my area, suggesting the student pay attention while doing this both to whether the material seems to mesh well with the student's talents and also to whether they find it enjoyable/engaging. I find it very informative to see how this goes and to chat with the student after they've grappled a little with this material; I tell them I don't think either one of us should make a definite decision until after they do this. Of course I try to make it clear that it's fine to come back with questions about the material. This also buys me a little time to learn more about the student -- like Lee Mosher mentioned e.g. how they did in coursework.

Some of the students who have approached me seemed to think combinatorics (my area) would be the easy route through grad school, which I do not believe is true at all -- so I try to communicate that it's an area where on the one hand questions may sometimes have simple statements, but on the other hand may require a lot of ingenuity to solve. Based on this experience with students, I think it's also important to make sure students aren't making decisions based on misconceptions. So I second everything Lee said too.

Others here have surely had many more students than I've had so far, but I did have the experience of being approached by a large number of students right after starting a tenure track job, so gave this a lot of thought then.

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I have a strong opinion on this topic: a potential advisor must have an excellent reason to refuse to advise a graduate student who meets certain minimal requirements. The department has accepted the student. Presumably the student has successfully passed prelim exams, etc. The department as a whole has promised to help the student in their pursuit of a PhD. In my opinion, it is inappropriate to tell a student that, although the department promised to help, I personally think you do not deserve / warrant my advice. There are obvious exceptions: too many current advisees, personality conflicts leading to unhealthy working relationship, etc. Agreeing to advise is not a guarantee that the student will make progress, and if they do not, both parties should re-evaluate the relationship. However, faculty have an obligation to the PhD candidates admitted to the program. They should accept advisees unless there is an excellent reason to refuse.

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I think there is a difference in how much of this responsibility should fall upon a tenured faculty member vs. a not-yet-tenured assistant professor. –  Patricia Hersh Jun 30 '12 at 17:06
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While this is what is asked for, I would just like to stress that this answer refers to a US-style system. And, for example, in various European systems the general situations is completely different. –  quid Jun 30 '12 at 17:33
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Whether you think the student deserves your advice is not the only issue in deciding whether to become a student's advisor. You can also fulfill your responsibility to the student by telling them (if it's true) that you don't think you would be their best choice for advisor, and helping them to find an advisor that better fits the student's specific research interests, expectations, working style, level of independence, etc. –  JeffE Jul 1 '12 at 1:03
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@JeffE -- It sounds to me like you are addressing a different question than the one posed by the OP. I agree that there are times when a different advisor would be a better fit with a student. Unfortunately, many of the faculty I have met who use "better fit" as a reason to refuse advisees are the same ones who refuse administrative duties, who show up for office hours as the mood strikes them, etc.: it is just an excuse for avoiding a duty they don't want. –  Jason Starr Jul 1 '12 at 14:14
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@Jason: that may sometimes be the case, but not always. I think there are also quite a few people who are overwhelmed by the amount of advising, administrative, etc. responsibility that falls upon them, in some cases because others aren't carrying their weight, and I think it's an important issue for such people to figure out how to be effective in deciding which such things to take on and in finding good ways to make sure the other things get done too. –  Patricia Hersh Jul 1 '12 at 14:34

I have a strong opinion on this topic: a potential advisor must have an excellent reason to refuse to advise a graduate student who meets certain minimal requirements.

I have developed an equally strong opinion in the opposite direction: a graduate student should show his ability to surpass the so called "minimal requirements" by far and large to even start talking about my becoming his adviser. Unless you want to end up defending PhD yourself a second time with your tongue and hands disconnected from your body and operated by remote control, you'd better make the student undergo a few severe tests over an extended period of time. If he survives, he's worth trying. A good place to start is to give him a tough but self-contained paper in your field and ask him to read it within a month and present it to you.

I do not believe in any "promises" or "obligations" to graduate students. We give them an opportunity to learn and to prove themselves worthy, but that's about it.

Sorry for "being argumentative", but since we touched the moral grounds in this question, you should keep in mind that the moral standards vary a lot from place to place and from person to person, so I would hate having you swayed by Jason's argument without being aware that not everyone shares his point of view. In short, make your own choice on the matter. You have as clear head and keen eyes when evaluating a potential candidate as everyone else.

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I agree with this quite strongly. We produce too many weak Ph.D.'s, and too few mathematician I know seem to understand the negative impact of this on our field and ourselves. Most seem to believe that if the person ends up outside of academic mathematics, then no damage is done. I learned during a brief tenure working on Wall Street that the opposite is true. Sharp non-mathematicians can detect weak math Ph.D.'s, and it shows them that a math Ph.D. is not worth as much as they might have thought. –  Deane Yang Jul 1 '12 at 21:18
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I generally support fedja's point of view and I want to add another argument suporting it. Often, students looking for an adviser have no clear idea of the effort required and your expectations. Giving them an initial taste of your demands is in my view very helpful to all involved. If that initial experience is too scary for a prospective student, then maybe it is wiser for him/her to find a different adviser. There is however a delicate balance. When I assign some difficult reading and a tight deadline I also add that he/she can stop by and ak questions. –  Liviu Nicolaescu Jul 2 '12 at 16:19

To gauge aptitude you can look at how the student did on the qualifying exam or exams that are closest to your subject. To gauge interest you can see if the student has taken advantage of nearby seminars and conferences in your subject, and you can talk to the student about what they got out of those experiences.

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