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I am accepted to a math PhD program and have a visit in a few weeks. I only have a few days to tell the university which professors I would like to meet.

Problem: I also still don't know what I would like to work on (which I stated explicitly in my SOP) and the departments has ~100 faculty members. I started to go one by one and see if I like what they do but what would make a good topic?

Reading the papers from professor A things look "easy", I don't know the solution to the problems but I'm in familiar territory: it is number theory, a junior high school could understand the problem, and maybe high school could understand some solutions.

The vast majority of the time, for other professors, I don't understand anything at all. Sometimes I have a clear disgust (seeing lots of integrals/computations), sometimes I feel it is too hard (Langland related algebra), ...

I wonder how discomfortable I should be with a subject? I would be sad to end a PhD with seemingly "no additional knowledge" (if I choose prof. A) but conversely I would also be sad if I struggle on something too hard for me or for which I have no appetite even after spending time understanding it. Finally I don't have enough time to spend hours on each professor's topic to see if I would like it.

What is a good way to approach this?

closed as off-topic by Buffy, user3209815, corey979, Buzz, gman Jan 28 at 11:28

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    Are you excited about the research? That's more important than your comfort. – Thomas Jan 27 at 22:19
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    I was very confused by the two Thomas's. – user74089 Jan 27 at 22:26
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    Only you can answer this. There are two kinds of risk here and the tradeoffs are yours alone to make. Different people would choose differently. I've voted to close since you have already laid out the dilemma and the risk. You can be a success or not on either path, but your actions would be different on the two paths. – Buffy Jan 27 at 22:48
  • @Gradstudent I felt the need to comment due to this double-up. Also, the correct plural is Thomasi since it's Greek. :P – Thomas Jan 28 at 1:04
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Pick the ones who interest you to meet with. Probably some function (topics I like, big names). I.e. y= f(x,t).

Who you meet with is not going to make your final decision on what school to go to. But for sure you need to meet with those who you think are seriously "in zone" for being your advisor. You need that scoop. I would even make a stink if you don't meet with a key guy (their time is limited but so is yours...you are only making on visit...have seen candidates get a breakfast or lunch meeting or at least meet with grad student representative).

In terms of what work you should do, I strongly recommend to do something you are confident in. This stuff is hard enough so you need an edge. Also make it something you are interested in. This stuff is hard enough so you need some enjoyment. See. Multifactorial. Not f(x) versus f(t) but f (both). maximize, maximize. but each variable needs to be above average. Say above 7 on a 0 to 10 subjective. Don't let a 10 on one allow a 5 on the other.

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Well I'm just a grad student still but I did learn some things. You should not feel "wedded" to any particular choice before you get to know them well. At my program some entering students seemed set on working with some professor because he/she did cool research, but found out within a semester that the professor didn't do much to help students.

Here is what I think based on my own experiences: You want to have an adviser who you feel comfortable asking stupid questions to and who won't make you feel stupid.

You should get an adviser who is responsible and who has the time to meet with you on a regular basis. Some mathematicians are so busy that they don't spend enough time with their students.

Ideally the adviser is an authority on whatever subject you work on and has written papers in top journals. One possibility is to go on MathSciNet and see how many citations he/she has. This is not a perfect measure, though. If you are at a well-regarded research university, chances are that the faculty there are reputable.

You want an adviser who will support you when you apply for jobs, academic or non-academic. Unfortunately this can be hard to tell. I know a former grad student who got a postdoc, in his words, "no thanks to my adviser." One thing you can do here is to see what a potential adviser's students wound up doing. If possible, talk to them.

Also, not to deter you, but this is just based on talking with other grad students from various parts of the country: It seems like lots of math PhD students are not very happy with their adviser. At conferences when I chat with other grad students, it is rare to hear a student feel very positive about their experiences. Many of them express frustration. It seems unusual to find someone who really checks off all the boxes.

  • Thanks. But then how come new students end up being phd students of those "professors who do complicated stuff"? They just went there in something they had no idea of? (I have an MS already and yet it's hard for me to imagine anyone knowing anything about those topics even with an MS) – Thomas Jan 28 at 0:18
  • You don't have to know what your future adviser does before you start the program. You take classes with them and say that you'd like to know more about what they do and if they are accepting students. Then you might do a reading course where you learn about some topic under that professor's supervision. Or a reading course with another professor. Meanwhile you ask students who had worked with other potential advisers for their opinions. Hopefully by the time you finish qualifying exams you will know. – user74089 Jan 28 at 0:31

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