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I completed my PhD in pure math but wound up in industry immediately after completing the program. I dislike industry but love academia and research; and so as quixotic as it is, I would like to find some sort of academic position. It's been suggested to me that finding a mentor in academia would be helpful. I've tried doing so but haven't had much luck with my networking (and, honestly, if I had a stronger academic network, I wouldn't have this problem in the first place). Any more concrete suggestions for finding one? Frankly, I'm not sure what I'd have to offer over a real grad student or postdoc, which positions are already limited and competitive.

Specifically, I would want to find a mentor who would be willing to help me with some sort of research project and to:

1) Help me find suitable research topics: ones that are amenable to completion by someone working by himself, yet are nontrivial enough to be worthy of publication. (This is normally something one picks up in grad school, but my advisor assigned me very specific research problems and refused to allow me to change them).

2) Chat about math with occasionally. (Being in industry, I don't really have anyone to talk about nontrivial math with or bounce ideas off.)

3) Get the results published and promoted, if the project is successful. (Simply, say, posting a preprint on the arxiv without any further promotion wouldn't really be conducive to getting an academic position.)

So, how should I proceed?

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If you have already gotten a Ph.D., then the first thing that I would suggest is to begin to move yourself out of a student mind-set. What you are describing sounds like a thesis advisor to me, not a mentor, particularly the part about helping you identify research topics.

Instead, I would recommend that you start looking for a collaborator. Don't ask: "What can I give to this person?" ask, "What am I interested in?" and "What skills and techniques could this person help with on this project?" Most academics are quite happy to share their knowledge but very jealously guard their time. If you approach with a highly specific request for information that a person has, they are likely to share it (even if just by pointing you at a publication that contains what you are looking for). If it connects to something interesting enough to them, it might turn into a collaboration, and in a collaboration there is often also de facto mentoring and guidance by the senior partner.

Another thing that I would strongly recommend is to start attending conferences. This is where you will hear people talk about problems, both ones that they have identified and solved and ones that they have identified but that nobody has solved. Watching this can both help you learn about which problems are considered interesting and how to scope them, and also help you identify possible good collaborators, as you start engaging with these problems yourself.

  • It does sound like a student's mind-set; in fact, what I want (although it's not a thing) is to have a second, better thesis advisor. As it stands, though, a collaborator would be a great idea if I can get my foot in the door and find one. Crashing conferences, for example, is a bit difficult from industry. Still, it is a good place to start. – anomaly Jun 7 '15 at 4:08
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    @anomaly Why do you think coming from industry is "crashing" a conference? Researchers from industry are quite welcome at most scientific conferences---and I speak as somebody who has been a highly active academic researcher at a company since 2008. Your biggest challenge will likely be finding the time and money to go: if your company is not willing to support you attending conferences, you may end up using time off and paying out of your own pocket. – jakebeal Jun 7 '15 at 4:15
  • It would be a bit of a stretch to call my position an industry researcher, and it's not in the area (namely, certain areas of pure math) I'd want to attend conferences in. I would be, as you said, taking time off and paying out of my own pocket. I don't mind doing so, but I wouldn't have the company's support. – anomaly Jun 7 '15 at 4:39
  • You most certainly are a researcher in industry: it is just that your research has nothing to do with the fact of your industrial appointment. You will still be welcome in any but the most bigoted of scientific conferences. – jakebeal Jun 7 '15 at 4:44
  • Ah. :) Thanks, I'll check to see what relevant conferences I can make it to. – anomaly Jun 7 '15 at 5:12

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