Finding a mentor

Question

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?

Answer 1

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.