I finished my PhD in Algebraic Geometry/Number Theory in 2013, and made the decision not to apply for postdocs: very few of my fellow students had found academic positions I had the feeling the unless you're a superstar/potential-Fields-medalist (which I'm not) it's very hard to build a career as a pure mathematician. Also I don't think it's fair on my wife and her career to ask her to move cities every few years while I'm doing postdocs ... and it looks like this is a common requirement for early career researchers these days.

So I've been working as a Data Scientist for the past 3 years, and I'm really hating the feeling of working in the business/corporate world ... it all feels so short-term and meaningless, and I also miss the intellectual challenge of pure research.

This leads to my question. I'm thinking about applying for some postdocs with the aim of going back into academia. My dilemma is do I try and find something in a "pure" field that I feel excited about, like algebraic geometry, representation theory, string theory or quantum computing? Or should I apply for something I don't feel so passionate about but that's currently more well-funded, and that builds on my skills from my work in industry, like genomics, computer vision or speech recognition ... will my passion grow as I go deeper into the field?

I want to be realistic and responsible about my career/life choices, but I also don't want to get stuck doing something I don't care about.

I know it's a bit of a vague question, but I would love to hear if anyone's had a similar experience.

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    Sorry, but this really isn't something we can answer for you. Is there something specific you want to know about, that could help you make the decision? – ff524 Dec 18 '16 at 2:31
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    It's a great question, but the question seems to be which of several absolutely reasonable alternatives is better for you. You are the world's leading expert on your own proclivities and preferences, so as stated at least, I think you are the only one who can answer your question. – Pete L. Clark Dec 18 '16 at 2:33
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    There is a logistical approach to this which it sounds like you haven't considered yet. I have most commonly seen this approach taken by trailing spouses, which, let's face it, are most often women. A creative solution to the problem has been found, and you don't need to be a woman to give it a try! Here it is: You look for a host department in the town where your partner is situated, and ask for an unpaid affiliation, either part time or full time. You ask for some shared office space there. You attend seminars. You get to know people there. You work on projects, quasi-independently.... – aparente001 Dec 18 '16 at 20:31
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    ...in short, you function like an unpaid postdoc, only you don't have a supervisor. That doesn't mean you can't set up one or more mentoring relationships, though. For a potential mentor, you may take a look at the faculty in the host department, or other departments in that university; you may also look farther afield. You could in principle do this while holding onto your current job, but it would work best if you went to part time rather than staying full time. It can be very exciting to take a fresh start in research, casting your reading net... – aparente001 Dec 18 '16 at 20:34
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    ... as wide as you like, and following your nose. After some time doing this (we don't know how long, but you might want to give yourself a defined time limit), you will probably have an easier time figuring out the direction you want to go in. – aparente001 Dec 18 '16 at 20:35