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I am currently a year or two away from a PhD in differential geometry. I love doing research, and I would like to make my career doing research in some form (preferably mathematical), but I have no idea the jobs that are out there for pure mathematicians, or what skills are required in order to obtain them. For what it is worth, I don't care about the money - as long as my family is not starving, I'm fine with a lack of significant disposable income.

So, I ask:

1) What are some areas (broad or narrow) of industry in which I should consider looking for employment? Specific company recommendations are fine also; right now I have very limited knowledge of what's out there.

2) How should I tailor my skillset to be competitive for industrial jobs in math? Right now I have a fairly diverse mathematical education, and rudimentary knowledge of a few programming languages, but not much else that might be useful to an employer. What do you recommend I learn (either through courses or on my own) while I'm still in school?

Note: I have avoided asking about professorial positions because, while I'm not a bad teacher, and a position at a research institution would be great, I lack the prestige that comes with graduating from a top-tier school and I want to remain realistic about my job prospects.

Thanks for your time,

EDIT: Recommended reading suggestions are also appreciated.

  • Are you insistent on doing research? On doing math? On doing something related to differential geometry? Can I assume that you're not so interested in teaching-oriented university positions? Would you take a job, as an example, working on the software that runs SE? – Alexander Woo Jun 7 '17 at 3:11
  • I am somewhat insistent on doing research. Not so insistent on doing math (though I would prefer it), and certainly not insistent on doing differential geometry (I love it, but I'm flexible). You are correct in assuming that I am not interested in a teaching-oriented position. As for the software development question: I would strongly consider taking such a position provided I would be more on the "research side" and less on the "coding or execution side" of the operation. Thanks for your questions. – MathIsArt Jun 7 '17 at 16:07
  • Have you checked out the AMS info: ams.org/profession/career-info/career-index – Kimball Jun 7 '17 at 21:23
  • Some of it, though admittedly not all. Thanks for the reminder about that reference. – MathIsArt Jun 7 '17 at 21:34
  • I personally think that many universities do an appallingly poor job of career counseling and job placement. Yours may be one of the ones that are lousy at doing this. But you should definitely try to milk the university for everything that it can give you along these lines. Try both your department and a more general career center. Take some time and work through all the steps the career center may ask of you. Summer could be a great time to do that. – aparente001 Jun 8 '17 at 3:40
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Within differential geometry, I agree that computer vision is the obvious answer. CV is a hugely important and growing field. Pursuing this might require you do a masters degree in computer science or do learning on your own, if you don't have a CS/ML background. After I got my degree, I found a job doing CS research related to my mathematics interests that was willing to fund me doing a CS masters program on the side. I had a CS background, but not a strong one, going in. What is more important than formal education is the ability to learn and adapt. If you learn enough to get your foot in the door and are quick enough to pick up what you need as you go, you'll do fine. There's a lot of online courses and resources for CS that would be a good place to start.

There is a large number of companies that look to hire people with mathematics PhDs to do research if you have a basic ability to code and as stats background, ranging from insurance companies (designing new risk models), to data science companies (designing new methodologies, or applying complex ones), to consulting firms (for all sorts of needs), to investment companies (predicting the market). Which places might be best for you to look at probably depends exactly on your background.

  • Thanks for your suggestion. I would like to get a job without having to pick up another degree, but I will look at jobs in CV and see if I can learn enough on my own to be competitive. – MathIsArt Feb 16 '18 at 16:53
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Discalimer: IANADG, I am not a differential geometrist...

Still, some potentially-relevant fields:

  • Architecture and materials industry: Surfaces and bodies with complex structures, their behavior, the forces applied to them, their expansion, contortion etc. with weather or with load changes and so on. Specifically, I can imagine a bunch of relevant applications in 3d-printing. This might be relevant (although it's not a specific workplace)
  • Car industry, for similar reasons
  • Computer vision and image/video processing: lots of geometry and lots of derivation going on there. Just as an example, read this (but )

I'll also make another, more concrete suggestion: Various countries have academic-oriented placement/recruitment agencies. While those obviously don't know you perfectly well and can't cater to your interests exactly, they could interest you in a selection of potential positions which you might find appealing - or, at least, will help you realize what kind of work is out there. Also, an up-to-date LinkedIn profile has a bit of that same effect.

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