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I finished my PhD program in pure math a few years ago and have been in industry since then. I would love to continue my academic career, but (long story short) I was treated badly by my program and left with the doctorate but without a postdoc or much in the way of a publication record or connections (thus making the doctorate close to pointless) I haven't had much trouble finding jobs in software engineering or government labs, but I haven't found the work there to be interesting or satisfying.

Like pretty much everyone who goes into math, I love math for its own sake, and I love research. Is there anything available outside of academia where I could undertake something close to pure math research? Ideally, I'd like to beef up my publication record and make some connections, but a tech company doesn't seem to be the right place to do that. Although the jobs are certainly there, coding and engineering really aren't my things, and I'd like something more strongly related to math and more academic and research-oriented in nature.

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My situation is different from yours, but analogous. I have observed a lot of academic discourse on MathOverflow, and even some on Math.stackexchange. I have registered for conferences online and participated, even without a current academic affiliation (industry affiliation is good but not required: check with conference organizers and your employer).

The real key is to find a group of people who will either a) work with you remotely (say by email) or locally (if you are lucky), or b) willing to critique and perhaps mentor you in some arrangement, or c) willing to spend a few minutes of time giving their opinion of what should happen, or d) willing to tolerate occasional communication and friendly interaction, on a fairly infrequent basis.

MathOverflow is a good way to start at d) and work your way up the chain. Answer a few questions, post some good (and I mean GOOD) questions, and you will more quickly find online presence to develop a relationship which may be useful in real life. You can show your technical chops, sometimes get the fast track on research, and get a lot out of it, even some socializing. However, follow the FAQ: MathOverflow is not for discussion, ill-formed questions, or solving homework, and they are not prone to giving hints to graduate exercises, especially if it smells like asking them to do the work for you. There are also some reasons to prefer math.SE over MathOverflow for submitting questions, but I think doing well at the latter will be more beneficial for you. My impression (but I could be wrong) is that your question above would not go over well at MathOverflow, since it deals more with "sociology of math" than with math itself.

It might be quicker to reach your goals by hanging out near a large Math department with free food, but I would bet cash money that the above is actually quicker. Good luck at MathOverflow. Once you get to b) or a), you will find out other opportunities outside academia to help you with research.

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  • That's a long and nontrivial path, but it's probably about as good as I can hope for. Thanks!
    – anomaly
    Commented Jun 13, 2014 at 20:35
  • It may seem long, especially if you have a particular goal. I'm enjoying the journey though; don't forget to do that part also.
    – Not Quite An Outsider
    Commented Jun 13, 2014 at 20:37
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If you are a US citizen living in the USA, you can work for NSA (which, if I recall correctly, is known to be the largest employer of mathematicians in the country) provided you pass their background check and satisfy their other requirements. However, your research will likely be classified, so you will not be able to publish it in the regular math journals.

Should you happen to be in the UK, their counterpart of NSA is GCHQ. Many other countries also have similar organizations.

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    Yes, those are definitely options, although you should think about whether you're comfortable with what your research might be used for.
    – Tara B
    Commented Jun 13, 2014 at 20:28
  • I'm honestly not sure how I feel about the NSA (I'm in the US). For that matter, my background was not particularly heavy in number theory or (mathematical) cryptography; I've done the standard algebraic and analytic number theory sequences and some elliptic curve theory, but not much beyond that.
    – anomaly
    Commented Jun 13, 2014 at 20:34
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    NSA takes all sorts, your mathematical background needn't be in cryptography or related areas (I know topologists who went into the defense industry)
    – Aru Ray
    Commented Jun 13, 2014 at 21:01
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    If you know what you're talking about in elliptic curve theory you, theoretically, already know some cryptography @anomaly.
    – Ben
    Commented Jun 13, 2014 at 23:46
  • Ben: Oh, I know, that's why I mentioned it. :) I did a decent amount of algebraic geometry in grad school, though no particular direct applications on the cryptography side.
    – anomaly
    Commented Jun 14, 2014 at 0:19
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Microsoft Research might match your requirements. They have much going on in the way of academic math yet are outside of academia itself.

They have many groups around the world that might match your requirements, but the Theory group in Redmond, USA seems a good start:

http://research.microsoft.com/en-us/groups/theory/

Apply directly at [email protected]

From the page:

Description: We work on fundamental problems in mathematics and theoretical computer science, interact extensively with the academic community and collaborate with other researchers at MSR on challenging applied problems. Among our areas of expertise are probability theory, combinatorics, statistical physics, metric geometry, fractals, algorithms and optimization. We host an amazing array of researchers in these areas: see a full list here.

Applying for Positions Applications for a Postdoctoral Researcher position for 2014 received by December 15, 2013 will receive full consideration. Apply here, and in addition, have your application material (including references) sent to [email protected]. Apply here for a summer internship and inform us that you have applied by emailing [email protected].

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    Thanks. I did apply to Microsoft Research immediately after grad school but didn't get in. (I was told that they didn't have any places open, which I would normally have just considered a polite dismissal, but Microsoft Research was one of the few places where I had a very strong contact.) Looking at their website and the blurb above, I notice that their members' backgrounds are strongly focused on applied math and combinatorics. My own background is in high-dimensional topology and algebraic geometry; I'm not sure they would be interested in me.
    – anomaly
    Commented Jun 14, 2014 at 11:54

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