My goal up through grad school had been to spend my life doing academic, research mathematics. I got screwed by my advisor and department, though, so that hasn't worked out. I would nevertheless still like to do math and somehow contribute. Is there any place outside academia that does serious, professional pure math? Ideally, I'd like to at least publish a few research papers on vaguely-mathematical topics, but it's hard to find jobs that even afford that; in fact, it's hard to find jobs that use math beyond the undergrad level. it seems like my best bet is finding something in security related to theoretical computer science, but that's not a field I have any interest in; besides, I'm not sure how interested the industry would be in someone coming in from a pure math background. So, is there any reasonable equivalent or approximation to research mathematics in industry; and, if not, what's the closest I can actually get to it?
4$\begingroup$ I don't have any good advise but I just want to express my deepest condolence. I hope that you'll eventually figure out some way and be able keep on doing mathematics. Best luck to you. $\endgroup$– BigbearZzzAug 20, 2016 at 21:06
1$\begingroup$ Post this on the academia thread $\endgroup$– Faraad ArmwoodAug 20, 2016 at 21:19
2$\begingroup$ @FaraadArmwood: But it's the opposite of academia. $\endgroup$– anomalyAug 20, 2016 at 21:25
2$\begingroup$ Trust me. There will be a lot of people who can address this on there. The name of the thread is misleading. $\endgroup$– Faraad ArmwoodAug 20, 2016 at 21:26
1$\begingroup$ @FaraadArmwood: (Continued from above) More to the point, math is very different from other fields in that it's really not done in industry. It's trivial to find this sort of position in engineering and other applied fields, and there's a revolving door between academia and industry in computer science. There's really no math beyond the undergrad level involved outside academia. No one in industry cares, for example, about representation theory beyond what would be covered in the standard introductory group theory class, if even that. $\endgroup$– anomalyAug 20, 2016 at 21:31
This has been here for a while, so I'm not sure it is still a current issue for you. I'm sorry an academic career hasn't worked out to be as you hoped.
If you are serious about commercial sector employment, you need to look at it from a commercial point of view. Some large commercial companies are getting interested in basic research, but it seems to me there is still a clear commercial aspect to their hiring--at least from a long-term point of view. If they are going to pay you \$100K a year, it will cost them at least \$200K a year to have you around (social security tax, health insurance, admin and facilities costs, and so on). So they are asking themselves what you can do for them that makes it worth $200K a year over the long run to have you around.
Many government agencies are similarly task-oriented but in terms that are not always expressed conveniently in dollars (e.g., political objectives, security, etc.). There is much more unadvertised abstract math research in the government sector that you might imagine. The only way to find out is to make applications that mention the full range of your abilities and interests and see how agency recruiters interpret your resume. For example, I can almost guarantee there is a lot of mathematics with security implications for what you call 'theoretical computer science' that does not pop immediately to mind. But publishing results in journals will probably not be involved.
I think you need a fresh perspective and I can't recommend specifics that are sure to be helpful. So generalities: Go to meetings, talk with recruiters, have lunch with nonacademic colleagues about their interests, participate on this site with a 'name' and 'profile' that make you traceable to the persistent, put your (real) name on Linked In (if you can deal with the email traffic that will generate), and so on. One decent 'thread' out of dozens may be all you need.
2$\begingroup$ Thank you for your comment; it still is an issue. I have tried the government route, but it's been difficult to find something truly research-oriented. The projects I've worked on have been outside my control to decide on or steer (and security-type projects generally don't advertise their details beforehand); and, as you said, there are few opportunities for publication. There are certainly plenty of places that will hire people with backgrounds in math, but there are few that actually involve doing anything with that math. $\endgroup$– anomalyOct 24, 2016 at 6:46