Doing Math Research in a "non-mathematical" environment

Question

I have graduated with a PhD in pure mathematics about 18 months ago and right after my graduation, I started working for a private college, teaching some low level courses such as College Algebra and Calculus. I have not done any research since my graduation but I always feel that my life is incomplete without research level mathematics. My college has a good environment in many ways but not mathematically.

But I still want to pursue my dream of doing some research in mathematics. Here are some facts about my situation:

1. Changing Job: For personal reasons, I do not want to quit my job, at least for now. I may consider a new job after five or ten years. But I would not mind finding a part-time job.
2. Funds: My college provides a very small fund for my academic usage, including purchasing books, travelling to conferences, etc.
3. Personnel: There are only a few mathematics teachers here and none of them is doing any research level mathematics. So I can hardly find any mathematical support in my college.
4. Motivation: I will not get promoted or receive any salary raise, whether I publish any paper or not. So my motivation will be from love of mathematics and (possibly) another job in the far future.
5. Resources 1: I do not have access to good data bases such as MathSciNet. My school library carries very limited books in my area but I can go to a good library in another university if needed.
6. Resources 2: There is a good university within a reasonable driving distance and there are a few mathematicians there in my field.
7. Time issue: During the semesters my spare time is very limited. I have more free time during the winter and summer break that I am willing to devote to mathematical research.

Any suggestions for me to do my research in this environment will be greatly appreciated.

Answer 1

The proximity of a large university can be a big plus. Here are some things you might find helpful:

• Get in touch with the people in your field there, telling them you are in the area and are interested in keeping up with mathematical activities in their department. Ask to be added to their mailing list for seminar announcements, etc.

• Try to arrange your teaching schedule so as to be able to attend seminars at the big university at least occasionally; regularly, if possible. If there is dinner after the seminar, try to go. Talk with the faculty (and the visiting speaker) and look for shared interests, that might lead to things you could collaborate on.

• See what kind of access you can get to their library. At minimum, you should be able to walk into their library and use MathSciNet, read books, download papers from their journal subscriptions, etc. You can probably also arrange borrowing privileges, and possibly remote access, either as a member of the general public (maybe for a fee) or as a professional courtesy based on your affiliation with your own institution. The university's faculty in your area might be able to help if you run into bureaucratic hurdles with this.

Also, don't discount your own institution's library. Even if they don't have much in the way of books and subscriptions, it is very likely that you can get almost anything you want via inter-library loan, albeit with some delay. Get to know your professional librarians.

And a note regarding funding: it's not unusual for conferences to have some travel funding available for participants. (This is more common for smaller specialized conferences than for big general events like the Joint Math Meetings.) Fresh PhDs like you usually get first priority for this, so try to take advantage while you can.

Answer 2

Any suggestions for me to do my research in this environment will be greatly appreciated.

I don't have primary experience in the field of mathematics, but you describe issues similar to those faced by those in other fields. @DanRomik and @NateEldgredge gave excellent advice. I'd add these (relatively minor) issues you might want to consider:

• If possible, you may wish to gain the support of the head of your department. This has several advantages, not the least of which is having a senior member of staff on your side. Of course, you need to be careful because the current research direction (or lack of it) may be due to his or her vision. Weigh the benefits against the risks.

• If you meet resistance to the pursuit of your independent research agenda (institutional or otherwise), make sure that you document that your work was done outside of your official responsibilities. Most universities have policies on outside work and intellectual property. Review these so that you can be clear where you stand in case there's a dispute.

• Given your recent minting as a PhD, you might want to consider re-establishing linkages with your former group and university, perhaps seeking an honourary appointment with your former supervisor's lab. An honourary appointment with the math department of the nearby university would be good to explore, too. An honourary appointment may carry specific perks that you can leverage. In mine, the appointment comes with little expectation but with an email address, library privileges (document delivery and interlibrary loans excepted), internet access and a hot desk.

• You might harness the interest of students and faculty in your college towards your field. There might be a group of students or colleagues in your college that might agree to meet fortnightly, say, over wine and cheese to review the latest development in the field, discuss a journal article or work on a problem. Think of the early days of the Royal Society when there were no formal scientists (the term hadn't been invented), just a group of gentlemen (they were all males) with an interest in natural philosophy meeting regularly to talk about their interests.

Good luck to you.

Answer 3

Regarding your point #5 (database access), there are alternate online resources which are superior to what is likely available through university subscriptions: I am at an ivy league university with its attendant resources, and when I'm off campus I get my papers and online book pdf's via Ukraine, rather than navigate my library website.

Regarding points #3 and #6, having someone to bounce your ideas off is extremely important. Cultivate that contact, as alternate perspectives are vital for robust ideas. If you have no personal or professional relationship with these people, and your work is outside their direct research interests, be aware of the magnitude of what you're asking. It's quite a significant ask to drop what they're doing to focus on your project, especially as you may not be well situated to notice its flaws.

Good luck and keep going.