My research area has very few research positions, would it still be possible for me to stay in academia? I am a PhD student in mathematics.  I felt quite lucky that I got into this program.  My research is also going ok, and I got some confirmation from my advisor that I should be able to graduate in a year or two if I keep up with my work.  So things were mostly good.  But a recent conversation with my advisor completely changed my view about my situation.

We just finished one of our projects and naturally got to the question of when I should graduate.  Then We start to discuss my plans after graduation.  He asked me whether I want to find a job in industry or stay in academia.  I said I want to remain in academia, find a postdoc, then a tenure-track position, etc.  He then told me that there are very few places that have postdocs in my area, and indicated maybe I should look for schools that majorly focus on teaching.

I was very shocked.  I always wanted to stay in academia and thought about going to good research schools.  In fact we talked about this when I first asked to be his student.  But for some reason, he kept asking me the same question every once in a while.

I went home and start search on mathjobs.org for positions in my area, which I probably should have done three years ago.  There were almost nothing.  There are two postdoc positions, both are from not very well-known schools, I don't quite have interests in applying to either one of them.

I am quite lost.  On one hand, I wish I knew this much earlier on.  I wish my advisor would have told me before he helped me pick this area.  I also should've done some research on that myself.  Now I just have so much regrets in my heart.

On the other hand, I think it's time to be realistic and rethink my plans.  I wonder if it is still be possible for me to get a postdoc (possibly in one of the two places) and later go to a top-ranking school for tenure-track positions?  If a school don't have anyone in your area, would they hire you as a tenure-track AP?  I am not quite fond of teaching, I can bear it if it's part of my job being a researcher, but I would not want to do this as my sole job.

If that is not possible, what kind of job can a math PhD get?  I had some experience in industry before as well, but I don't quite like that job.  Are there research-type positions in companies that would appreciate a math major?  If so, what kind of knowledge/skills should I pick up now?
I wonder if it is still be possible for me to get a postdoc (possibly in one of the two places) and later go to a top-ranking school for tenure-track positions? 


Yes, this is possible. But, unless you are making definitive progress on famous open problems which are well-known to everyone in your field.... then it is very unlikely and you should not count on it. (And perhaps even if you are.)

Most academic jobs involve both research and teaching. For example, I work at a research university with a Ph.D. program and a 2-2 teaching load. I definitely have time for research, but teaching is a big component of the job, and if I didn't enjoy teaching I would not want to do this job. (Moreover, if I wasn't good at teaching, then the hiring committee probably would have picked up on this and not offered me the job in the first place. Most people who are good at teaching, enjoy it.)

I think you are wise to investigate your other options. I've known people who decided not to pursue (or continue with) academic careers, and for the most part they were able to find good jobs. Software companies like to hire mathematicians, and you might learn programming if you don't know it already. Some mathematicians successfully go into finance (and make boatloads of money doing it.) Actuarial work is another possibility. In any case, these sorts of jobs don't generally just "happen"; you have to proactively think about what you do like and look for opportunities.

Good luck to you!