I am currently a data scientist working in natural language processing, with an undergrad background in math and CS, and a masters in CL/NLP. Mathematics was always my preferred area, but I wasn't sure I wanted to do mathematics graduate studies, so I moved into CL/NLP due to the relatively high amount of jobs. I realize now that I don't really have any genuine interest in NLP, and that a lot of my spare time has gone into reading and thinking about math and occasionally more theoretical CS. I work in a research environment, and I like research work but I wish I had more responsibility, and more opportunities to connect with other people interested in things that I'm interested in, via teaching or collaboration.
For all these reasons I'm considering returning to graduate school for mathematics, with the goal of obtaining a PhD and moving on to teach and do mathematics research.
My question is about the degree of choice in working location. I live in New England and have a wonderful network of family and friends who are very supportive. Keeping as close of a connection with them as possible is a priority for me. If after a PhD and a postdoc I was able to get a position teaching at a small to medium college or university in greater New England, and still do some research, that would be the ideal.
I don't think I would be a competitive candidate for PhD programs like Harvard or MIT, but given my background I think other good math graduate programs in Massachusetts are reasonable possibilities for PhD applications, possibly after getting a masters in math first. When I try to find outcomes for people who have graduated from these programs, a lot of people have the kind of jobs I would hope for but often times outside the area. How often is something like this a choice versus necessity? Are there specific ways (besides good performance in grad school and making connections) to help make this result more likely?