I am in the second year of a three-year PhD in algebraic topology — though not in topological data analysis or anything practical — and I am beginning to think about job prospects and life after my PhD.
I have been fortunate in that my PhD has gone well so far — I've written a few preprints — and I (hopefully!) won't have much difficulty finding a postdoc. However, I am not sure if I want to go down that route. I love research but I hate teaching, and, more than that, I am really tired of being poor and having no job (or even geographical) stability. I have a partner with a non-academic job and I don't want to abandon her and to go to Canada or something in a year's time. Continuing in academia would seem to prolong the problem for another ten years at least (and that's assuming I don't fail as a postdoc which is a big if). Thus, I am wondering what jobs are available for those who earned a PhD in algebraic topology, or, indeed, in pure maths generally?
I spoke with my advisor, but he never seriously considered a career outside academia himself and doesn't really see the point in not "trying a postdoc." The other questions I could find on Stack Exchange mainly address people who only realise they don't want to be academics just before their PhD defence. Is there any way I can spend my final year as a PhD student to make myself more employable?