I'm curious if it is common or quite rare for mathematicians to change their area of expertise, whether it be after their PHD or mid-career, how radical this change might be, whether it's often for reasons of evolving tastes or rather conforming to the type of research done at their institution, and any other thoughts anyone has on how mathematicians stake out the fields they will be producing research in, thanks =].
[Math] Do mathematicians Switch Fields of Expertise
career-developmentsoft-question
Best Answer
I think it's rare for people to make a radical shift all at once, largely because it takes a long time to master a field. However, it is much more common to start in field $X$, get interested in an adjacent field $X'$, then in an adjacent field $X''$, etc. Iterate this enough times, and you end up someplace quite different from where you started.
If you are interested in working in a field which is a little different from your usual one, the best way is to seek out a collaborator in that field. Probably my most productive collaboration started because I got interested in a problem in a field in which I was not an expert and approached someone who was.