TITLE: Do mathematicians Switch Fields of Expertise?
QUESTION [17 upvotes]: 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 =].

REPLY [6 votes]: It is not that uncommon for interests to drift, but the commonly cited examples (e.g., Grothendieck, Quillen, Serre, Mazur, Gelfand, Witten) of impact on relatively distant fields are extremely atypical. The fact that famous mathematician M was able to do top work in subject X, and then again in a faraway subject Y (and later in Z, and ...) says more about famous mathematicians than what is possible under more common conditions.  Late-career changers of specialty such as Mumford, Smale, Freedman or Langlands demonstrate that there is more freedom with a Fields Medal or without teaching obligations.  Somebody of more ordinary abilities and circumstances may be more limited.
In computer science Len Adleman spent a year in a biology lab and learned the techniques that he used to found DNA computing, but his case is similar to that of the Fields winners.
Paul Cohen's work in set theory might be an example but he switched to a field that had not reached maturity, still had its most basic questions left open and was not a densely populated research area at the time.  Mumford and Langlands both ventured out of very technical, mature subjects into what was at the time relatively open mathematical territory.
Hales' work on computational approaches to the Kepler conjecture and proof formalization was a switch from his original interests in representation theory.
It's hard to cite lower-profile examples, because they are less visible and not heard of as often.  Changes are most common in the first few years after the doctorate.