I am a economics major student who will be applying for PhD programmes pretty soon. I am quite interested in economics, but I find myself even more interested things related to probability theory, such as stochastic processes. And if I ever get into a econ PhD programme, I'm pretty sure that I should be looking for co-advising from the math/statistics department if allowed.
So I am curious about what happens in academia if you ever find yourself more interested in a topic that you don't have a degree on. If you can write some good papers during your PhD, can you find good career opportunities in that field in academia even if you did not start out as a "professional" scholar in that field?
Any idea would be very much appreciated!!
My father, a retired engineering professor, told me that some fields that are "feeder" fields into others, lend themselves more easily to the "crossover" process.
In your case, mathematics is a "feeder" field to mathematical economics. My father felt that it was relatively easy for a math (or engineering) PhD to cross over into economics (as he did in his later years), because most economists feel that their field does not have enough mathematics. In fact, many senior economics professors of his time recruited graduate students with strong "quant" backgrounds to work with them.
The reverse is not true. Most mathematicians would find it hard to take an Economics PhD "seriously" as a mathematician. It is said that mathematics is the "queen" of sciences, so its practitioners don't feel the need to cater to "lesser" fields.