Recommended reading: Physicist Freeman Dyson?? brilliant essay (PDF) in Notices of the American Mathematical Society classifies mathematicians and physicists as either ??irds??high-level theorists and synthesizers—or “frogs”—empiricists and problem-solvers and shows how the two approaches have contributed to the progress of science. You can skim over the bits where the discussion of math or physics gets a bit sticky; the analysis is well worth the effort.