Not always. I am a physicist. In my thesis I was working on "Moiré fringes" that many people had touched but nobody had truly thought about. As I saw them on X-ray topographs of SIMOX bicrystals, I was working in "reciprocal space" like everyone else (you don't need to know what that is to get the point of the story). And I could show mathematically that the fringes we studied were related to the integral over the change in reciprocal space. It took me months (I am not a mathematician, see?) to understand that a spacial integral over reciprocal space yields a straight-forward displacement field. From that day on, we were studying 3D-displacement fields at Angstrom scale and had a fast way to map defects in those new semiconductor materials. Once the algorithm was there, it was so trivial that I quit the field forever :-).
Lucien Szpiro on the difference between mathematicians and physicists
