Maybe it's a pure/applied split? When I'm investigating a physical system, doing the mathematics often tells me something qualitatively different from what I w

Maybe it's a pure/applied split? When I'm investigating a physical system, doing the mathematics often tells me something qualitatively different from what I was expecting, and I find that my expectations were wrong more often than I screwed up calculations. I don't mean to trivialize what goes into doing the calculations - what I mean is that I'm constantly solving math problems that force me to revise a flawed understanding of a system. That's what I mean by "mechanical" - I have to remain disciplined and resist the temptation to reason by analogy to something I may not even understand completely. If you care, I came to applied mathematics via nuclear engineering.