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.
You're not doing math, you're using mathematical tools. Calculations are effectively arithmetic, and that's not doing math any more than typing code is doing programming.
It's a lot more complicated than that, but setting up the equations is the doing of math - solving the equations is just manipulation, and that's using, not doing. The difference is important - conflating the two leads to many misunderstandings.
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.