This reminds me of the need for math in the sciences and engineering vs. the way math is studied at a typical math department. You need to know how to use calcu

This reminds me of the need for math in the sciences and engineering vs. the way math is studied at a typical math department. You need to know how to use calculus and differential equations to be an engineer, but you need to understand the fundamental principles underlying those techniques to a much greater degree as a math major (and as a math graduate student, even more so).