It always struck me how my math classess seemed to focus on the mechanical exercises and never let us glimpse at the true genius of what we were brainlasly repeating with them.
However, I think I could say the same for many of my classes. As an Engineering student, I'm sure most of my physics classes are way beyond what I will ever use when I leave university (trig btw, heavily used for most of this classes). I think the same reasoning could be applied here, instead of repeating painful exercises consisting basically of memorizing and rearranging formulas, let the student wonder at the context and history behind each of the subjects and the problems that were solved with them.
This is a problem affecting education systems in a deeper level than the math curriculum, it comes down, I think, to something the author points at, which is this widespread notion that education is supposed to be something that "prepares tomorrow's workforce" instead of it being a source for inspiration and enlightenment.