I’ve come to a realization over the last couple of weeks.
Math, as most of us know it, from algebra through Calculus, isn’t really for mathematicians. It’s for engineers, physicists and the like. Those subjects are all about giving those folks the tools they need to solve certain classes of problems.
This has really been driven home by my Differential Equations class (which is pretty late in the Calculus sequence). Every new technique we’ve learned has been directly related to some real-world problem involving related population models for predators and prey, voltage flow in simple circuits, physics problems involving springs, situations where different fluids are mixed in a vat, … you get the idea.
Post-calculus, once the engineers and the physicists have left the room, math is finally for the mathematicians. And the problems get more esoteric, more abstract and less formula-driven.
I’m learning to come to terms with it, but it’s like an entirely new subject altogether.