The Renewal Equation

Today I read more of Infinite Powers. I’ve finished the section on Archimedes and moved on to the next protagonist of Strogatz’s tale, Galileo. What I read about him today proved interesting. I don’t think I ever knew that he discovered the properties of falling bodies, not by dropping balls vertically, but by rolling them down ramps. Perhaps if I had ever taken a traditional physic course, I would have learned that. On the other hand, perhaps this is an example of the tendency in science education to present results without explaining how they were discovered. My scientist father has lamented the disservice that approach does to the subject.

I suppose the analog in math education is the fact that nearly all pre-college math courses are focused on calculation rather than proof. (Traditionally, the exception was geometry, but I think that is often calculation-focused now, as well. My course was, for the most part.) I don’t know whether that is a disservice or not. For me, proof is the most exciting thing. I enjoyed math in middle school and high school, but didn’t truly love it until I was aske to discover and prove facts for myself. I think I’m probably in the minority there, though. Most people, to the extent that they are interested in math at all, are interested in its applications.