“Calculus Is So Last Century.” by Tianhui Michael Li and Allison Bishop. The Wall Street Journal, 2/5/2016.
Math came alive for me when I took calculus. It was trigonometry I hated. Trig involved a lot of memorization of equations, called identities, expressing the relationships of the sines, cosines, tangents and such, which for me, obscured any beauty in its concept. Yes, they showed how the identities were derived, but the identities were the point, not their derivation, which was just algebra, anyway.
Calculus had obvious beauty right from the start. What happens when you divide something into infinitely small slices, or extend something out to infinity? You can’t physically do either, but mathematically you can. The concept that it is possible to do things mathematically that cannot be done practically was alone worth the course.
My calculus course was followed by a course on differential equations that was even better. Those practical problems that were impossible to solve with algebra, could now be solved with the concepts we learned in calculus. Plus, it had all of those iconic symbols that scientific geniuses scribbled on blackboards. My thin book of problems was somehow lost over the years.
(I would have never thrown it out, and it was a close second to my all-time favorite text book that I found at a book sale, The Principles and Practices of Embalming, by Fredrick and Strub (a real page-turner, I kid you not! Embalming, by the way, covers the entire preparation of the body for a funeral, not just replacing blood with formaldehyde. It also involves sewing the eyelids shut, and injecting the sunken sockets with bathtub caulk. That body lying in the casket is not sitting up and saying “Hi!” no matter how natural it looks. But I digress.)
I grudgingly admit the WSJ authors are correct when they point out calculus is the handmaiden of physics invented long ago by Isaac Newton and is of no practical use in daily life, although calculus is the study of the rate of change, and the world is nothing if not constant change. What students need now, they say, are courses like statistics on handling large amounts of data that are now available on computers. They are probably right, but, even when I was back at Penn State, one of the department heads said, “Sure we would like to add other courses, but what would we drop to make room for them? We only have you for four years.” I had to wait years later for a statistics course given by the company I worked for, and it was interesting and very useful.
Still, I loved my calculus courses. They are like the memories of old girlfriends I haven’t seen for 60 years, even though they are far off in my past, and I rarely consciously think of them. I learned from them, and I am a better person from having known them. I am a better husband to my wife now because of them (the girlfriends, not the calculus courses).