I was an indifferent student of math growing up. I wasn’t bad at math exactly, but I didn’t much like the subject (except for geometry, which I took in high school from a brilliant and generous teacher who had left off being a rocket scientist–literally–so that he could teach young people). I pretty much stopped taking math as soon as I was allowed to in high school–I stopped out at algebra III.
A couple of years later, in a spasm of optimism, I signed up to take a 7:00 am calculus class to meet my math requirement in my freshman year of college. I was influenced in this fool’s errand by one of my heroes, my writing professor Tom Lyon, whose hypoglycemia obliged him to teach at 7:00 and 8:00 am exclusively. I believed that something would blossom in me, and I would develop into the scholar and writer I was destined to be, a scholar and writer like Tom Lyon, if I got up every morning for calculus in the early hours.
Alas, my 7:00 am calculus teacher was no Tom Lyon: I remember her as earnest and competent, but not particularly skilled or experienced as a teacher. Probably, given that I was a freshman at a land grant university in a 7:00 am calculus class, she was a relatively new graduate teaching assistant. More importantly, what seeds of knowledge she sowed my way fell on rocky ground, or weedy ground–I remember not a lick of calculus from that class. Practically my only memory of that whole term was one morning watching the sun stream into the room late in the quarter and feeling the joy of being an 18 year-old in springtime.
Somehow I managed to pass that class despite all the time I spent gazing out the window. And 25 years later, somehow I managed to get a master of science degree in environmental science without much knowledge of calculus. I knew enough to be able to recognize that something was a calculus problem–the same way I might recognize that the people next to me are speaking Portuguese–but as for using calculus to model a problem or make a useful prediction about the world, the little glyphs and grammars of differential equations were utterly alien to me.
The gaps in my math knowledge were worse than this, actually: I remember as I was gathering the last data for my thesis that my classmate Alison Jacobs had to explain to me the formula for the slope of a line (y=mx+b) for about 30 seconds before I realized that she was talking about something that I had studied for months and months in junior high school. It comforted me a bit to learn later that the great E. O. Wilson had gotten his PhD in biology at Harvard without calculus–in Letters to a Young Scientist he talks about sitting in calculus class as a 32 year-old assistant professor, trying to atone for his crime of omission. But for me, it has been hard to shake the sense that however well I might use words to describe the thicket of the world, I’ll never know the trails by which I might, using math, penetrate to the heart of things.
I had to climb over my own emotional palisades, then, to set out on a journey to teach myself calculus at age 45. For me, coming back to differential calculus via Khan Academy has felt less like atonement and more like the discovery that someone I had regarded as homely in high school showed up at the 30 year reunion looking like a knockout. Somehow over the thirty years since I first sat in that 7:00 am calculus class, I have discovered that I’m in love with mathematics.
So far as I can tell, there’s no direct benefit to me in learning calculus or any other kind of math. No matter how good I may get at it in middle age, there will always be others around me who know math better and who use it more naturally than I. And what would I use calculus for anyway? I’m no better an English teacher or outcomes assessment specialist because of it. One could argue that I’m a worse English teacher because of it, opportunity costs being what they are–every hour I spend learning about limits and differentiation is an hour I don’t spend honing my knowledge of composition theory or something else I might actually use in the classroom.
But I don’t want to stop myself: I study math because math has become beautiful to me. Perhaps it seems more beautiful to me because it has no obvious use to me. I’m long past the spring term of my life now. Perhaps I can love math now because “the heyday of the blood is tame”–though in so many areas of life I feel I am entering a second youth, or even a long-delayed first youth. I never became, never will become, the scholar that Tom Lyon was in my life. But I’ve come back to scribbling out derivatives at 7:00 in the morning as I did when I was 18. The morning sun in springtime fills me with a different kind of joy.
Screenshot credit: Khan Academy