Alec Wilkinson - A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age

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For

James Wilkinson,

Sara Barrett,

and

Sam Wilkinson

As I made my way home, I thought Jem and I would get grown but there wasnt much else left for us to learn, except possibly algebra.

HARPER LEE, To Kill a Mockingbird

I dont see how it can harm me now to reveal that I only passed math in high school because I cheated. I could add and subtract and multiply and divide, but I entered the wilderness when words became equations and xs and ys. On test days I sat beside smart boys and girls whose handwriting I could read and divided my attention between his or her desk and the teachers eyes. To pass Algebra II I copied a term paper and nearly got caught. By then I was going to a boys school, and it gives me pause to think that I might have been kicked out and had to begin a different life, knowing different people, having different experiences, and eventually erasing the person I am now. When I read Memories, Dreams, Reflections, I felt a kinship with Carl Jung, who described math class as sheer terror and torture, since he was amathematikos, which means something like nonmathematical.

I am by nature a self-improver. I have read Gibbon, I have read Proust. I read the Old and New Testaments and most of Shakespeare. I studied French. I have meditated. I jogged. I learned to draw, using the right side of my brain. A few years ago, I decided to see if I could learn simple math, adolescent math, what the eighteenth century called pure mathematicsalgebra, geometry, and calculus. I didnt understand why it had been so hard. Had I just fallen behind and never caught up? Was I not smart enough? Was I somehow unfitted to learn a logical, complex, and systematized discipline? Or was the capacity to learn math like any other attribute, talent for music, say? Instead of tone deaf, was I math deaf? And if I wasnt and could correct this deficiency, what might I be capable of that I hadnt been capable of before? I pictured mathematics as a landscape and myself as if contemplating a journey from which I might return like Marco Polo, having seen strange sights and with undreamt-of memories.

We reflect our limitations as much as our strengths. I meant to submit to a discipline that would require me to think in a way that I had never felt capable of and wanted to be. I took heart from a letter that the French philosopher Simone Weil wrote to a pupil in 1934. One ought to try to learn complicated things by finding their relations in commonest knowledge, Weil writes. It is for this reason that you ought to study, and mathematics above all. Indeed, unless one has exercised ones mind seriously at the gymnasium of mathematics one is incapable of precise thought, which amounts to saying that one is good for nothing. Dont tell me you lack this gift; that is no obstacle, and I would almost say that it is an advantage.

I could have taken a class, but I had already failed math in a class. Also, I didnt want to be subject to the anxiety of keeping up with a class or slowing one down because I had my hand in the air all the time. I didnt want a class for older people, because I didnt want to be talked down to and more cheerfully than in usual life, the way nurses and flight attendants talk to you. I could have sat in a class of low achievers, a remedial class, but they arent easy to find. I arranged to occupy a chair one afternoon in an algebra class at my old school, where twelve-year-olds ran rings around me. The teacher assigned problems in groups of five and by the time I had finished the first problem they had finished all of them correctly. They were polite about it, and winning in the pleasure they took in competing with one another, but it was startling to note how much faster they moved than I did. I felt as if we were two different species.

Having skipped me, the talent for math concentrated extravagantly in one of my nieces, Amie Wilkinson, a professor at the University of Chicago, and I figured she could teach me. There were additional reasons that I wanted to learn. The challenge, of course, especially in light of the collapsing horizon, since I was sixty-five when I started. Also, I wanted especially to study calculus because I never had. I didnt even know what it wasI quit math after feeling that with Algebra II I had pressed my luck as far as I dared. Moreover, I wanted to study calculus because Amie told me that when she was a girl William Maxwell had asked her what she was studying, and when she said calculus he said, I loved calculus. Maxwell would have been about the age I am now. He would have recently retired after forty years as an editor of fiction at The New Yorker, where he had handled such writers as Vladimir Nabokov, Eudora Welty, John Cheever, John Updike, Shirley Hazzard, and J. D. Salinger. When Salinger finished Catcher in the Rye, he drove to the Maxwells country house and read it to them on their porch. I grew up in a house on the same country road that Maxwell and his wife, Emily, lived on, and Maxwell was my fathers closest friend. In the late 1970s, as a favor to my father, Maxwell agreed to read something I was writing, a book about my having been for a year a policeman in Wellfleet, Massachusetts, on Cape Cod, and this exchange turned into an apprenticeship. Maxwell was also a writer. Around the time he spoke to Amie, he was writing So Long, See You Tomorrow, which is the book I give to people who dont know his work, because it is regarded as one of the great short novels of the American twentieth century, and I know that if they like it they will probably like the rest of his writing. I loved him, and I wanted to know what he had seen in calculus to delight him. He died, at ninety-one, in 2000, so I couldnt ask him. I would have to look for it myself.

The following account and its many digressions is about what happens when an untrained mind tries to train itself, perhaps belatedly. It is the description of a late-stage willful change, within the context of an extended and disciplined engagement, not a hobby engagement. For more than a year I spent my days studying things that children study. I was returning to childhood not to recover something, but to try to do things differently from the way I had done them, to try to do better and see where that led. When I would hit the shoals, I would hear a voice saying, There is no point to this. You failed the first time, and you will fail this time, too. Trust me. I know you.

After a time my studies began to occupy two channels. One channel involved trying to learn algebra, geometry, and calculus, and the other channel involved the things they introduced me to and led me to think about. While it was humbling to be made aware that what I know is nothing compared with what I dont know, this was also enlivening for me. I am done doing mathematics, so far as I was able to, but the thinking about it and the questions it raises is ongoing. The structure of my narrative reflects this dual engagement. It is organized more or less according to the order in which I learned new things, much as in a travel book one visits places along the writers path.