A DIVINE LANGUAGE
{Learning Algebra, Geometry, and Calculus at the Edge of Old Age}
By Alec Wilkinson
287 pages. Farrar, Straus & Giroux.

Writing a book is hard enough, so authors will sometimes use it as a chance to embark on something they have always wanted to do — take up dance, learn to juggle, travel the world, have more sex. The longtime New Yorker writer Alec Wilkinson took a decidedly different tack, choosing instead to chronicle his sustained efforts to do something he knew he hated.

In “A Divine Language,” Wilkinson begins by admitting that he passed high school math only because he cheated. His memoir recounts the year he spent, not long ago, when he was well into his 60s, trying to learn the algebra, geometry and calculus that had confounded him decades before.

Needless to say, Wilkinson didn’t exactly do this for fun, even though he identifies as a “self-improver.” As he was getting older, he wanted to see if his teenage confusion reflected a lack of mathematical skill or a dearth of discipline. He ran into one of his colleagues, Calvin Trillin, who asked Wilkinson what he was working on. When told it was a book on math, Trillin peered at him and deadpanned, “For or against?”

It turned out to be a fair question, given Wilkinson’s penchant for personalizing mathematics, taking it to be some sort of sadistic taskmaster that was out to get him, tormenting him on purpose. In the early pages of “A Divine Language,” Wilkinson recalls how his younger self despised the subject for “its self-satisfaction, its smugness and its imperiousness.” Later he writes: “Doing algebra again was like meeting someone you hadn’t seen in years and being reminded why you really never liked him or her.”

I kept waiting for the kind of happy reconciliation that never quite comes. Instead we get Wilkinson declaring that math “was a brute, malign and mechanical thing.” He confesses that by the end of his journey, he was still consumed by “an indignant resistance.”

This, then, isn’t a chipper story of personal growth — and for that I was grateful. Wilkinson has accomplished something more moving and original, braiding his stumbling attempts to get better at math with his deepening awareness that there’s an entire universe of understanding that will, in some fundamental sense, forever lie outside his reach. He spent a year holed up with his shoddily written textbooks, pestering his mathematician niece whenever he got stuck, isolating himself to the point where it was almost impossible for him to have a normal conversation with anyone.

“Perhaps unconsciously and self-destructively, I have chosen a task designed to show that I am less than who I had believed myself to be,” he writes. “It was meant to be a lark, and it has become a reckoning.”

“Lark” sounds a bit more pleasurable than what he actually had in mind. He had wondered from the beginning if this journey might be doomed. As he intermittently points out, pure mathematics tends to be a young person’s pursuit. Older people are generally slower and less bold, more prone to fitting things into familiar frameworks instead of noticing novelty. His niece also predicted he might be stymied by his tendency to “overthink.” He calls this tendency something scarier: “paranoia.” He describes himself as so worried about missing something in a problem that he would fixate on each and every element without developing any sense of the whole.

Part of this hypervigilance flows from the fact that he wasn’t fluent in the language, and at his age he never will be. He compares the experience of being bewildered when working out a mathematical problem to reading some prose or poetry he doesn’t quite understand. He can persist in reading because he will often sense something later about its larger design, even if some of the specifics continue to elude him.

Mathematics is different. When Wilkinson doesn’t grasp a detail in a problem, he knows that he is missing something foundational. Sure, over the course of the year he may have obtained what he calls a “low-grade proficiency” at factoring polynomials and finding derivatives, but “simple competence didn’t resemble the capacity to have thoughts in another language.”

Still, even if he doesn’t particularly enjoy doing mathematics, he likes thinking about what mathematics is — whether it is something created or discovered, for instance, and how its practitioners remain preoccupied with beauty, or what Bertrand Russell called “a stern perfection.” Wilkinson notes how the harmonic structure in music is connected to mathematical forms. He reflects on the role of education, and whether mathematicians were simply taught better than most of us to recognize patterns, or whether they are differently equipped, neurologically speaking — perhaps like those animals that see more colors than we do.

Wilkinson introduces us to a few people: a mathematician who didn’t come up with his pioneering proof until he was 55; a game-theory savant who was the first person to win more than a million dollars at a poker tournament. But aside from soliciting the advice of his niece (who gets so exasperated that she stops answering some of his calls), Wilkinson spends much of his time in conversation with other books — by mathematicians like Russell and Euclid, but also by writers like Beckett, Joyce and Dostoyevsky.

As enjoyable as these bits are, Wilkinson can get so frustrated with the actual math part that I wondered at times at his refusal to talk to a tutor. “That’s against the rules that I had set for myself,” he writes. “It would be as if I had determined to build a house and was calling in a carpenter for the parts that were hard or seemed to be beyond my capacities. If I did that, I wouldn’t be able to regard my house as my own work.” This makes zero sense; it’s not as if the tutor would have done his math problems for him, let alone written this book. But I suppose that his own resistance to anything so straightforward is part of the point.

Because what Wilkinson achieves by the end isn’t so much a command over mathematics as some humility toward it — a willingness to accept it, despite his frustrations, in a kind of détente. He becomes more aware of “an unfolding, moment by moment, on an apparently spectacular scale of something that no force can interrupt, something that is perhaps force itself. A trembling quality to life, both fearsome and fragile, a pattern that even to a novice like me is as clear as the grain in a piece of wood.” The world seems bigger to him than it once did. He can sense new melodies, even if he doesn’t know all the words.