On one of those dark nights in February when remnants of old snow sat in dirty piles next to the street, hiding any hope of spring, my grandmother confessed to me that she had led a secret life.
I was briefly home from college. My parents had a rare evening engagement, and Grandmother had offered to feed me. The conversation had been predictable: adventures of the cousins, plans for her summer trip, my activities at college. We returned to the subject of school several times, and as we cleaned the dinner plates she turned to me and casually remarked, "You know, I took calculus in college."
I didn't respond at the time, for I was a young man who didn't know that few grandmothers had attended college and fewer still had even heard of calculus. In hindsight, her statement was every bit as provocative as if she had said that she'd fought with the Loyalists in the Spanish Civil War or dealt baccarat in Monte Carlo. All I had to ask was "Why did you take calculus?" and I would have discovered my grandmother's secret life, a life that had lain dormant for nearly 60 years.
From my current vantage, I realize that Grandmother showed ample evidence of rare talent. Her checkbook, for example, was not a dull record of household finances, but a field for mathematical exploration. Balancing that checkbook was not a chore, but a mental adventure. Sitting at her kitchen table, she would work through the figures with pencil in hand, completing most calculations in her head. I long thought this a quirky grandmotherly trait. But it hinted at her mathematical skills more than anything except her love of cards.
Bridge, canasta, solitaire, hearts, kings-on-the-corner, go fish. She loved to play cards and she tried, desperately, to teach her grandchildren that love. She suffered our impatience with difficult games, our inept play. She cheated against herself to let us win and had to avert her eyes to avoid seeing the cards we so gracelessly held.
As one of the older kids, I had caught on to the fact that she was leading us through the play, and had also learned that she was very, very good at cards.
One summer, in her backyard, we played a hard series of games, no holds barred, cards carefully shielded from the opponent. She anticipated my every move. When each game reached a climax, she would look in my eyes and tell me what remained in my hand. "You have the jack of diamonds," she would say, or "You are void in clubs," and she would be right. When I asked how she knew, she would smile and say, "I just figured it out." It never occurred to me that she was counting cards and estimating the probability that I held a certain hand.
My real insight into her life came many years later, when my poor card playing had been replaced by graduate study in mathematics. I was sitting in a dusty seminar room, waiting for a wild-haired, ill-clad speaker to begin a talk on a vital, newly emerging field of mathematics, which none of us expected to understand. Above the din of pre-seminar conversation, I caught the words of a senior professor: "I came here in 1933 to teach calculus. That was the first year that engineers were required to take it."
In an instant, my grandmother's words returned to me, and I realized her life held a story that I had not understood. I could not explain why she had taken calculus in the early 1920s, more than a decade before the subject was standard fare for engineers. I spent a restless hour, oblivious to what proved to be the most exciting talk of the term. Over and over, I pondered what might have motivated her, why she chose that course of study, what she hoped to do with a mathematical degree.
But by then, it was too late to ask her, and no relative could explain. I gathered my courage and called her alma mater, the University of Michigan, and requested her college records: a grandson demanding to see his grandmother's grades. With surprisingly little hesitation, they agreed. About a month later I sat at a long library table with a little gray records box that contained my grandmother's secret life.
THE box told a story much bigger than I'd anticipated. My grandmother and five other women earned mathematics degrees in 1921. Their teachers were not second-rate lecturers, relegated to women's classes, but well-known pioneers, scholars who helped establish the study of mathematics in America.
Her calculus professor was Louis Charles Karpinski. I knew that name. He was an important link to European mathematics, had written a dozen books, and was a rigorous professor in the Germanic tradition. Taking calculus from him was something like taking physics from Einstein.
The six women had been recruited by Prof. James Glover, who saw 50 women complete a degree in mathematics during his career. Professor Glover thought that mathematics made a good career for women, and helped them find work in the booming Midwestern economy of the 1920s. Some were actuaries for insurance companies. Others did financial calculations for manufacturing concerns. A few worked for the Army and computed the paths of artillery shells. One became regional director of the United States Census, and a couple were human computers, who did calculations before we invented electronic replacements. All this in an age when women had no dormitory on campus and were not allowed to enter the student union building.
My grandmother's mathematical life never strayed beyond family bank records and the accounting book of grandfather's gas station. She used her talents to sustain their business during the Depression. She never calculated a gun trajectory in anger nor computed a manufacturing plan that extended beyond her kitchen. But she knew the algebra of a checkbook and the calculus of a deck of cards. She could look with the eyes of a mathematician. That was her secret life.