When the Soviet Union launched Sputnik, humbling the United States, American educators responded by questioning the curriculum they’d been raised on, launching the New Math. From kindergarten through high school, their lessons focused on abstract ideas instead of methods learned by rote. Most people hated it. Even Charles Schultz was contemptuous, showing Sally’s confusion over joining sets, number sentences, and one-to-one matching. (“All I want to know is, how much is two and two?” she sobs at the end of a comic strip.)
Nonetheless there was one person who appreciated the New Math. His name was Mel Bochner. He’d studied philosophy in college. He was a conceptual artist.
An impressive body of Bochner’s art, focusing on drawings from the Cold War years through the present, is currently on view at the Art Institute of Chicago. The best of it is anything but academic. Even the least attractive work is appealingly irreverent. In myriad ways, the New Math guides all of it. Philosophy, especially the oracular writing of Ludwig Wittgenstein, provides additional support.
Dozens of books have been dedicated to the New Math – and dozens more devoted to disparaging it – but the underlying motivation can be understood in a single sentence published in a 1961 issue of American Mathematical Monthly. Mathematics is “the study of general abstract systems, each one of which is an edifice built of specific abstract elements and structured by the presence of arbitrary but unambiguously specified relations among them,” argued the distinguished mathematician Marshall Stone. The New Math was predicated on the radical idea that everyone from the earliest age was a mathematician in the making.
Several of Bochner’s works crib from the New Math directly, making mischief with class assignments. For instance, “Four Sets: Rotations and Reversals” derives from an elementary school handout showing the numbers zero through one hundred in several different arrangements. Bochner drolly translated these semi-arbitrary patterns into quasi-abstract compositions. The visual appeal derives from a sense of orderliness just beyond reach.
“Four Sets” was drawn in 1966, a year after Sally broke down in tears. Over the next decade, Bochner assigned himself ever-more-tortuous mathematical tasks. Non-standard number lines were a specialty, generated by turning a sheet of paper as he counted, upsetting their expected linearity yet conforming to their own internal logic. He described his approach in terms of “serial art systems”, enumerating operations such as “progression, permutation, rotation, [and] reversal”.
What made Bochner’s work conceptual was the literalism with which he approached the purest of abstraction, turning paradox into a form of play. To make a spread of random numbers, for example, he’d rub Letraset numerals on the page while randomly moving the paper.
Concurrently Bochner made drawings directly on gallery walls. Often these took the form of dimension lines with numbers indicating the measurements of the room. On first glance these drawings bring to mind the fiction of Jorge Luis Borges, especially “On Exactitude in Science”, where he describes a map as big as the country it charted. A second point of reference is Wittgenstein’s Philosophical Investigations, particularly his observation that “There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris.”
But Bochner chose well by deciding to be an artist instead of a writer or philosopher. His “Measurement” works are not describable or explainable outside of themselves. They have to be drawn. Each requires a wall. As he eloquently wrote in the title of a 1970 text, “No thought exists without a sustaining support”.
The New Math exercises that Bochner appropriated and reinvented are built upon this premise, which reveals the genius of the New Math even if the premise was insufficiently explained to Sally and most everyone else who suffered in the wake of Sputnik. By handling his sustaining support literally, Bochner made palpable the workings of the mathematical mind. He outperformed the textbook writers at articulating why mathematics has so much more power than mere checkbook addition. And he provided an example that will stand the test of time – demonstrating the capacity of the New Math to generate compelling new art.