Armed with a knack for patterns and symmetry, mathematical sculptors create compelling forms

Abstract

When he was growing up in the 1940s and 1950s, teachers and parents told Helaman Ferguson he would have to choose between art and science. The two fields inhabited different realms, and doing one left no room for the other. “If you can do science and have a lick of sense, you’d better,” he recalled being told, in a 2010 essay in the Notices of the American Mathematical Society (1). “Artists starve.” Helaman Ferguson’s Umbilic Torus SC , a 65-ton, 28-foot tall bronze sculpture at Stony Brook University, is a nod to representation theory: the study of different ways to look at forms in abstract algebra. Image courtesy of Stony Brook University. Ferguson, who holds a doctorate in mathematics, never chose between art and science: now nearly 77 years old, he’s a mathematical sculptor. Working in stone and bronze, Ferguson creates sculptures, often placed on college campuses, that turn deep mathematical ideas into solid objects that anyone—seasoned professors, curious children, wayward mathophobes—can experience for themselves. Mathematics has an intrinsic aesthetic—proofs are often described as “beautiful” or “elegant”—that can be difficult for mathematicians to communicate to outsiders, says Ferguson. “It isn’t something you can tell somebody about on the street,” he says. “But if I hand them a sculpture, they’re immediately relating to it.” Sculpture, he says, can tell a story about math in an accessible language. Bridges between art and science no longer seem outlandish nor impossible, says Ferguson. Mathematical sculptors like him mount shows, give lectures, even make a living. They teach, build, collaborate, explore, and push the limits of 3D printing. They invoke mathematics not only for its elegant abstractions but also in hopes of speaking to the ways math underlies the world, often in hidden ways. Robert Fathauer’s Three-Fold Hyperbolic Form exhibits negative …