Configurations, 2009, 17:1–18 © 2010 by The Johns Hopkins University
Press and the Society for Literature and Science.Subject Headings:
Mathematics - Philosophy.
Imagination (Philosophy)In lieu of an abstract, here is a preview of the article.
"[I]f mathematics is the study of purely imaginary states of things, poets must be great mathematicians."
—Charles Sanders Peirce 1
I prove a theorem and the house expands:
the windows jerk free to hover near the ceiling,
the ceiling floats away with a sigh.
—Rita Dove 2
A few years ago, mathematician, writer, and regular contributor to NPR Keith Devlin wrote that mathematics is about rendering the invisible visible and about inventing symbolic worlds into which the mind can enter. "Is there a link between doing mathematics and reading a novel?" Devlin asks. "Very possibly," he answers. 3 Imagining a conversation between two invented characters or the intricate imagery of a poem arguably requires a similar kind of mental process as imagining "the square root of minus fifteen," as mathematician Barry Mazur has demonstrated. 4 "Of all escapes from reality," wrote mathematician Giancarlo Rota, "mathematics is the most successful ever." 5
Not that literature is about escaping from reality, of course. It and all the visual and performing arts, as well as every discipline in the humanities and sciences for that matter, often share with mathematics a common goal: that of describing and/or addressing the "really real." Questions of reality, truth, and certainty are at the core of the philosophy of mathematics: Does mathematics afford us entry into reality and truth? Does it provide us with certainty? Contrary to Platonist beliefs about the ability of mathematics to give us these things is the stance that mathematics is actually about multiple realities, relative truths, complexities, and ambiguities. In essence, doing pure mathematics (not merely doing computations) is an exercise in imagination
