Mathematics in Twentieth-Century Literature and Art: Content, Form, Meaning by Robert Tubbs

Case studies of math’s influence on the arts, some more pertinent than others

The late Robert Tubbs was a professor of mathematics at the University of Colorado. In his book Mathematics in Twentieth-Century Literature and Art, published in 2014, Tubbs explores instances where math and art intersect. Although the book delves into some complex mathematical concepts, the text is accessible to a general reader with an interest in math, the arts, or both.

This book consists of ten chapters, each of which follows a similar structure: (1) Tubbs opens with a simple, obvious example of how mathematical concepts were employed in the creation of a work of art or literature. Kazimir Malevich made paintings of geometric shapes, for example. Jasper Johns used numbers in his paintings. Poet André Breton included mathematical imagery in some of his surrealist writings. In these examples, the artistic connections to mathematical concepts often seem tenuous at best and leave the reader thinking, “Well, duh!” (2) Tubbs, proceeds, however, to discuss the work of a particular mathematician and explain his concepts and theories to the reader, such as David Hilbert’s explorations into non-Euclidean geometry, Gotlieb Frege’s use of set theory to define what a number is, Eduard Zeckendorf’s theorem involving Fibonacci numbers, and Charles Howard Hinton’s books on the fourth dimension. (3) Finally, Tubbs then caps the chapter off by presenting a work of art or literature with a more complex relationship to the mathematical concept at hand. These examples are often by a lesser-known artist, for example painter Alfred Jensen, writer Albert Wachtel, or poet Paul Braffort. These works, however, bear a more integral relationship to math than the more obvious examples covered earlier in the chapter. Tubbs frequently draws upon works by dada and surrealist artists. The experimental musical compositions of John Cage are also discussed. In the literature category, many of the works covered are by members of the Oulipo group, a French movement whose members often employ mathematical structures in their work.

In considering this tripartite division of each chapter, the third portion was really what I expected when I purchased the book, and the second part of each chapter taught me much about mathematics. In the opening portions of each chapter, however, the loose connections between the art discussed and mathematics often felt forced and sometimes pointless (e.g. Are Johns’s number paintings really math?). In his preface, Tubbs states that he hopes “this book will appeal to non-mathematicians interested in literature or the arts who are curious about twentieth-century trends and the occasional glimpses of mathematical ideas in those trends.” That would be me. My education was in art, not in math, so naturally I learned more about math from this book than I did about art. Tubbs does a commendable job of explaining higher-level mathematical concepts and theories to lay readers. The beginnings of chapters at times feel too elementary because Tubbs is starting at square one for the general reader, but by the end of the chapter some intellectual heavy lifting may be required. I will confess I found the math confusing in a couple passages, but not so much that I lost my bearings as to what Tubbs was saying about the art.

This book is not so much a comprehensive history of the use of mathematics in art but rather a collection of interesting case studies. The ten chapters somewhat call to mind Martin Gardner’s old Mathematical Games columns in Scientific American, but with a focus on the arts. Like “mental floss” for Mensa candidates, Tubbs draws the reader’s attention to artistic and literary curiosities and trivia while teaching them complicated mathematics along the way. The coverage has more breadth than depth, but Tubbs brings up a lot of intriguing works that artists and writers seriously interested in this topic will want to track down for further investigation.

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