Simplicity: Ideals of Practice in Mathematics and the Arts

Simplicity: Ideals of Practice in Mathematics and the Arts is a seemingly disconnected collection of essays, lectures, and theoretical musings from a conference of the same name. Contributions jump from philosophical musings on the ideas of Kant to the history of Metafont and its supposed contributions to effortlessness in typesetting. The underlying current, however, takes the reader through attempts to define what constitutes a “simple” mathematical proof or work of art. This reviewer is not convinced that any particular essay is provides perfect illumination on what is a “simple” idea. Yet, several essays do provide some insight and, perhaps more importantly, an interest in what a “simple proof” could mean and how to accomplish it.

In particular, the essay What Simplicity is Not (Maryanthe Malliaris and Assaf Peretz) provided insight not through defining “simple,” but by giving counterexamples to statements regarding simplicity. Perhaps the most striking example of these counterpoints revolves around the idea that simplicity is a necessary component for a proof. In the striking sentence, “Proofs which are not simple still work!” the authors give hope that even clumsy, time-consuming proofs have validity. Note, Malliaris and Peretz do not attempt to define what “not simple” means in this essay. In doing such, they have provided a way (with examples and quotes) to lead individuals into a direction of just creating a proof, and worrying about optimizing it later.

Other essays in this collection are obviously tied to the idea of mathematics in art, but not always the typical “find x” mathematics that so many readers might be expecting. Instead, authors approach the idea of simplicity in art as if they were approaching a proof: art is generated through conceptualization, analysis, and execution of an idea. In particular, the essays on Metafont and ASCII follow this format.

Overall, this book feels disjointed as a read-through collection but interesting to read in a non-linear fashion. The contents could have been reorganized to introduce the idea of simplicity (and what it is not) and then provide examples ranging from more theoretical/philosophical discussions of mathematics to the heavily mathematical discussions on art. Finally, as with any conference proceeding involving visually motivated lectures (especially those incorporating videos or photographs), the thousands of words contained within this text simply do not describe the whole picture.

Megan Sawyer is an assistant professor of mathematics at Southern New Hampshire University in Manchester, NH.