This book had its origins in Greece in 2005 with an organizing conference where a group called THALES + FRIENDS began with the goal of bridging “the chasm between mathematics and other forms of cultural activity.” At a second conference in 2007, fifteen of the attendees presented essays on the subject of mathematics and narrative. Those essays then became the basis for this book. The fifteen authors include mathematicians, historians, philosophers, professors of literature, and a novelist trained in mathematics. The title refers to the words (“Do not disturb my circles”) attributed to Archimedes before a Roman soldier at Syracuse killed him. The editors find in these words something emblematic of the contrast between mathematics and stories –— the conflict between the stable and tranquil world of mathematics and the drama of the world outside.

While the general subject of the essays is the relationship of narrative to mathematics, the treatments are so wide-ranging and divergent that this review cannot do justice to them all. At best it can provide a glimpse of a few of the main ideas. The word “narrative” is used with a diversity of meanings throughout the book, sometime articulated and sometimes not. A working definition from one of the authors, David Corfield, describes narrative as a serial structuring device, usually chronological, which may or may not have the conventional aspects of storytelling such as plot, character, setting and so on.

Six of the essays consider the history of mathematics, where mathematical ideas are central but the form is often narrative. Amir Alexander portrays the history of mathematics as an assembly of stories whose structures follow basic narrative patterns. The stories are not merely the re-telling of past events but contribute to form the meaning of those events in a crucial way. Colin McLarty offers an analysis of the origin myth arising from the Hilbert’s proof of the existence of finite complete systems of invariants for forms and Gordan’s reported denunciation of this as theology and not mathematics.

Mathematical biography is a related form of narrative, one shaped by the unique circumstances of a life. Peter Galison explores this idea by looking at the lives of John Archibald Wheeler and Nicolas Bourbaki. The contrast between the two is profound — one real, one a fictional construct, one with a machine-like view of mathematics, and the other seeing an ordered structure outside of time. Galison sees in these contrasting perspectives a deep reflection of the idiosyncrasies of personal origins.

Barry Mazur’s contribution suggests a taxonomy of mathematical narratives: origin stories (problems from the non-mathematical world inspiring mathematical investigation), purpose stories (describing the external, non-mathematical purpose of a mathematical narrative), raisins in the pudding (ornamental or unnecessary anecdotal digressions), and dreams (stories of a grand vision).

The last three essays explore the influence of the mathematical style of thinking on the study of narrative. For example, David Herman looks at existing formal models of narrative and reflects on the concept of model as it might apply to the theory of narrative.

The scope of this book is perhaps too broad and the questions too ill-defined to make this more than an untidy package of interesting and widely divergent ideas. Even many of the individual essays suffer from a lack of coherence and focus. The essays on history and narrative are perhaps the best and most focused.

It was surprising to me that none of the essays mentioned, except in passing, narratives related to the discovery and proof of mathematical results. How wonderful it would be if more papers in mathematics told a story: this is why the work is of interest, this is how the proof came about, and this is what it means.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.