Steve Abbott, The Proof Stage: How Theatre Reveals the Human Truth of Mathematics (Princeton: Princeton University Press, 2023) 396 pp. $35.00/£30.00 Hb. ISBN: 9780691206080
Near the middle of The Proof Stage, his absorbing new book on mathematics and theatre, Steve Abbott gives an account of Samuel Beckett’s strange, wordless play Quad (1981):
‘…there is no text left to subvert; he constructs the entire piece out of mathematical components. The patterns are rigid and deterministic; the symmetry elegant. Harking back to the permutations of [Beckett’s novel] Watt, the four walkers appear in every possible arrangement; and their colors and percussion accompaniments allow us to experience the combinations in multiple sensory ways. The difference is that Watt appeals to mathematics as a potential survival mechanism. By the time Beckett creates Quad, mathematics is all there is’ (179).
Abbott argues that seeing Quad in mathematical terms gives it meaning and positions it as the logical end point of Beckett’s lifelong quest to write a play with ‘no actors, only the text’ (Bair, 1978).
This passage captures some of the strengths of Abbott’s book: the skill and clarity of the writing; the deftness with which he marries detailed reading and wider significance; the thorough knowledge of a writer’s work beyond the text being discussed, and the ability to draw on it with a light touch; and the attention to performance as an essential component of the analysis of mathematics and theatre. These qualities make Abbott’s book not only a joy to read but the most authoritative, comprehensive, and accessible account we have of the relationship between theatre and mathematics.
The Proof Stage compellingly argues that the domains of mathematics and theatre have much more in common than people might assume, and that theatre has engaged deeply and innovatively with mathematics for centuries. Focusing predominantly on post-1800 to the present, but cleverly arranging his material thematically rather than plodding chronologically through it, Abbott discusses geometry, incompleteness, infinity, arithmetic, code-breaking, proofs, and many other core mathematical concepts and fields. He also brilliantly conveys a short history of mathematics as he explains ideas and breakthroughs.
Few theatre scholars are equipped with the mathematical knowledge to be able to write such a book. Abbott is uniquely qualified to write the definitive book on this topic not just because of his mathematics expertise (he is Professor of Mathematics at Middlebury College) but for his first-hand experience in the making of plays that engage with science and mathematics. The book benefits immensely from that deep understanding of theatre from a performance and not just textual perspective. He is rare in his genuine cross-disciplinary activity and his hands-on theatrical experience and he also draws on his design and teaching of undergraduate theatre and science courses. This book will no doubt become required reading for such courses, which proliferate across North America and Europe.
The Proof Stage provides a balance of familiar and unfamiliar ‘math plays’. Abbott devotes two chapters to the mathematical playwright par excellence, Tom Stoppard, allowing us to track the development of Stoppard’s profound and sustained interest in the interrelationship of mathematics and theatre spanning his entire career. He also features a chapter on Beckett, and devotes much discussion to Dürrenmatt and Frayn, revealing hidden depths and new angles to their works through the route of mathematics. But he also brings to light less well-known ones, like Jon Mighton and Stanislaw Witkiewicz, as well as giving us a fresh perspective on the work of Alfred Jarry. Another strength of the book is the brief biographies of each playwright and mathematician he introduces.
Abbott is not afraid to venture into literary-critical territory, either, as when he posits a new way of understanding the rise of realism in the theatre by linking it to the fall of Euclid:
‘…the realism attached to Euclid’s geometry would be undermined in an irreparable way. In fact, by the time Ibsen and Strindberg were writing their groundbreaking plays, this insurrection in geometry had already happened, but the repercussions were only just starting to surface. What is most surprising of all is where these two stories cross. When the non-Euclidean revolution in mathematics finally hit its stride, it helped inspire alternatives to theatrical realism by providing a template for how art could be liberated to pursue entirely new forms’ (79).
This claim frames Abbott’s discussion of Witkiewicz and Jarry, one of the most original chapters in the book and a necessary starting point in order to understand later playwrights like Beckett and Stoppard. While theatre scholars may balk at the characterizations of Ibsen and Strindberg as straightforwardly realist, Abbott’s argument opens up new ways of approaching this pivotal moment in both theatre history and mathematics and how they unexpectedly intersect.
There is a narrative energy to this book, stemming from the genuine enjoyment and relish the author displays for his subject. Abbott’s tone is just right: lively, authoritative, curious, and keen to share his love of the subject. The many puns throughout the book are great (e.g., ‘A Bounced Czech’)—they are infectious, and help to convey a sense of fun and levity without being tiresome or childish. Abbott’s delight in both language and mathematics is a winning (and necessary) combination, particularly when—for the non-mathematically inclined—the explanations can get highly technical and, frankly, may lose such readers. Yet they are vital to ensuring the mathematical authority of the book and they are an essential element to its argument.
Readers will notice the scarcity of women playwrights in this book; rarer still are writers of color. All the writers named in the marketing for the book and on its book jacket are white men. Although a few of the characters discussed in the book are non-white, as in Complicite’s A Disappearing Number, that’s not the same thing as including plays by women or other minority writers. Abbott recognizes this overwhelmingly white male focus as a core problem not only for the book but for the field of mathematics. He acknowledges ‘the dearth of women playwrights discussed’ (13) in The Proof Stage, and points to the wider domain of theatre and science as more ‘generous’ in the number of plays by women (he mentions Shelagh Stephenson, Caryl Churchill, Timberlake Wertenbaker, and Lauren Gunderson in particular; others one might add include Anna Ziegler and Deborah Gearing). Ideally, Abbott’s book will attract new researchers who can build on his invaluable work to address this dearth, and perhaps also encourage the writing of new mathematical plays by a more diverse range of playwrights.
Kirsten Shepherd-Barr, University of Oxford
Bair, Deirdre, Samuel Beckett: A Biography (Harcourt Brace Jovanovich: New York, 1978).
Beckett, S., The Collected Shorter Plays (Grove Press: New York, 1984).
