**Sarah Hart, Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature (New York: Flatiron Books, 2023) pp. 290. £16.99 Hb. ISBN: 978-1-250-85088-1**

Sarah Hart has written a highly accessible and entertaining reflection on the interactions between mathematics and literature. *Once Upon a Prime* is intended for a general reader with no assumed academic background on either side of the cultural divide. While most of the titles in the BSLS reviews list fall into the category of traditional humanities scholarship, this book is better described as an informal and very personal account of the author’s long-term interest in unearthing connections between mathematics and the literary arts. Hart’s voice is engaging and inclusive. It’s also quite funny. The author is an accomplished mathematician, and an overriding message of her book is that mathematics is not an elitist endeavour to be practised by a chosen few. By exploring numerous ways that mathematical concepts are incorporated into poems and novels, Hart finds an effective way to make her case for the beauty and relevance of her chosen discipline. She describes her agenda more holistically: ‘My goal in this book is to convince you not only that mathematics and literature are inextricably and fundamentally linked,’ she writes in the introduction, ‘but that understanding these links can enhance your enjoyment of both’ (2). Although Hart does indeed engage in a mutually enlightening two-way conversation between math and literature, a preponderance of the discussion is devoted to illuminating the wonder of mathematics for the uninitiated.

*Once Upon a Prime* is organised into three sections. The first focuses on the role of mathematics in giving shape to different literary forms. Using the metaphor of a house, Hart likens this use of mathematics to an architectural tool for creating structure. With the foundation in place, the second section proceeds to furnish the house via an investigation of mathematical metaphors and the symbolism of numbers. Mathematical characters move in to take up residence in the final section where Hart surveys a host of novels featuring explicit mathematical themes. Her treatment is more broad than deep, and the narrative moves quickly from one example to another, especially early in the book. The density of the insights is impressive. Some of the examples are familiar but many are not, a consequence of Hart’s evidently deep well of references to draw on from across eras and cultures.

One of the book’s most convincing arguments for the kinship between mathematicians and writers is the use of self-imposed constraints as a catalyst for creativity. This is particularly compelling in the discussions of poetic meter and rhyme schemes. How delightful is it that every Germain prime is a proper candidate for generalising the sestina, that Bell numbers were anticipated in Japanese *Genji-ko*, and that the Fibonacci numbers first emerged in Sanskrit poetry? Extending her argument to the novel, Hart reveals how a decreasing geometric pattern in the chapter structure of *The Luminaries* connects to the inward spiralling of the narrative. Eleanor Catton herself explains it as ‘a wheel, a huge cartwheel, creaky at the beginning and spinning faster and faster as it goes’ (48). Every discussion of writing under mathematically-inspired constraints inevitably finds its way to Oulipo. Hart anchors her analysis of this topic to Jacques Roubaud’s two axioms: (i) a text written with some constraint should refer to that constraint, and (ii) if a mathematical idea is employed, then some consequence of that idea should be employed. These principles effectively moderate the haphazard or capricious tendencies of so-called potential literature while foregrounding its creativity and cleverness. Hart’s larger point is that whatever mathematical contrivance is in play should contribute to the impact of the art itself, an argument she makes gracefully and with good humour where it is required.

In Part II of *Once Upon a Prime*, Hart’s exploration of mathematical metaphors is not as compelling in the overall thesis connecting literature and mathematics as her earlier chapters on structure. That said, enlisting heavyweights such as Tolstoy, Melville, Poe, and Joyce makes its own impact and also makes for entertaining reading. Although the discussion of the cultural symbolism of different integers veers toward the elementary, the strangely muddled transcription of Euclid’s parallel postulate in the choreography of Stephen Dedalus’s departure from Leopold Bloom’s abode in *Ulysses* is dazzling. The experiments revealing the tautochrone property of the cycloid in *Moby Dick* have a similar effect. Mathematical allusions on this scale open up a distinctive new window into some of the most widely studied works of western literature.

The last section of *Once Upon a Prime* contains a few longer mathematical sojourns, each inspired by some literary catalyst. From the giants and dwarfs of Swift, Rabelais, and Tolkien, we get an insightful analysis of the physics of scaling. The fictional detectives created by Arthur Conan Doyle and Dan Brown provide the context for an insightful introduction to cryptography. Michael Creighton’s *Jurassic Park* is the launching point for a user-friendly discussion of fractals. These examples illustrate Hart’s propensity to use literature as a motivation to teach some interesting mathematics. Yet it is not always clear how the mathematical lessons pay dividends in the form of a richer understanding of the novels that inspired them in the first place. In the book’s final chapter, however, Hart is at her interdisciplinary best. Using a few early examples of the unemotional, hyper-logical mathematician as straw men, Hart enchantingly shows us the deep humanity of Mark Haddon’s Christopher (from *The Curious Incident of the Dog in the Nighttime*), Tom Stoppard’s Thomasina (from *Arcadia*), and Alice Monro’s Sofya Kovalevskaya (from *Too Much Happiness*.) Hart’s candidly confessed sympathy for the historical Kovalevskaya is particularly moving. For nine chapters, Hart keeps her impeccable good humour regarding the slights and insults directed toward women that permeate the long history of mathematics and its portrayal in literature. Acknowledging the substantial progress of the last few decades, she finds a powerful and personal means to let us know there is still work to be done as she celebrates the richly human way that Monro crafts Kovalevskaya’s remarkable story.

**Stephen Abbott**, Middlebury College, Vermont