# The Mathematics of Literature

### Sarah Hart's new book Once Upon a Prime argues that math and literature are bound together in many interesting ways. I examine her claims and the book's content.

It's a common casual assumption that literature and mathematics are two very distant points on the map of disciplinary space. They are oil and water in our minds. We think these two have distinct provenances and destinies. Any attempt to intermingle them will fail spectacularly. Sarah Hart, professor of mathematics at Birkbeck, University of London, thinks this mindset is wrong. In her new book, *Once Upon a Prime*, she aims to disabuse a popular audience of this notion. This formidable task compels Hart to delve deep into classical and contemporary texts, the intellectual backgrounds of their authors, and obscure literary movements dedicated to experimenting with the structure of language. She then draws on her disciplinary expertise to translate this esoterica into digestible bites of juicy knowledge that show us just how connected math and literature are.

*Once Upon a Prime* is divided into three parts, roughly three chapters per section. I am surprised Hart didn’t opt for some clever structural symmetry in the book layout (other than 3 being a special number of sorts) given that many examples of this are recounted in the text. Maybe I missed something!? However, I did find the organization of the work compelling, an ambitious attempt to cover the many ways mathematics can be part of literature. The first part discusses the "fundamental structures of literary text, from plot in novels to rhyme scheme in verse." To me, this is really the most important and substantial way that math informs literature. The second portion is focused on the use of mathematical metaphors in literature. And the final section illustrates how mathematics can be deployed creatively in literature and takes a critical eye at some well-known uses: *The Life of Pi*, Sherlock Holmes, *Alice in Wonderland*, and *Flatland*.

*Once Upon a Prime *is an engaging read. There is a lot of interesting, entertaining, and edifying information distributed throughout the text, but the middle section drags and feels a bit like random trivia. There is a discussion of the anthropology of culturally significant numbers that emanates borderline astrology-like vibes too. Such things strike me as only superficially math-related. I also wish the first section, especially "The Geometry of Narrative" chapter, was expanded significantly. For instance, Hart mentions Vonnegut's "Shape of Story" lecture (shown below) but doesn't engage comprehensively or deeply enough with these ideas. I was disappointed by this as the introduction led me to believe this content would figure prominently in the book. Fortunately, Hart does provide a detailed analysis of the structure of verse, including several interesting examples, though the analysis is primarily focused on rhyme schema. There is a discussion of meter, but I found it somewhat confusing relative to more traditional descriptions of how meter functions. It would have also benefitted the book to explore if there are certain poetic structures that are more inherently pleasing than others to humans. Connecting math to beauty first makes connecting it to literature and art more persuasive. Don't the ostensibly recurring patterns in visual, auditory, and literary arts suggest a universal structure to beauty? Or are the structures variable enough across time and culture to suggest otherwise? Some of these topics may be outside the scope of Hart’s book, but I think exploring them would have made the book resonate with a broader readership and would have provided a deeper link between math and art for readers.

After finishing, *Once Upon a Prime* I confess I am not entirely persuaded by the premise. I grant that literature has structure and that this can be described mathematically or statistically. But this seems like a reading a bit much into a superficial observation. If we accept the Chomskyite theory of universal grammar (probably our best theory of language), can't we make claims about structure for all spoken or written communication? How does literature differ in this respect? Maybe Hart would concede this and argue that there are certain mathematical structures that elevate language aesthetically. Or that narrative structures are distinct from and elevating relative to basic linguistic forms. Unfortunately, claims to along these lines aren't tendered. Instead the treatment of how math functions in literature is mostly as a playful and experimental exercise. Hence, we are blessed with lots of discussion about Oulipo or the "workshop of potential literature." This was a group of French intellectuals who essentially tried mathematical experiments in literature, such as writing whole novels without using certain letters (i.e. a lipogram). I enjoyed learning about Oulipo and their members, but this seemed tangential (to use a mathy term) to the purported central claim of *Once Upon a Prime*.

Despite the grab bagginess of the book, Hart communicates complex ideas clearly and accessibly. There is a lot to amuse readers within the book, and there are only a few instances where Hart belabors or indulges concepts beyond what would be tolerable to most readers. She also always shows her work, sketching out the equations and computations that accompany the described math. Still, the reading experience can feel a bit like being inside a pinball machine. Hart bounces from topic to topic rapidly and sometimes wanders various tangents down too far before returning.

Although my criticisms of *Once Upon a Prime* may seem strong, I really appreciate the attempt made by Hart. In fact, the effort of making a book like this was probably a bit too ambitious. A lot of this content is seriously esoteric. For instance, part of the real-life inspiration for this book was Hart coming across the geometrical term “cycloid” in *Moby Dick*. In actuality, each section (or even some of the chapters) could have probably been given book-length treatments. These concepts and topics simply aren't the most general-audience-friendly, and it takes a lot of work to make them digestible. Hart does accomplish that, but has to make editorial sacrifices on that account. It certainly took considerable creativity and economy to even acceptably assemble this work. Hart’s book deserves our attention and praise. Considering all this, I recommend this one to more adventurous readers. It's unique, making its weaknesses quite tolerable, if not educational in some ways. And honestly, I did enjoy many portions immensely: the section on cryptography, the miscellaneous history of mathematical and literary figures, and the various esoterica one could only find in a book like this.

Did she get to The Divine Comedy? That seems like a book where mathematics and geometry etc play a dizzying role and the experience of the math is part of the aesthetic experience and meaning of the story itself.