Book review: “Once Upon a Prime,” by Sarah Hart

Vacation’s all I ever wanted. But books were all the escape I needed.

Despite my near innumeracy, math has always enthralled me. As we know from Norton Juster’s “The Phantom Tollbooth,” numbers can be magical. Even as a kid, I used to marvel at that neat trick for multiplying two-digit numbers by 11. How much is 11 times 63? Simple. You just add the 6 and 3 together and place the resulting 9 between them. Your answer is 693. This works for larger numbers, too, with a bit of adjustment. Being bookish even as a teenager, I happily studied a paperback of George Gamow’s classic of popular science, “One, Two, Three … Infinity,” read with pleasure the essays and stories in Clifton Fadiman’s collection “Fantasia Mathematica,” and puzzled over the first of Martin Gardner’s many collections of his recreational math columns from Scientific American.

All three of those authors loved words and stories as well as numbers. So too does Sarah Hart, as she demonstrates in “Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature.” Now professor of geometry at Gresham College in London, Hart is the first woman to hold this position. It’s an honor with a long history that runs from the 17th-century scientist Robert Hooke to the 20th century’s Roger Penrose. The goal of her book, she tells us, “is to convince you not only that mathematics and literature are inextricably, and fundamentally, linked, but that understanding these links can enhance your enjoyment of both.”

In her introduction, Hart stresses that poetry and mathematical proofs are both things of beauty and patterned elegance. As she points out, even nature-loving William Wordsworth, in his poetic autobiography, “The Prelude,” speaks of the beguiling charms of geometry, “an independent world/ Created out of pure intelligence.”

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The Gresham professor often sounds as if she were conducting a class and pausing occasionally to scribble formulas on a blackboard. She frequently addresses the reader as “you” and begins each chapter by announcing what she’s about to “show” us. Her prose throughout is clear, direct and jokey, a near necessity given some of the more ferocious mathematical arcana in “Once Upon a Prime.”

The book is wide-ranging. Early on, Hart lists several mnemonics for remembering pi, the ratio of the circumference of a circle to its diameter. For instance, the phrase “How I wish I could calculate pi” will give you pi’s first seven digits: Just count the letters in each of the words and you arrive at 3.141592. A few pages later, we learn about primes, those numbers like 2, 3, 5, 7 and 11 with only two factors — that is, they can be evenly divided only by 1 and themselves. A 6 isn’t prime because of its additional factors: Besides 6 and 1, it can also be evenly divided by 2 and 3. To me, this seemingly random mix of primes and non-primes — called composites — implies some strange mystical undercurrent running beneath the orderly march of the cardinal numbers.

In other chapters, Hart intersperses the exposition of mathematical theorems — the Fibonacci sequence, the Koch curve — with reflections on meter in poetry, Kurt Vonnegut’s whimsical graphs of fiction’s basic plot arcs, the arithmetical substructure of Eleanor Catton’s Booker Prize-winning novel “The Luminaries” and much else. Chapter 3, for example, explores the French “Ouvroir de la littérature potentielle,” a “workshop for potential literature” composed of both mathematicians and writers, each hoping to learn from the other.

The most dazzling works of the Oulipo, as it’s commonly referred to, include Georges Perec’s “La Disparition” — a novel written without using the letter e — and its companion “Les Revenentes,” which excludes all vowels except e. Hart also explicates such wordplay tours de force as Mark Dunn’s “Ella Minnow Pea” (say its title aloud) and Christian Bök’s “Eunoia,” which consists of five chapters, each of which uses just one of the five vowels (excluding y). In Claude Berge’s Oulipian mystery, “Who Killed the Duke of Densmore?,” the detective knows that the duke’s murderer must be one of seven “lady friends,” all of whom paid him a visit at overlapping times during the fatal evening. Hart then demonstrates how an interval graph determines the identity of the murderer.

Many readers will be particularly drawn to the chapter about “choose your own adventure” novels and those interactive plays in which the audience periodically votes on what should happen next. How do the creators of such works keep the number of options manageable? Consider that a play with four pauses, each offering two different courses of action, would require actors to memorize 31 possible scenes. We learn how a “theater tree” can ingeniously cut this number in half. From here, Hart segues into a consideration of B.S. Johnson’s “The Unfortunates,” a loose-leaf novel in which the first and last chapters are specified but the 25 others can be arranged in any order. How many different orders are possible? A mere 15.5 septillion.

The middle section of “Once Upon a Prime” turns the reader’s attention to mathematical symbolism. Hart begins by scrutinizing the magical numbers 3, 7, 12 and 40, which recur so often in folklore and fairy tales. Why is it always the third son who behaves differently from his two older brothers and thus wins the princess? “The narrative reason for this,” she explains, “is obvious — we require two repetitions to get to know the pattern, so that the breaking of the pattern in the third iteration can surprise or amuse us.”

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In the book’s final third, Hart examines the use of math in Herman Melville’s “Moby-Dick,” George Eliot’s “Daniel Deronda,” Jonathan Swift’s “Gulliver’s Travels” and the works of James Joyce. She offers an especially acute and extended analysis of the two-dimensional world of Edwin Abbott’s “Flatland,” mentions that “The Inheritors,” a science fiction novel by Joseph Conrad and Ford Madox Ford (writing as Ford M. Hueffer), involves fourth-dimensional beings, and deduces why the main action of Yann Martel’s “Life of Pi” takes 227 days: That number can be rejiggered into the fraction 22/7, which when divided out yields an answer very close to pi. She also touches on Lewis Carroll’s Alice stories, investigates the fractal chapter ornaments in Michael Crichton’s “Jurassic Park” and reminds non-Sherlockians that Professor Moriarty was an authority on the “binomial theorem.” Hart ends by confessing her fondness for Sydney Padua’s 2015 graphic novel, “The Thrilling Adventures of Lovelace and Babbage,” which is “set in a parallel universe where the two protagonists” — the Victorian computer visionaries Ada Lovelace and Charles Babbage — “have managed to get the Analytic Engine to work and use it to fight crime and generally be awesome.”

“Once Upon a Prime” is generally awesome, too, though some parts may require patience and close attention. At least that was my experience, but then I can do little more with numbers than make change and count my blessings.

The Wondrous Connections Between Mathematics and Literature