Sarah Hart is a respected pure mathematician and a gifted expositor of mathematics. When promoted to full Professor of Mathematics at Birkbeck College (University of London) in 2013, she became the youngest STEM professor at Birkbeck and its first-ever woman Mathematics Professor and one of only five women Mathematics Professors under the age of 40 in the United Kingdom. Educated at Oxford and Manchester, Dr. Hart currently holds the Gresham Professorship of Geometry, the oldest mathematics chair in the UK. The chair stretches back in an unbroken lineage to 1597. Dr. Hart is the 33rd Gresham Professor of Geometry, and the first woman ever to hold the position.

Below, Sarah shares 5 key insights from her new book, *Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature*. Listen to the audio version—read by Sarah herself—in the Next Big Idea App.

### 1. Literature is full of mathematical structure.

It’s often said that mathematics is the language of the universe, and that’s quite true. The reason is that the universe is bursting with pattern, symmetry, and structure. Mathematics is the best tool we have for describing and understanding these things. So, of course, it’s vital to science.

We are part of the universe, and we take an innate pleasure in pattern and structure, so it’s only natural it would show up in our forms of creative expression—whether that’s music, art, or literature. We can see it in poetry, in the rhythmic structure and rhyme schemes of sonnets, or in the precise numerical constraints of a haiku. What’s less obvious is the mathematical structures at the foundation of many brilliant works of fiction.

Take Eleanor Catton’s *The Luminaries*, which won the Booker Prize in 2013. It’s an amazing book about the gold rush in New Zealand in the 19th century and the intertwined lives of people in a mining community there. It’s got everything: murder, love, betrayal, opium, and £4,096 of stolen gold. It’s a meditation about the interplay between choice and fate, and how forces beyond our control can compel us in certain directions.

One of the ways Catton illustrates this tension is by using a framework of astrological symbolism. Twelve characters associated with the 12 different astrological signs, and two key characters associated with the Sun and the Moon. On top of that, there are 12 parts. The really interesting mathematical pattern is that every chapter in the book is half the length of the one before. This halving structure is a fantastic device in the book because you feel events pick up the pace, the gears tightening, and the walls closing in on the central characters. When you get to that very final chapter, you see that unbeknownst to them, their fate has already been sealed. The total length of the book is the length of the final shortest chapter, multiplied by *2 ^{12}-1*. And, it gets better—remember the stolen gold? That £4,096? Well, guess what

*2*is?

^{12}4,096.

Eleanor Catton hid that gold right there in the structure of the book, and it’s a beautiful use of mathematics.

### 2. A little mathematics can increase your enjoyment of your favorite books.

A boy stranded at sea for 227 days with a Bengal Tiger named Richard Parker. That’s the setting for Yann Martel’s wonderful novel *Life of Pi*. The boy gives himself the nickname Pi and, as he says, “that Greek letter that looks like a shack with a corrugated tin roof, in that elusive, irrational number with which scientists try to understand the universe, I found refuge.” Pi, the mathematical constant relating the circumference of a circle to its diameter, is a fascinating number, and, as Pi Patel says, it does indeed go on forever. It is “irrational”—it cannot be written as a fraction or a decimal that terminates. In *Life of Pi*, we can never be sure whether Pi’s dreamlike experience was real or invented. So, in a play on words, the “irrationality of Pi” is a key theme of the novel.

“But how can the story of Pi come to a finite end, when as an irrational number, its digits go on into infinity?”

Because the digits of Pi go on forever, we can never know it exactly. For Pi Patel, this is a cause of frustration, as he wants things to have clearly defined endings. “That’s one thing I hate about my nickname, the way that number runs on forever,” he says. “It’s important in life,” he says, “to conclude things properly. Only then can you let go.” But how can the story of Pi come to a finite end, when as an irrational number, its digits go on into infinity?

Yann Martel has a brilliant solution, and the clue is in an interview he gave, explaining why Pi’s companion is a tiger. It was going to be a rhino, he said, but “rhinos are herbivores, and I didn’t see how I could keep a herbivore alive for 227 days in the Pacific. So finally I settled on what now seems the natural choice, a tiger.” This 227 is clearly carefully chosen. It cannot be a coincidence that the fraction 22/7 is a very good approximation to Pi. Unlike Pi, it is a rational number—we can write it as a simple, straightforward fraction; we can know it precisely. Martel’s clever sleight of hand, in bringing 22/7 to mind with a 227-day voyage, appears to achieve the impossible: it makes Pi rational. So, a little bit of mathematical knowledge can unlock a lovely extra layer of meaning to our experience of this beautiful book, among many others.

### 3. Literature is full of mathematical symbolism.

Fiction is full of mathematical imagery and allusions. Tolstoy, Proust, Vonnegut—they all use mathematical metaphors. But mathematical symbolism is also present at a much more elemental level. Numbers themselves are an absolutely basic part of the human psyche, and some numbers have immense cultural and literary resonance. In fairytales, you’re likely going to meet three bears, seven dwarves, 12 dancing princesses, and 40 thieves.

The number three, in particular, is endemic in Western culture, and not just three little pigs, three billy goats gruff, three good fairies, and the three wishes we invariably are given. How about the three witches in* Macbeth*? Plus, you can’t escape the threes in the three books of Dante’s *Divine Comedy*—he even invented a whole new rhyme scheme with three lines in each verse. Three is there in our everyday idioms; three cheers, not two, and we learn our ABCs, not our ABCDs. It’s even in political slogans: *Read my lips! No new taxes!*

Three really is a magic number, and it also has some pretty special mathematical qualities. Three is the smallest number of points that can define a shape—a triangle. With two points you can’t escape a boring straight line. With three, we can move up to the next dimension and spring to life as an actual shape.

“Three really is a magic number, and it also has some pretty special mathematical qualities.”

The same thing is going on in the many stories, and also jokes, that have a three-part structure. With three brothers on a quest, say, the first one fails, that’s one data point. The second fails too, now it’s a pattern, a line. Finally, when the third brother succeeds (or, if it’s a joke, does something stupid), that serves as the surprise that breaks our expectations. It gives us another dimension of insight, just like making that mathematical triangle.

Three, by the way, is also the biggest number of points that you can draw on a page so that they are all equally distant from each other. So it’s got connotations of equity and balance as well, just like the Three Musketeers: “All for one, and one for all.”

### 4. Mathematics is a thread running through every part of culture.

The fact that there are so many profound links between mathematics and literature may surprise us. As a society, we have forgotten what was natural throughout history until very recently—the enjoyment of mathematics as a standard part of a cultural education. It was not so long ago, in fact, that a President of the United States could have had geometry as a hobby, and managed to find a completely new proof of Pythagoras’s Theorem—it was James A. Garfield, if you are interested.

Scholars often combined mathematics and literature. Geoffrey Chaucer, author of *The Canterbury Tales*, one of the first works of literature written in English, also wrote a treatise on astrolabes. Centuries before that, Persian scholars like Omar Khayyam were poets, mathematicians, and usually astronomers, too. Back another few hundred years in India, Sanskrit texts on mathematics were written entirely in verse. To fit with the meter of the verse, they would use a huge range of metaphors for numbers. For example, “fire” meant three, for the three sacrificial fires of Vedic tradition; “hand” meant two, as we have two hands. You could incorporate these words into the poetic structure.

We also have the famous mathematical textbook the *Kama Sutra*—OK, perhaps that’s not quite accurate, but it does describe 64 arts that women should study. Along with singing, dancing, flower arranging, and other things, there are encryption and arithmetical recreations.

“We have forgotten what was natural throughout history until very recently—the enjoyment of mathematics as a standard part of a cultural education.”

In Ancient Rome and up until Renaissance Europe, mathematics was part of the seven liberal arts. You began with the trivium: Grammar, Logic, and Rhetoric—the basics of writing, thinking, and speaking. Then you got to the good stuff, the quadrivium: the arts of Arithmetic, Geometry, Music, and Astronomy. Arithmetic is number, and Geometry is number as it manifests in space. Music is number as it manifests in time; Astronomy is number in space and time. There was no artificial humanities-sciences divide; mathematics was—and is—part of everything. It is a cultural touchstone that has been incorporated into literature from the Ancient Greek plays of Aristophanes right through to the present day.

### 5. Some of our greatest authors have been mathematics fans.

There are writers who have a real affinity for mathematics. They like mathematics, they are good at it, it’s part of the furniture of their minds, and that’s completely obvious from their writing. A bit of mathematical insight can shed new light on their work.

Reading the books of Herman Melville, for example, can show you just how many mathematical allusions some authors use. Melville enjoyed mathematics and actually won an award for it at school; the prize, quite naturally, was a book of poetry. What better gift for a mathematician? All his books have mathematical allusions, *Moby Dick* most of all. As a metaphor for loyalty, he uses a circle—the constancy of the distance from the circumference to the center. He uses mathematical symmetry as a symbol of virtue: Ishmael tattoos statistics on his body, and Ahab carries out mathematical calculations on his ivory leg. Melville even references a beautiful mathematical curve called a cycloid, which is probably the loveliest curve that most of us have never heard of!

The story of the cycloid is a piece of mathematical history that really adds to the fun if you know it. It was studied by Galileo, Descartes, Fermat, and Isaac Newton, among others. It’s such a lovely curve that the mathematician and philosopher Blaise Pascal reported that he thought about it to distract him from the pain of toothache. People were obsessed with it and had furious arguments about who had first discovered its intriguing properties, one of which Melville describes in *Moby Dick*.

If we haven’t had the chance to befriend mathematics, we miss out on something else: the great solace of mathematical beauty. The great Victorian novelist George Eliot uses a lot of mathematical symbolism in her writing, and no wonder. She loved mathematics so much that it couldn’t help but come out in her fiction, and she found it real consolation at difficult times. Recuperating from a stressful experience, she writes to a friend, “I take walks, play on the piano, read Voltaire, talk to my friends, and just take a dose of mathematics every day.” This was her recipe for mental harmony, and that same satisfaction we get from reading a wonderful novel or an exquisite poem can be found in, and comes from the same place as, the pleasure of an elegant piece of mathematics.

Mathematics is a powerful tool, but it’s more than that. It’s a search for beauty, meaning, and truth—exactly what literature is. Inside our greatest literature, inside all of us, there is beautiful mathematics waiting to be enjoyed.

*To listen to the audio version read by author Sarah Hart, download the Next Big Idea App today:*