The wondrous connections between mathematics and literature

“Call me Ishmael.” This has to be one of the most famous opening sentences in all of literature, and I’m embarrassed to say that — until quite recently — I didn’t get beyond it.

“Moby-Dick” was, for me, one of those books that languished in the guilt-inducing category of “things you should have read a long time ago,” and I just never got around to it. Plus, I am a mathematician. And despite my interest in literature, my intellectual priorities did not include 400-page novels about whales — or so I thought.That all changed one day when I overheard a mathematician friend mention that “Moby-Dick” contains a reference to cycloids.

Cycloids are among the most beautiful mathematical curves in existence — the French mathematician Blaise Pascal found them so distractingly fascinating that he claimed merely thinking about them could relieve the pain of a bad toothache — but applications to whaling are not usually listed on their résumé.

Intrigued, I finally read “Moby-Dick,” and was delighted to find that it abounds with mathematical metaphors. I realised further it’s not just Herman Melville; Leo Tolstoy writes about calculus, James Joyce about geometry. Fractal structure underlies Michael Crichton’s “Jurassic Park” and algebraic principles govern various forms of poetry. We mathematicians even appear in work by authors as disparate as Arthur Conan Doyle and Chimamanda Ngozi Adichie.

There have been occasional academic studies on mathematical aspects of specific genres and authors. But the more holistic connections between mathematics and literature have not received the attention they deserve.

In fact, they are often pitted against each other. In the British education system in recent decades, students are often forced to choose between studying either math and science or the humanities. I recall that at the end of my very last English class at school, in 1991, the teacher gave me a lovely handwritten note with a long list of books she thought I might like, saying, “Sorry to lose you to the lab.”

I was sorry to be considered lost, too. But I wasn’t lost. I love language; I love the way words fit together; I love the way that fiction — like mathematics — can create, play with and test the limits of imaginary worlds. I went off to Oxford to study mathematics, very happy to be living one street away from the pub where my childhood literary heroes C.S. Lewis and J.R.R. Tolkien had met each week to discuss their work.

The idea that one would have to choose between mathematics and literature is, I think, something of a tragedy — not only because the two fields are inextricably, and fundamentally, linked, but also because understanding these links can enhance your enjoyment of both.

The perceived boundary between math and literature is actually a very recent idea. For most of recorded history, mathematics was part of every educated person’s cultural awareness.

Plato’s Republic put forward the ideal curriculum of arts to be studied, which medieval authors split into the trivium (grammar, rhetoric, logic) and the quadrivium (arithmetic, music, geometry, astronomy). Together, these are the essential liberal arts. Indeed, mathematical references in literary works go back at least as far back as Aristophanes’ “The Birds,” first performed in 414 B.C.E.

The 11th-century Persian scholar Omar Khayyám, to whom the poetry collection known as the Rubaiyat is attributed (modern scholars believe it to be the work of several authors), was also a mathematician, and created beautiful geometric solutions to mathematical problems whose full algebraic solutions would not be found for another 400 years. In the 14th century, Chaucer wrote both “The Canterbury Tales” and a treatise on the astrolabe. There are innumerable such examples, not least that of Lewis Carroll, who, of course, was a mathematician first and an author second.

There is a deeper reason we find mathematics at the heart of literature. The universe is full of underlying structure, pattern and regularity, and mathematics is the best tool we have for understanding it — that’s why mathematics is often called the language of the universe, and why it is so vital to science. Since we humans are part of the universe, it is only natural that our forms of creative expression, literature among them, will also manifest an inclination for pattern and structure.

Good mathematics, like good writing, involves an inherent appreciation of structure, rhythm and pattern. That feeling we get when we read a great novel or a perfect sonnet — that here is a beautiful thing, with all the component parts fitting together perfectly in a harmonious whole — is the same feeling a mathematician experiences when reading a beautiful proof.

The mathematician G.H. Hardy wrote that “a mathematician, like a painter or poet, is a maker of patterns. … The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: There is no permanent place in the world for ugly mathematics.”

As a mathematician, it’s been one of the great joys of my career to uncover and explore these connections.

That fitting together, that structure, is probably most visible in poetry, but all writing has structure. Letters form words, words form sentences, sentences form paragraphs. Just like the point, line, plane hierarchy of geometry, constraints, or rules, can be imposed at any stage — it’s not whether to have a structure, it’s what structure to choose.

The French author Georges Perec wrote a novel (“La Disparition,” or “A Void” in the English translation) without once using the letter E. Eleanor Catton’s Booker Prize-winning “The Luminaries” imposes a precise numerical rule on its chapters, each of which is half the length of the last. In both cases, the mathematical constraint echoes and enforces the novel’s themes. The constraints we choose inspire us to create, to see what is possible — and it’s just the same in math.

This article originally appeared in The New York Times