Ideas - How mathematics is essential to literature

Episode Date: March 10, 2026

Mathematics is everywhere: said high school math teachers in every classroom. But did you ever think math could be linked to literature? And not just in works from the literary greats of the past but for example Michael Crichton's Jurassic Park. The relationship between math and literature are fundamentally creative, says Sarah Hart who speaks to Nahlah Ayed about how these two things that seem so polar opposite are deeply intertwined.Sarah Hart's book is called Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature.

It's becoming pretty clear that U.S. President Donald Trump is ripping up the political playbook. And when it comes to what it all means for Canada, well, as they say, it's complicated. But our podcast, two blocks from the White House, is a way to make sense of it all. Join me, Willie Lowry and senior Washington correspondents, Paul Hunter and Katie Simpson every week as we break down the headlines from Capitol Hill with a Canadian spin. Find and follow two blocks from the White House on your favorite podcast app, including YouTube. This is a CBC podcast. So it's 1588 and a young Galileo is looking for a job. Welcome to Ideas. I'm Nala Ayad.

And the job he wants is Professor of Mathematics at the University of Pisa. The people to impress if you want that job are the Florentine Academy. So he's invited to give a couple of lectures. at the Academy, and what do you think he's going to talk about? He talks about the shape and the size and the location of Dante's Inferno. The geography of Dante's Inferno isn't exactly an intuitive subject for an aspiring mathematician. Or is it? Exploring imaginary worlds is exactly what mathematicians love to do all day long.

Sarah Hart is a mathematician herself. If you think about it, in reality there is no such thing as a perfect mathematical circle, only approximations. There's no such thing as a perfect straight line that goes off to infinity in both directions. These are abstractions. They focus on the underlying ideas, and those help us to uncover the deeper truths. And this is actually exactly what literature does as well. Sarah Hart is Professor Emerita of Mathematics at Burbank College in London, England. She argues that once you start looking, the connections between math and literature are everywhere.

Leo Tolstoy writes about calculus, James Joyce, about geometry. Mathematicians appear in work by authors as disparate as Arthur Conan Doyle and Chimamanda in Gozi Adichie. And how about the fractal structure that underlies Michael Crichton's Jurassic Park, or the algebraic principles governing various forms of poetry? And Sarah's own work offers a notable addition to that remarkable literary tradition. I'm the author of Once Upon a Prime, The Wondrous Connections between Mathematics and Literature. Sarah joined me from CBC London to trace these remarkable connections. I have to say that if I were a novelist, and one day I hope to be, I'd find it just thrilling to write the scene for a party that featured all the literary greats that you've uncovered who love mathematics.

So what I imagine is a dinner party featuring people like Herman Melville, James Joyce, Edgar Allan Poe, George Eliot, and maybe even some sort of more contemporary authors like Jan Martel or Eleanor Cate. Yeah. Why, Sarah, why do so many of our most celebrated authors share these twin passions for writing and mathematics? Well, for me, it's because mathematics is really a key part of human creativity. Our minds, our brains, delight in pattern and structure. And, you know, you see it everywhere in our forms of creative expression, whether that's the rhythms and patterns of music with the beats that we sort of sing along to and count along to unconsciously, or the symmetries and beautiful designs and patterns in art, or in literature, those patterns and structures that authors use to give substance and delight to their work. And so for me, literature and mathematics have these strong connections because mathematics

is all about structure and pattern. It's the language we use to describe those things. So it's not surprising for me that the greatest literature and the greatest authors often enjoy mathematical patterns themselves. The universe is full of underlying structure, pattern and regularity, and mathematics is the best tool we have for understanding it. 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.

Mathematics then is the key to an entirely different perspective on literature. So what mathematics does is in geometry, for example, it has these idealised objects like straight lines that go on forever and circles that are absolutely perfect. Now, those don't exist in the real world. You can't have, straight lines do not go on to infinity. Circles are not ever perfect. You can't draw physically an absolutely perfect circle.

They are abstract ideas, fictional things, that allow you to get to. a deeper truth. And for me, literature, a great novel, it's doing the same thing. It's taking an imagined world, a situation that you put your characters in that simplifies a lot of what's, you know, it's not reality. It simplifies to focus on human nature and what human beings do in extreme situations to get at a deeper truth. So it's almost the same kind of process that mathematics and fiction are doing to explore and understand the world. Before we get any deeper, I just want to pause and acknowledge here that this picture that you're painting of mathematics might be a bit counterintuitive for those who have an aversion

to mathematics. And I wonder just how you begin to explain that to the non-believers. I mean, yeah, it's so sad that people are put off and are afraid of what, you know, they perceive mathematics is. And the way I try to explain it or to think of. it is, you know, mathematics is not arithmetic. It's the same way that literature is not spelling. You know, if you're trying to learn to write, it's useful if you can perhaps spell enough for people to understand what you're meaning, but that isn't what the creative impulse, what telling a great story is about. And it's the same with mathematics. You know, there are some technical skills that are useful, that numeracy, that's, that.

we need perhaps if we want to become professional mathematicians but appreciating the loveliness of symmetry does not require you to be able to say what's seven times 14 the what's seven times 14 I know that would strike terror into the hearts of many people right because they're oh no I've been tested I don't know the answer it's 98 but same thing with spelling you know how do you spell hieroglyphics I don't know but I can tell a great story about ancient Egypt you know it doesn't need me to be able to spell the word hieroglyphics. So for me, that is the difference and you can appreciate and enjoy and love mathematical ideas without ever once having to do a very complicated long multiplication. I love the hope contained in that statement. Think of the nursery rhymes of

your childhood. I bet you can still remember the words. That's the power of pattern. Our mathematical brains delight in it. The subliminal counting of rhythm and rhyme feels so natural that it helps us remember, hence the oral tradition of poems telling the deeds of great heroes. Many traditional rhymes involve counting up cumulatively, adding a new line with each verse and counting back to one every time. There's an old English folk song, Green Grow the Roshes-O, which builds up to 12. The last line of every verse is the melancholy, one is one and all alone, and ever more shall be so. Meanwhile, the Hebrew, Echadmi Yodea, who knows one, Rhyme, traditionally sung on Passover, uses rhythm and counting to teach children important aspects of the Jewish faith.

It ends with four other matriarchs, three other patriarchs, two other tablets of the covenant, one is our God in heaven and on earth. I want to get a bit more the way you think about mathematics and what it is that makes it so compelling. You describe math itself as a form of creative expression and one that actually is one of our most ancient forms of creativity at that. That again might seem surprising to people who aren't mathematicians. What does creativity look like within mathematics? Creativity within mathematics, I think, is about choosing the path that you are going to follow because in mathematics, you can't do anything from nothing. You need to have some ground rules. So, you know, we call these

axioms. They're kind of the set up, the rules of the game. And then you can explore and play within those constraints. So to draw a literary analogy, you know, if you're going to write a poem, you want to know, well, what kind of poem? Shall I write a sonnet? Shall I write a Villanelle? Whatever it's going to be. In mathematics, we have the same kind of playground that we can make. So we might say, okay, I think it's going to be fun to play with something about triangles, for instance. So then we have to say, well, what do we mean by that? And we set up some ground rules. And the creativity comes in several ways. One way is looking at and choosing what's going to be productive and interesting to explore.

You know, some things are dead ends. If there's too many rules, then it becomes very boring and sterile. If there are no rules at all, we can't get anywhere. So the kind of the middle ground of just enough structure, but not too much, that we're stifled, which, again, in all sorts of other creative forms of expression, we get this same tension. That's one part of the creativity. And the other part is the way in which when you want to find out, new things, it helps or you're better at it if you can make unexpected connections,

which again, you know, if you're thinking about writing, a brilliant metaphor, we'll join together ideas that are surprising that we don't think of as being linked, but then we immediately say, oh yes, that's exactly the right way of thinking about whatever it is. You know, in mathematics we have the same thing. You can say, I can think about this idea over here, a circle, maybe if I think about it in terms of something algebraic from over in another part of my experience, let's try what happens if we join these together and what can we make. Those kinds of explorations which require a lot of creativity are the most fruitful in mathematics. Mathematics is often viewed as being quite separate from literature and other creative arts,

but the perceived boundary between them is a very recent idea. For most of history, mathematics was part of every educated person's cultural awareness. More than 2,000 years ago, Plato's Republic put forward the ideal curriculum of arts to be studied. There is no artificial dichotomy here between mathematics and art. The 11th-century Persian scholar Omar Kayam, to whom the poetry collection known as the Rubaiat is attributed, was also a mathematician, creating beautiful geometrical 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. The sort of perceived boundary between math and the creative arts is deep, but it is in fact a relatively recent construct. How did the ancient Greeks think about math in terms of its relation to the liberal arts? Yeah, so the ancient Greeks had these ideas of the seven liberal arts that we now call them. So the trivium was kind of the three basics of learning how to speak, how to argue, you know, rhetoric, those kinds of things.

Logic. And then the logic, yes. And then the quadrivium, the four follow-on arts that you would do if you were a more advanced student, they were viewed as mathematical arts. And I'll tell you what they were. So one of them is arithmetic. which, yes, mathematical. Then you've got geometry, also mathematical. Astronomy, okay, yeah, sort of science-y.

But then music was the fourth one. And the way that these four were perceived is that, okay, arithmetic is number, geometry is number in space, music is number in time. It's counting over time, right? All the patterns that come from that. And then astronomy is number in space and time.

So there's this way of thinking of number in all these different categories and music is right there in amongst them. It's one of the mathematical arts. You know, there's no false dichotomy here. It's something you can do with rhythms and patterns and numbers. And so these kinds of connections were just absolutely natural in ancient Greece. And you get, you know, Pythagoras is doing experiments with music and. playwrights Aristophanes writes about geometry in his plays and has mathematicians who are characters in his plays. So there's this crossover. The earliest known works by a named author in the whole of human history were created by a remarkable woman named Enheduana, who lived over 4,000 years ago in the Mesopotamian city of Er. She wrote perhaps the very first collection of poems,

a cycle of 42 temple hymns. but as high priestess of the moon god Nana she would have needed knowledge of astronomy and mathematics as well these come together in her poetry both in her use of numbers particularly the number seven and in mention of calculation and geometry the final temple hymn speaks of the mathematical activities of the true woman of unsurpassed wisdom

she measures the heavens above and stretches the measuring cord on the earth You know, you get this across the world. So in early India, lots of people were mathematicians and poets and astronomers. They were all doing all of those things together. It all worked together. It all worked together. Mathematics was often written in the form of poetry. Mathematicians studied poetry and looked at, you know, what possibilities there are for rhythm and meter and pattern and rhyming. So these things are just naturally, they kind of segue into each other in a very natural way and nobody has to fit into a little box. and say, I'm only doing mathematics, and therefore I'm only doing science. You mentioned in ancient India that mathematical proofs were written as poems. What do you think those poems offered the mathematicians that a purely numerical notation couldn't?

So part of it was at that time, there wasn't the shorthand notation of algebra that has developed since. So things would have been, if written at all, written kind of in full words. But in fact, mostly at that time, it was an oral tradition. So a poem helps you remember. If you learn a poem, that's going to help you remember because you remember the rhyming parts or perhaps the rhythmic patterns. And so this was a way to transmit knowledge in the form of poetry. If you're doing some kind of geometric proof, you give a few short lines that have to follow a particular rhythm that help you to. remember them. And then what I really love about these Sanskrit poetry that does mathematics

is that sometimes you have to fit in your ideas. Well, often you have to fit them into a particular rhythm. That means you sometimes need different words for concepts than you would normally use because the one you would go for instinctively, like if you want to say the number 17, maybe 17 doesn't fit into the meter of your verse. So what I really really, love is that there were different words that could be used for numbers depending on how you wanted to fit it into your poem. So, for example, the word teeth could be used for the number 32, because that's how many teeth people have. Oh, wow. Or hands. Hands, you have two hands, so that could mean two. Or hand, you have five fingers, so that could mean five. So, you know,

you have these really lovely, different ways and they're great, creative ways to talk about different numbers within the poems that just give this wonderful mixture to it of different words and concepts that people were familiar with at that time and they would get to know

what these different words all signified in which numbers so it would mean you could write a poem with numbers but instead of saying the word for the numbers you have all these lovely

other meanings that kind of creep in so you can bring the flavour that you want to the verse and the rhythm that you need. in a very creative way. Mathematical language continues to be figurative.

When we need new words for things, we reach for metaphors. Once these words have been established for long enough, we tend to forget that they have other layers of meaning, but sometimes circumstances can intervene to remind us. As a master student, I spent a semester studying at the University of Bordeaux in southwest France, learning a subject called algebraic geometry in French, I got a distinctly agricultural vibe from the word gerb, which until then I had previously been aware of only in the phrase,

jeerbe de bleat, wheat sheaf. Those few months of study opened my eyes forever to the creative, metaphorical language underpinning much of mathematics. Back to this idea of the divide between literature and maths, that divide erodes yet further when you start thinking about how often certain numbers appear in fairy tales and myths across time, you know, like the number three,

from the three fates and the Holy Trinity to Macbeth Three Witches, I could go on. What do you think the repeat appearance of certain numbers like three in our art and literature reveal about how math helps us make sense of an order our world? So yeah, you're right, there are these certain numbers that just crop up over and over again

in stories in folklore, in religion, just texts. Some of them are for different reasons than others. So we quite often get things like big powers of 10 to indicate big numbers that we aren't really specifying. So you might say, you know, if I've told you once, I've told you 100 times is something I may possibly have said to my child. Maybe I have told them 100 times. It feels like that. But big numbers that we see are, you know, in Ireland, you may get wished 100,000 welcomes. Or 1,000 farewells. 1,000 farewells. You might get, happy birthday, may you live 100 years.

And those numbers, they are big numbers mathematically. They are obtained by taking 10 and raising it to different powers. 10 squared is 100, 10 cubed is 1,000. So you can see what's happening kind of mathematically. But of course, the reason for tens is a biological one. We have 10 fingers. So often with these numbers, there is something more than just mathematical things going on. There's a biological reason or a physical reason.

or sometimes an astronomical reason. So seven is a number that happens quite a lot. I mean, in fairy tales we have snow white and seven dwarves, but also then seven days in the week and lots of sevens in the Bible and other religious texts. Seven probably has an astronomical reason, dating back many, many thousands of years, when the only things that looked a bit like planets,

sort of stars that move in the sky against the other constellations, The ones we could see were the sun, the moon, and then the five nearest planets, Mercury, Mars, Venus, Saturn and Jupiter. We could see those with the naked eye. And so you can see seven of these special things, these wandering stars. The Greek word for that is planetos. That's where we get the word planet. We can see them and those seven things then acquire all sorts of mystical significance and resonances. And that means the number seven takes on symbolism and we see it everywhere. But then you see things being done to it. Like in the Bible you get sevens, but then you get 77s and 777s. That is a kind of mathematical magnification of this number. So in all of these kinds of situations, there'll be a mathematical thing that we do with this number.

And then maybe some other reason, you know, a symbolic reason why we start off with the number. Of course, it's not just in fairy tales that we encounter numbers. Dante's divine comedy has a huge amount of mathematical metaphor, with several numbers being accorded special significance, but it's the number three that is most fundamental to both its construction and its symbolism. No doubt the reason for this is the great spiritual importance for Dante of the Trinity, God the Father, God the Son, God the Holy Ghost. There are nine, three times three, circles of hell,

split into three parts corresponding to the three main kind, of sin that get you admitted. And in the very last canto, when Dante is on the verge of ascending to the vision of God, he sees three circling spheres, three colored, one in span, three perfect rainbows, in other words. If I can say something about the number three, because that I think, as you've pinpointed, this is one of the most common of these pattern numbers that they're called. And as you say, fairy tale characters three, Billy Goat's Graff, Goli Lox and the Three Bears, You know, you get three little pigs.

Exactly. So many fairy tales have this structure. You'll have three brothers going on a quest or something like this. And for me, that three that happens in stories and you also get it in jokes, right? You often get jokes that have three characters and two of them are sensible and one of them is an idiot. What's happening for me there is something about the mathematics of the number three. Because if you think about a story with, let's say, three brothers, they go on a quest. And we've all heard a story like this.

So the oldest brother goes off and he thinks he's great. but he fails. Okay, so that's one data point. That's one point in space. Now the second brother goes off on the quest and he also thinks he's great and he fails. Now we've got two things, two observations. We've got two points. Now, in geometry, two points define a line.

Right. So what we got with a line? We have a line. We have a direction of travel. We have an expectation. And now when the third brother comes along, the youngest one, he's overlooked, no one thinks he'll achieve anything. He comes along.

We're walking along this line of expectation. But actually, when you have three points in space, you can do something more exciting than a line. You can go up a whole other dimension and make a triangle. We've gone up literally another dimension in complexity. And the brother then, the third brother, the youngest one, he departs from the line. He succeeds in the quest. He surprises us. So three is the smallest number that this works for.

It's the smallest number of times some sort of event can be repeated where you first set up. an expectation and then you confound it. You confound expectations and it's a surprise. And in a joke, the surprise is, you know, someone doing something ridiculous in the narrative, in a fairy tale, the surprise is that the third person to try this thing succeeds. And so it makes for a really nice story. And, you know, fairy tales are the simplest kinds of stories. They're very powerful because of simplicity. There's no characterization or anything. It's like, this happened, then this happened. Then everyone lived happily ever off. Right. It's surprise and resolution. Yeah. Yeah. So it's got the setup and the resolution in kind of the minimum number of possible repetitions.

And that minimum number is three. I've never thought about the rule of three as having a dimension. Yeah. Yeah. This is the way that we get up to the next dimension. Otherwise, you're just on a boring narrative line. It's a great line. Oh, I love it. And we'll follow that line in another direction entirely in just a moment. This is Ideas. I'm Nala Aied.

Hi, I'm Jamie Poisson and I host the Daily News podcast Front Burner. And lately I'll see a story about, I don't know, political corruption or something and think during a normal time, we'd be talking about this for weeks. But then it's almost immediately overwhelmed by something else. On Front Burner, we are trying to pull lots of story threads together so that you don't lose the plot. So you can learn how all these threads fit together. Follow Front Burner wherever you get your podcasts. Poetry is a sort of inspired mathematics, which gives us equations, not for abstract figures, triangles, spheres and the like, but equations for the human emotions. Ezra Pound said that in 1910. And he wasn't the only great poet to show a deep appreciation for math. Here's how Edgar Allan Poe described his poetic craft. One tenth of it, possibly.

may be called ethical. Nine-tenths, however, pertain to mathematics. From the mathematician's side of the equation, that feeling of admiration has long been mutual. It's impossible to be a mathematician without being a poet in soul. The poet must see what others do not see, must see more deeply than other people, and the mathematician must do the same.

That decidedly poetic, quote, comes from 19th century Russian mathematician Sophia Kovalyskaya, an academic and writer whose belief in the parallels between poetry and math make her something of a kindred spirit to my guest, Sarah Hart. When you describe your work as a mathematician, you often talk about it in terms of aesthetic terms, that it's kind of a thing of beauty. And I'm wondering if you could explain what makes math beautiful to you.

I think what makes mathematics so beautiful is the feeling that everything fits together so beautifully. And the neater, the argument that you can come up with, the more elegant the reasoning that you can employ, there's more satisfying it is. And the aesthetic enjoyment that one gets from doing mathematics is when you come up with an argument or a piece of reasoning that just absolutely nails it. And I imagine it must be, you know, if you're a great poet and you come up with the perfect little metaphoral way of explaining a few lines of poetry that encapsulates a particular human emotional feeling. That's a similar kind of thing. Yeah, I've nailed it and I've done it in just a few lines. And it's a really general thing that covers so much of our experience. You know, that's what I love about mathematics. Mathematician G.H. Hardy wrote that a mathematician, like a painter or poet, is a maker of patterns. The mathematician's patterns, like the painters or the poets, must be beautiful.

The ideas like the colours 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. A true mathematician is not a mere calculating whiz. they must also have intuition, a sense of the beautiful. This idea of mathematics being beautiful does crop up in your book quite a lot. One good example is when you talk about the cycloid. Oh, yeah. It's a shape considered beautiful by mathematicians.

It's described as the Helen of Geometry. But I want to just say this, that Blaise Pascal recounted thinking about it to relieve the pain of toothache. Yeah. Really, it's that beautiful? Yeah, I mean, you can genuinely get really so, up in thinking about these lovely ideas. So, yeah, the cycloid is one example.

And you make a cycloid by rolling a circle just along a row. Like a wheel. Like a wheel. Yeah. So put a dab of paint on your bike wheel. Roll it along. You'll get these kind of, yeah, arch-like curves that really grabbed the imagination of mathematicians because they didn't.

It was a shape that they hadn't seen before. Actually, mathematicians have talked about this that maybe you've got a stressful time, But you can go away into a room and just think about mathematics for a little while and kind of forget about other things. And it's just this beautiful crystalline world where everything makes sense and there's nothing horrible. You know, genuinely mathematicians often feel like that about their work. They can just immerse themselves. It feels like utopia in some ways. Yeah.

Yeah. And poets as well have written about this. So Wordsworth wrote about geometry as this, you know, this beautiful. perfect edifice that it almost feels like no harm can come to you when you're in the world of geometry. So it's a very appealing thing. In his prelude, Wordsworth speaks of geometry bringing a pleasure quiet and profound that can beguile your sorrow. Mighty is the charm of those abstractions to a mind beset with images and haunted by herself. And especially delightful unto me was that clear synthesis built up aloft so gracefully. An independent,

world created out of pure intelligence. Another kind of resonance between mathematics and poetry and the way we consider them in terms of, you know, the aesthetic value is that they both are putting a prize or a value on concision, on brevity. You know, a poem at one extreme, maybe the haiku form is the most extreme. It has to get its message across very, very concisely. Every single sound, syllable word counts. And so you try to use the most efficient ways, and that's still beautiful,

but the ways that express big ideas in a few words. And actually, mathematics wants to do the same thing. When we look at a mathematical proof, what we prize as mathematicians is explaining, you know, why this idea, why this concept has to be true for, say, all triangles, you know, Pythagoras's theorem is true for all right-angled triangles. And you can prove it in just a few lines. And that's something, a universal thing that we've expressed in just, I don't know, five or six lines. And that is, no, the epitome of being concise, right?

An elegant argument that covers everything like a beautiful poem. Submitting yourself voluntarily to a particular constraint spurs creativity. The discipline required means you have to be inventive, creative and thoughtful. In haiku, with their 17 syllables, no syllable can be wasted. On a rather less exalted level, the humorous limerick form has to get from set up to pay off in just five lines. The Irish poet Paul Muldoon made the brilliant comment that poetic form is a straight jacket in the sense that straight jackets were a straight jacket for Houdini. This may set the record for most uses of the word straight jacket in a sentence,

but the sentiment is exactly right. The constraint itself is part of the genius of the work. Those kinds of constraints can spur a remarkable amount of creativity for poets. Do you think that's true elsewhere in literature as well? Yes. One of the books I write about is Eleanor Katton's The Luminaries, which is it's a very long book. It is not haiku, but it's a fabulous book. It came out in 2013. It's got murder and intrigue and love and stolen gold and all this stuff. But she has this brilliant structure that every chapter is half the length of the one before. And what that gives you is when you're reading it, you feel the pace is kind of picking up.

And you feel like the gear wheels are turning and the tensions ratcheting up. And it's kind of like you're spiraling inwards and inwards and onwards to the heart of the story. And that effect is created with this nice mathematical pattern. That sounds very similar to another example that you write about in your book. And that's Amor Tolls, who used math to kind of organize a gentleman. in Moscow, which I'm sure people have either read or watched on television. What's the constraint that he used there? Yeah. So again, this is a genius constraint. And I think, you know, the difference between good literature and bad literature is the constraint is not just a random thing.

And so here's what he does. In a gentleman in Moscow, as you probably recall, you have this wonderful character, Count Rostov, who is under house arrest at the Metropole Hotel in Moscow for many years. 32 years. 32 years. So any mathematician, listening will be thinking 32, oh, that's a power of two. Is there? Is there something going? Yes, there is. So the constraint here is not a spatial constraint of the length of chapters.

It is a chronological one because Count Rostov goes into the hotel on the day of the summer solstice, June the 21st, and we hear about that day, and then we hear about one day later, and then two days later, and the time periods through over which we visit him, and we hear about, you know, what's happening, keep doubling and doubling. So eventually you get to one year later, then two years, four years, eight years. And there's a midpoint of the story where that little progression, that doubling and doubling, pivots. And we start halving again.

So then it goes down to an eight year gap, four years, two years, one year, and then right the way down to one day. It's like an accordion. It's brilliant. And the reason that he does it, he does it in this accordion-like structure because it reflects actually human memory. We remember the recent past with great granularity, and then the distant parts of granular, and then the middle bit seems to speed past. So that structure, which is a mathematical structure of doubling and halving, is perfect for the book. And that is what elevates it too.

It's not just a random imposition. It works absolutely brilliantly. Yeah. I mean, as you say, it's not random. It's very deliberate. In an interview, the author talks talked about the structure being a very valuable tool in artistic creation, much as the rules of the sonnet are valuable to the poet.

He said, adopting the rules and trying to invent within those rules something that's new and different and that the structure of a novel can do the same kind of thing. Here's what I want to ask you. Given everything that you're saying, you know, that good mathematics,

like good writing, involves, you know, an appreciation of structure and rhythm and pattern. Are you going kind of further than saying that there's a natural structure to good literature? Maybe that you're saying that literature, in fact, requires structure or a mathematical basis to actually be good. I think you can write a novel without consciously saying I'm doing a mathematical thing here.

However, any good novel will be tightly structured. There's just no way around it, you know, if you have a novel. So one example of a structure that perhaps may not feel particularly mathematical, but it is a structure is a novel that is done just through the medium of writing letters, for instance. So that's a kind of form for a novel. But then within that, you know, you said, well, that is a constraint because the lengths of these letters will be constrained. And there'll be, you know, certain there'll be an interchange. There's a pattern of backwards and forwards.

So some constraints are more mathematical than others. I would say any good piece of writing must have a structure to it that otherwise, you know, it just won't read very well. We appreciate structure. And even if reading a newspaper article, we may not be thinking about the structure that the journalist has employed, but there definitely will be a structure there. There's an opening paragraph that grabs our attention.

Then you go deeper and then you come out and you summarise. So all of these things that are part of the craft of the writer, whether that's a nonfiction or a fiction writer or a poet or a novelist, those things are definitely involved. And I would say that I don't want to make a blanket rule, but many of the best, the best novels, the best pieces of poetry, the best writing, give a lot of thought to what structure to use. And you have to get that right if your literature is going to be truly great.

You may be thinking, why would a writer bother with some fancy structure? Why not just write a good story? This, I would argue, is a false dichotomy. All writing has structure from the get-go. Language itself is built of component parts, each of which has patterns. The decision is not whether to structure your work, rather it's what structure to choose. Within each of these levels, writers may choose to add additional structural constraints. This added structure works best when it feels most natural,

when it fits with the narrative themes or the design of the plot. So mathematics is to some extent built upon constraints, but it is also routinely moving beyond those constraints. You write that literature like maths allows you to, to, quote, test the limits of imaginary worlds. What did those imaginary worlds look like to you? In mathematics, it might be something like a geometry where you find that you're trying to prove things, you know, Pythagoras's theorem or other kinds of things.

And you come up against a situation where you can't prove the thing that you think might be true. So you push things to their limit and you see, well, what happens if I tell? take away this thing or if I break that thing, what do we get then? And, you know, in mathematics, we want to take ideas to their logical conclusions and see what happens. And actually, in literature, Lewis Carroll, this is what he does in his stories. So, you know, in Alice in Wonderland, he has Alice go to this amazing world where she can grow and shrink by eating and drinking various different things. Now, if that were possible, you would be able to swim in a lake of your own

tears. And that's exactly what Alice does, you know, at the beginning of the story, she grows, she cries, then she shrinks back down and then she's swimming around in her own tears. So, you know, this is a logical consequence of the axiom that you can grow and shrink, right? And so it's a really kind of mathematical way of thinking about surreal mathematics, I would call it, but it's very entertaining. I'm glad you brought up this example because Lewis Carroll wasn't just an author. He was, in fact, a professional mathematician. He was, yeah. His real name was Charles Dodson, yeah, and he was a mathematician at Oxford University. And how do you think that background kind of informed this absurd flavor in Alice in Wonderland? So Lewis Carroll or Charles

Dodson was someone who absolutely through his life was playful. And I know for me that's the characteristic of good mathematicians as well as often good writers. He's playing with in a kind of mathematical way the ideas that he encounters in this invented world. The most Famous works of fiction written by a mathematician are surely Lewis Carroll's Alice's Adventures in Wonderland and its sequel through the looking glass. Their playful mathematics and mind-bending logic enhanced a surreal and dreamlike quality of Alice's imagined worlds. For me, although there are a good many overtly mathematical references in his work, it's his entire approach to storytelling that reveals his mathematical cast of mind. All his fiction and poetry has a reductioad absurd and flavour to it.

that in fact is common to both mathematics and children's games of make-believe. You observe the internal logic of the game, precisely as mathematicians do. We agree on the ground rules of our mathematical playground, and then we explore. That is part of actually mathematical training, mathematical thinking, is you have to test ideas to their limits. You can't just sort of say, this seems to work, so I'm just going to assume it always works. You have to really, really stress test it. You have to, and that's what a mathematical proof ultimately is the result of doing.

If you can't find a place where this thing falls down, then perhaps it's always true. But you have to then really reason that out and explain why it's always going to work. And in order to find the argument that does that for you, you've got to think, well, what if, you know, maybe I think this whatever statement is true for all numbers, well, then I've got to try it for this kind of number. I've got to write for prime numbers and square numbers. And eventually you build up some evidence and then you try and prove it in generality. Well, those skills that you learn mathematically for Lewis Carroll become part of, you know, his very personality.

You know, all the letters he writes, he writes letters to lots of different people in his life. And they have little puzzles in. They have puns. They have logical ideas that sort of twisted around. He really love puns and silly ideas like this. And it comes from his mathematical thinking, I think, just ten. testing ideas to their limits. We can't finish this conversation without talking about what you call

performative arithmetic, where authors just make the math up, you know, and Gulliver's travels or the DeFinci codes. But before we get into the details, I was wondering just as a mathematician, how does that sit with you? Does it drive you mad when math is kind of made up? Okay. I think in order to maintain my happy, relaxed exterior, I have to. You know, not let it bother me.

I think that's a thing. So you know that, you know, you might get some Hocum. And in general, I don't object to Hocom because I can, you know, immerse myself into the enjoyment. I don't mind if, let's say, you're watching, I don't know, Ant Man or something. And you think, well, this just couldn't work in the physical universe? Because wouldn't he still weigh this? And you start to ask yourself all these questions. I don't sort of worry about it at the time.

So I don't get angry about these things. But I just think, okay, let's explore. So particularly if an author is perhaps maybe saying something a bit uncomplimentary about mathematicians at any point, you know, but then they get something mathematical wrong. I sort of think, ha, you know, I've got you there. But I enjoy, I enjoy this sort of mathematical hyperbole that sometimes authors employ. And I think the performative arithmetic that I talk about is where often the author is trying to. give a veneer of believability or respectability to some fictional thing that they're describing. And throwing some numbers at it can often give that kind of idea of this is a factual thing.

This is a real place. So there's an example in Gulliver's travels where he goes to an island, the floating island of Laputa, and on this island, actually, there are people who have so obsessed with both mathematics and music, which of course are the same thing in different ways, really. They're obsessed with mathematics and the things they eat are take the form of mathematical shapes, including a cycloid at one point. And then when they wander around the island, because they're mathematicians, according to Jonathan Swift, they are so distractible. Their minds wander off into these rarefied realms of higher, you know, algebra, that they have to be accompanied at all times by a servant who carries a small bag of pebbles and occasionally will just hit them across the face with it to run.

Bring them back to reality. A lot of flattering picture. Yeah, thanks. Thanks very much. So I'm going to now take you to task on your arithmetic. So yeah, it's just really fun to notice these things in Swift's writing and others. In Jonathan Swift's 1726 novel, Gulliver's travels, the intrepid traveller Lemuel Gulliver visits the miniature land of Lilliput. He gives lots of detail about the precise dimensions of the people there,

and he describes how the King of Lilliput arranges for Gulliver to be fed. His Majesty's mathematicians, having taken the height of my body with the help of a quadrant, and finding it to exceed theirs in their proportion of 12 to 1, they concluded from the similarity of their bodies that mine must contain at least 1,724 of theirs, and consequently would require as much food as was necessary to support that number of Lilliputians. While we do not judge satirical novels by the plausibility of their science, this is still an irresistible challenge. where does this 1,724 come from? And is it correct? Spoiler alert, no, it's not. And if Mr.

Gulliver is going to bring my Lilliputian colleague's academic integrity into question with a howler like this, it's my duty as a mathematician to defend them. One last powerful example of inaccurate math that I think can tell actually a really powerful story. For example, in Orwell's 1984, where 2 plus 2 equals 5. And this is perhaps when bad math kind of stands in for truth being stood up on its head. Like it actually tells a whole other story by being inaccurate. How often do you see that? Yeah. So in that sense, mathematics does give you a truth,

something that, you know, you can't propagandise your way around it. You can't just decide that 2 plus 2 is 5 because it isn't. So, you know, that's a very powerful thing that we do see in writing. that mathematics is this symbol, this symbol of truth and sometimes also a symbol of beauty. So in Moby Dick, Herman Melville's novel, which, you know, he includes a lot of mathematical ideas. But one of the things that Ishmael talks about the narrator is that symmetry, so he's talking about how wonderful and amazing the whale is as a creature. And he talks about the symmetry of it being almost like a virtue. He sees symmetry as being a proxy for goodness, and this is actually an idea that goes back thousands of years.

You know, the ancient Greeks philosophers like Plato said that symmetry and very symmetrical objects must be at the heart of the universe because they're beautiful and because they're beautiful, therefore they're good. And them being good means the creator will use them. So they were really interested in things that were very symmetrical because they thought that's what the universe must be made of. mathematical ideas themselves are crafted into wonderful metaphors by writers like George Eliot and Herman Melville. There's a broader mathematical theme underlying Moby Dick, and that's the symbolism of mathematics as a way of understanding and to some extent trying to control our environment.

Mathematics helps us to navigate the unknowable universe, but it is a mistake to assume that analysis is the same as control, just as it is a mistake to reject mathematics completely. Ahab veers between the two extremes. He studies charts and records of whale sightings obsessively, convinced that he can predict where Moby Dick will turn up. But later, as his madness grows, he rejects the mathematical calculations of navigation, trampling his quadrant into pieces and ultimately sailing on instinct alone.

Mathematics is abandoned, leaving us a drift in the ocean. I want to go back to those authors that we talked about at the start, that party that I was imagining. I wonder what you think, that long list of authors from past eras who've referenced math in their work. And what do they tell us about math's place in our broader culture in their time compared to now? Yeah. So I think you get authors a few centuries back maybe people like, I don't know, Lawrence Stern who wrote Tristram Shandy or Herman Melville, Jonathan Swift, they have no kind of qualms, it seems, about. dropping mathematical ideas into the conversation in their writing.

They're not saying, oh, this is really weird, and I'm going to now say parallelogram. You know, they just talk about mathematical ideas as they might talk about ideas from other areas of culture. So for me, this is about the fact that at that time, people would learn mathematics and there wasn't, didn't seem to be as much of a, oh, only mathematicians do that kind of situation. So it's actually a really nice story about, how the philosopher Hobbs first learned about geometry. So it's told by his biographer John Albury. And so Hobbs is, he goes into a gentleman's study, right?

And there's a book of Euclid lying open. And Hobbs looks into it and he's amazed by something that he sees. And so then he decides he loves geometry and he's going to study it. But the point about that little story is that it begins with being in a gentleman's library, Euclid lay open. It's not he was in a mathematician's study. He was in a gentleman's library and so Euclid was there. So gentlemen would perhaps, and even some ladies occasionally, would just maybe they'd pick up some geometry and think about it. So you get this as being, it's not some weird thing that only certain people do.

Actually, anybody can enjoy learning about mathematics. And you get this in America, Abraham Lincoln enjoyed thinking about geometry. There was even a president of the United States who proved, found a new proof of Pythagoras's theorem. It was not a recent president. It was President Garfield. And he was just doing a bit of geometry for fun. He came up with a new proof of Pythagoras's theorem. And both sides of the house agreed it was a jolly good thing.

But having mathematics as a hobby seems in the past to have been much more normal. No, just not, okay, I happen to like geometry. I'm going to do a bit of it in my spare time. Like George Elliott did, you know, she really enjoyed thinking about geometry. And it cheered her up when she was sad. She had this wonderful recipe for a happy life, which was to every day, take a walk, read some Voltaire, play the piano, and do some mathematics, which sounds like a lovely, lovely day, I think.

You've really taken us on quite a journey, this long history of mathematics and literature. One thing that history really makes clear is just how ordinary, it was over much of our past for everyday people to just engage with mathematical ideas. So I'm wondering, as we're finishing your conversation here, what your wish is for those who are listening today who might crack a book now and then but really haven't tackled a math problem since high school. So my wish is that if you can open your mind a little to thinking about the beauty of patterns and where they might lead us and enjoy. those patterns without special knowledge, we can all enjoy them. And that's part of what mathematics

is, but it's also part of what human creativity is. So I would just say, don't be scared. Come with me. I'll take you on this journey. And, you know, you're going to have really seen new aspects of the literature that you already love and maybe some new literature that you haven't yet encountered. Sarah Hart, I'm going to borrow from the subtitle of your book. It's been wondrous listening to you. Thank you. Thanks for coming in. Thank you so much. Lovely to talk to you. Sarah Hart is the author of the book Once Upon a Prime, the wondrous connections between mathematics and literature.

Special thanks to Drew Kilman at McMillan Audio for giving us permission to use excerpts from the audiobook in this episode. This episode was produced by Annie Bender. Ideas is a broadcast and a podcast. If you like the episode you just heard, check out our vast archive. where you can find more than 300 of our past episodes. Technical production, Sam McNulty.

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