Leila Sloman in Quanta Magazine: Sarah Hart has always had an eye for the covert ways mathematics permeates other fields. As a child, she was struck by the ubiquity of the number 3 in her fairy tales. Hart’s mother, a math teacher, encouraged her pattern-seeking, giving her math puzzles to pass the time. Hart went on to earn a doctorate in group theory in 2000 and later became a professor at Birkbeck, University of London. Hart’s research probed the structure of Coxeter groups, more general versions of structures that catalog the symmetries of polygons and prisms. In 2023, she published Once Upon a Prime, a book about the ways math appears in fiction and poetry. “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,” Hart wrote. “Mathematics, then, is the key to an entirely different perspective on literature.”
Since 2020, Hart has been the professor of geometry at Gresham College in London. Gresham has no traditional courses; instead, its professors each deliver several public lectures per year. Hart is the first woman to ever hold the 428-year-old position, which was occupied in the 17th century by Isaac Barrow, famous for teaching another Isaac (Newton). More recently, it was held by Roger Penrose, a mathematician who won the 2020 Nobel Prize in Physics. Hart spoke with Quanta about how mathematics and art influence one another. The interview has been condensed and edited for clarity.
Why did you choose to write your book about the links between math and literature?
These links are less explored and less known than those between math and, say, music. The connections between mathematics and music have been celebrated since at least as far back as the Pythagoreans. However, though there has been writing and academic research about specific books, authors or genres, I hadn’t seen a book for a general audience about the broader connections between mathematics and literature.
How should people in the arts think about math?
There’s a lot of common ground between mathematics and, shall I say, the other arts. In literature, as well as music and art, you don’t ever start with nothing at all. If you’re a poet, you are choosing: Will I have a haiku with its very precise numerical constraints, or will I write a sonnet which has a certain number of lines, a certain rhyme scheme, a certain meter? Even something that doesn’t have a rhyme scheme will have line breaks, a rhythm. There will be constraints that inspire creativity, that help to focus you.
In mathematics, we have the same thing. We have some ground rules. Within that, we can explore, we can play, and we can prove theorems. What mathematics can do for the arts is help find new structures, show what the possibilities are. What would a piece of music look like that doesn’t have a key signature? We can think about the 12 tones and arranging them differently, and here are all the ways you can do that. Here are different color schemes you can devise, here are different forms of poetic meter.
What’s one example of how math has been affected by literature?
Thousands of years ago in India, poets were trying to think about the possible meters. In Sanskrit poetry, you have long and short syllables. Long is twice as long as short. If you want to work out how many there are that take a length of time of three, you can have short, short, short, or long, short, or short, long. There are three ways to make three. There are five ways to make a length-four phrase. And there are eight ways to make a length-five phrase. This sequence you’re getting is one where every term is the sum of the previous two. You exactly reproduce what we nowadays call the Fibonacci sequence. But this was centuries before Fibonacci.
How about math’s influence on literature?
A quite simple sequence, but it works very, very powerfully, is Eleanor Catton’s book The Luminaries, which came out in 2013. She used the sequence that goes 1,1/2, 1/4, 1/8, 1/16. Every chapter in that book is half the length of the one before. It creates this really fascinating effect, because the pace is picking up, and the characters’ choices are being more constrained. Everything hurtles toward its conclusion. By the end, the chapters are extremely short.
Another example of a slightly more complicated mathematical structure is what’s called orthogonal Latin squares. A Latin square is kind of like a sudoku grid. In this case, it’d be a 10-by-10 grid. Every number appears exactly once in each row and in each column. Orthogonal Latin squares are formed by overlaying two Latin squares so there is a pair of numbers in each space. The grid formed by the first number in each pair is a Latin square, and so is the grid formed by the second number in each pair. Furthermore, in the grid of pairs, no pair appears more than once.
These are very useful in all sorts of ways. You can make error-correcting codes out of them, which are useful for sending messages along kind of noisy channels. But one of the great things about these particular ones, size 10, is that one of the greatest mathematicians of all time, Leonhard Euler, thought they couldn’t exist. It was one of the very few times when he made a mistake; that’s why it was so exciting. A long time after he made this conjecture that these things couldn’t exist for particular sizes, it was refuted, and squares of this size were found in 1959. It was on the cover of Scientific American that year.