Mathematics and literature ran on parallel tracks throughout much of my life. I fell in love with mathematics, or at least numbers, when I first entered primary school at the age four and I had my nose buried in a piece of literature beginning at the age of three, when I taught myself to read, for at least the next five decades of my life. This duality became formalised in a way when I became a mature student in Germany at the age of thirty. I initially studied mathematics and philosophy for about three years but, as I’ve noted in the past, because the maths department weren’t interested in history of maths and my philosophy professor was a historian of mathematical logic, I changed to philosophy with English literature and history as my subsidiary subjects. Given this lifelong background I couldn’t resist Sarah Hart’s Once Upon a Prime: The Wonderous Connections Between Mathematics and Literature.[1]
Sarah Hart seems eminently qualified to have authored this book. After graduating with a PhD in maths from Manchester University, she moved to Birkbeck College in London in 2004, becoming a full professor in 2013, where her own research work was on group theory. Between 2020 and 2024 she became the first ever woman appointed Gresham Professor of Geometry, England oldest chair for mathematics set up in 1597 by Thomas Gresham, he of Gresham’s Law, to provide annual public lectures on the topic. The chair holders were originally required to hold their lectures in both Latin and English but as she writes: “…fortunately it’s well over a century since professors were required to deliver each lecture twice: once in English and once in Latin.”
On the literature side she writes in the introduction:
I know what you are thinking: Sarah, what do you do in your spare time? The answer is that, as I’ve always done, I read. Constantly and widely.
The contents of her book do more than simply confirm this claim.
The book is divided into three sections the first of which is titled, Mathematical Structures, Creativity, and Constraint. In the first chapter of this section, she analyses the mathematical patterns of poetry in all of its diverse forms, pointing out along the way that it is easier to remember something written in verse form than in prose. I, now over seventy, can still, like Hart, easily recite the nursery rhymes I learnt as an infant. Hart takes her readers through the world of nursery rhymes, counting songs, mathematical puzzles in rhyme form, a Hindu mathematical text written in verse, haiku, and the rhyme schemes and syllable structures of a whole spectrum of poems all of which are mathematical patterns.
The second chapter takes us from poem to stories and The Geometry of Narrative: How Mathematics Can Structure a Story. This is a fascinating multivariant application of mathematics to analyse story telling. Carrying on from here the third chapter introduces something, I’ve never met before a group of “mathematically minded writers and literature-minded mathematicians” who, sat down and created Oulipo, Ouvroir de littérature potentielle (workshop of potential literature). Totally mind-bending and absolutely fascinating and if like me you’ve never come across this before, I can only recommend you dive in.
We stay in the realm of experiment with the fourth chapter, Let Me Count the Ways: The Arithmetic of Narrative Choice, which examines narratives in plays and novels that at crucial points offers the viewers/ readers the possibility to choose, from a selection, the direction that the narrative takes. The possibilities are, of course, potentially endless and Hart invites the reader to view various schemes that manipulate the consumer to follow one of multiple paths to arrive at a predetermined conclusion for the narrative.
We now enter the second section, Algebraic Allusions: The Narrative Uses of Mathematics. The opening chapter here, Fairy-Tale Figures: The Symbolism of Number in Fiction takes a deep look at those numbers that occur conspicuously often in fairy-tales, myths, legends etc such as 3,7, 12, and 40. Is it just chance or is there a reason for it? To find out read the chapter.
The following chapter is Ahab’s Arithmetic: Mathematical Metaphors in Fiction and opens with a long section of how Melville developed an interest in mathematics and came to drop mathematical metaphors all over the text of his most famous novel. Melville was not the only author to do this and we also have sections on George Elliot, Tolstoy, and James Joyce. Makes you want to go back and read the books again, this time with a raised awareness for the authors often deep interest in mathematics.
We now take off for Travels in Fabulous Realms: The Maths of Myth. An exploration, which begins with perhaps the most famous account of fabulous journeys in the English language, Jonathan Swifts satirical novel, Gulliver’s Travels. We also visit Peter Pan’s Neverland, Voltaire’s Microméga, Harry Potter’s Hogwarts School, Mary Norton’s The Borrowers, a great childhood favourite of mine, and very briefly Tolkien’s Lord of the Rings. Here Hart jumps around between her sources investigating the mathematics of the plausibility of the fabulous creations that the authors present. Here I have one of my few quibbles with her book. She goes to great length to explain, with the calculations, that all the giants that one meets on these pages couldn’t exist because their bones wouldn’t carry the weight. My quibble is that she assumes that the bones of the giants have the same biology/chemistry as that of the normal creatures on earth, but do they? Otherwise, her analysis of the biology of the fabulous creatures presented, both gigantic and lilliputian, is fascinating.
The third and final section of the book is Mathematics Becomes the Story and it opens with a chapter titled, Taking an Idea for a Walk: Mathematical Concepts So Compelling They Escape into Fiction. This begins with another of my favourite books, Edwin Abbott’s delightful book on geometrical dimensions, Flatland, inspired by the fad for the fourth dimension that was all the rage in the late nineteenth century. Hart follows on with a digression over multiple dimensions before returning to the fourth dimension with Ford Madox Ford’s and Joseph Conrad’s The Inheritors. Not a book that I had come across before. We move onto the Flatland sequels Dionys Burger’s Sphereland, and A. K. Dewdney’s The Planiverse. We now move into completely other dimensions with a look at the maths in Michael Crichton’s Jurassic Park, which features fractals. Fractals also feature in John Updike’s Roger’s Version and Tom Stoppard’s play Arcadia. From fractals we move into the world of cryptography with Edgar Allan Poe’s The Gold Bug, which despite cryptographies long history, Hart tells us was the first story to feature it. Once the dam was broken there followed a flood of books and plays centred around cryptography.
The succeeding chapter is The Real Life of Pi: Thematic Mathematics in the Novel, which delivers what the subheading announces and begins with an analysis of the text quoted in the heading, Yann Martel’s Life of Pi. In the novel Pi Patel ruminates on the irrational number π that he carries as his name, leading Hart to do the same, landing at some point in Jorge Luis Borges’ The Library of Babel. This leads to all sorts of speculation on infinity, permutations, and combinations, then somehow landing up in topology. We exit Borges’ library and enter the world of Oxford mathematics don, Charles Lutwidge Dodgson, better known a Lewis Carroll. As to be expected Carroll’s works are full of references to mathematics and, even more so, formal or mathematical logic. In the dim and distant past when I was still simultaneously researching a MA and a PhD, on nineteenth-century British logical algebra, Carroll was one of my logicians. Somewhere in the middle of Hart discourse on Carroll, Douglas Adams puts in a brief appearance with his Hitchhiker’s Guide, another of my favourites, as indeed is Lewis Carroll.
The final chapter of this section, and indeed of the whole book, is Moriarty Was a Mathematician: The Role of the Mathematical Genius in Literature, a self-explanatory title. We enter with a brief nod towards the Millennium series, yet another personal favourite, in which the antihero Lisbeth Salander, comes up with a short proof of Fermat’s Last Theorem. Hart finds this highly implausible and also ventilates on why Last Theorem is a misnomer. We have biographies of notable mathematicians, as well as fictional mathematics, beginning with Isaac Asimov’s Hari Seldon from the Foundation novels. From the good guy, Hari Seldon, we move on to the bad guy, Professor James Moriarty, Sherlock Holmes’ nemesis. Enter the tortured, mathematical, genius, Beth Harmon in Walter Tevis’ The Queens Gambit and Guido in Aldous Huxley’s Young Archimedes. Following Huxley’s child prodigy, we have Apostolos Doxiadis’ grown up child prodigy in Uncle Petros and Goldbach’s Conjecture. This leads to a discourse on Goldbach’s conjecture. We have a mathematician as narrator in Holmes fan Mark Haldon’s The Curious Incident of the Dog in the Night-Time. We return to Fermat’s Last Theorem with Tom Stoppard’s play Arcadia, and this time Hart delivers a discourse on the theorem itself.
In the middle of her discussion of Arcadia and its central figure Thomasina Coverley, Hart takes a diversion to the real life Ada Lovelace and proceeds to perpetuate the myths. No, Ada did not work on the Analytical Engine, as Hart claims, she merely wrote a flowery description of its potentials in footnotes to her translation, from the French, of Luigi Menabrea’s article on it. These notes were co-authored by Babbage and contained nothing that he hadn’t already expounded in his notes and/or correspondence. No, Ada did not create the algorithm for determining Bernoulli numbers contained in Note G, as Babbage clearly states in his autobiography, he wrote it himself. Hart is also a fan of Sidney Padua’s highly dubious, history distorting The Thrilling Adventures of Lovelace and Babbage.
We have a real and highly significant, female mathematician up next in Alice Munro’s “fictionalised account of the last days in the life of Sofya Kovalevskaya,” Too Much Happiness. Hart uses this to give a brief biography of Kovalevskaya’s life and work. The chapter and the book closes with Chimamanda Ngozi Adichie’s Half of a Yellow Sun, a fictional account of the Nigerian-Biafran war, which features the fictional mathematician Odenigbo, who is inspired by the real black American mathematician David Blackwell. This leads to Hart ruminating about the difficulties black mathematicians have getting their due recognitions.
I have included fairly detailed sketches of each chapter in order to illustrate the wide range of literary texts and mathematical topics that Hart elucidates in her fascinating book. All of this is packed into a scant two-hundred and fifty pages. However, despite the expansive content packed into her book, Hart deals with each topic in admirable breadth and depth. She has a pleasant writing style and the book is highly engaging; I found it a great bedtime read. The mathematics presented is not difficult and very well explained, so anybody with a modicum of mathematical knowledge should have no difficulties with it.
There are no illustrations but some black and white diagrams where necessary to explain the mathematics. There are endnotes that add additional information to some points in the book. At the end there is A Mathematical Bookshelf, giving the bibliographical details of the books discussed and including a few bonus recommendations. This is followed by a good index.
If you like literature and are not averse to mathematics, then this is definitely a book for you, informative, entertaining, gently educational and definitely enjoyable.
[1] Sarah Hart, Once Upon a Prime: The Wonderous Connections Between Mathematics and Literature, Mudlark, London, 2023.