Once Upon a Prime, page 26
I remember hearing an academic, thankfully retired now, claiming that it’s not possible to introduce cultural diversity into the math curriculum. The “reason” he gave was that Black mathematicians are such a recent phenomenon that any of their work would be too advanced to explain to his undergraduate students. Utter nonsense, of course—I’d only that week been telling my first-year students about research on magic squares by the Nigerian mathematician Muhammad Ibn Muhammad Al-Fulani Al-Kishwani (who died in 1741). It was even worse when I remembered that the course this colleague was teaching was on what’s known as game theory, one of whose most important figures is the selfsame David Blackwell who mentored Odenigbo.
The word “trailblazer” is perhaps overused, but if anyone has earned it, it’s Blackwell. After earning his Ph.D. at the University of Illinois in 1941 at only twenty-two years of age—the seventh Ph.D. in mathematics ever awarded to an African American—he then did a year’s fellowship at Princeton’s Institute for Advanced Study but was prohibited from attending classes or doing research at Princeton University, which at the time did not admit Black students and had no Black faculty, despite the university’s collaborative relationship with IAS. Blackwell would go on to chair the Statistics Department at the University of California, Berkeley, for thirty years. But the first time he applied for a post there he was turned down because the wife of the head of the Mathematics Department, whose official role included hosting dinners for faculty members, refused to entertain the idea of having a person of color in her house.
Over the course of his career, David Blackwell published more than eighty academic papers and was highly influential in mathematics, with dozens of Ph.D. students, well-regarded textbooks, and a reputation as an excellent teacher. What’s he doing in Adichie’s book, though? Well, Adichie was brought up in Nsukka after the Biafran war. Her mother was an academic registrar, and her father, James Nwoye Adichie, was, guess what, professor of statistics at Nsukka University. I wouldn’t be so reductive as to say that Odenigbo “is” Adichie’s father—he certainly isn’t—but there are interesting crosscurrents in their stories. James Nwoye Adichie earned his Ph.D. at UC Berkeley while David Blackwell was department chair, and he would certainly have known him. Blackwell wasn’t his direct supervisor, but I’ve checked the records, and he did supervise at least two other Nigerian Ph.D. students. I like to think that the young Chimamanda heard her father speak of him.
I also had a look at James Adichie’s publications. It gave me pause to see a telltale gap between 1967 and 1974. That bland absence, so easy to overlook, but what turmoil and trauma it conceals. In Half of a Yellow Sun, when Olanna and Odenigbo return to their old home after the war, they find that most of their books and papers have been burned. Odenigbo “began to search through the charred paper, muttering, ‘My research papers are all here, nekene nke, this is the one on my rank tests for signal detection…’” This little detail is poignant. We can’t know what papers Adichie senior might have published between 1967 and 1974 if the war hadn’t happened, but such a title would fit nicely with his real-life paper “Rank Tests in Linear Models.” As Odenigbo and his family start to rebuild their lives after the war, “books came for Odenigbo from overseas. For a war-robbed colleague, the notes read, from fellow admirers of David Blackwell in the brotherhood of mathematicians.”
Chimamanda Ngozi Adichie has talked about the problem of the “single story,” in the context of stereotypes of “Africans.” She recounted how “a student told me that it was such a shame that Nigerian men were physical abusers like the father character in my novel [Purple Hibiscus]. I told him that I had just read a novel called American Psycho and that it was such a shame that young Americans were serial murderers.” Of course she does not actually think this, because she, and all of us, have been exposed to many stories of America and what it means to be American. The danger of having only a single story, a single version of an American, or a Nigerian, or, dare I say it, a mathematician, is that a single story creates stereotypes, and the problem with stereotypes, says Adichie, “is not that they are untrue, but that they are incomplete.” In literature, as in life, there are as many different ways to be a mathematician as there are different ways to be a person.
Acknowledgments
This is my first book, and I have been blessed with an amazing team supporting me every step of the way. Jenny Heller, my agent, has taken me from a vague thought of writing a book through to publication in the space of two years, and has been incredible. It has been a revelation to work with my editor, Caroline Bleeke, and her assistant, Sydney Jeon, who have made the book so much better in so many ways. Bob Miller and the whole Flatiron team have been fantastic, and have helped to make the daunting process of writing a book as smooth as possible.
I’m grateful to my head of department at Birkbeck, Ken Hori, and the dean of my school, Geoff Walters, for letting me take a sabbatical term in autumn 2021 to focus on the book, and to Maura Paterson and Steve Noble, my colleagues and friends in the mathematics group, without whom I wouldn’t have made it through the pandemic with even the modicum of sanity I have now.
The team at Gresham College have been brilliant in supporting me as Gresham Professor of Geometry. My program of lectures, focusing as it has on the links between mathematics and the arts and humanities, has quite a different flavor from some previous series, and I’m grateful that they supported my vision and let me run with it.
It was my appointment as Gresham Professor that led to Siobhan Roberts approaching me for a profile in The New York Times, and that article opened a lot of doors for me, so, Siobhan, I definitely owe you a good dinner next time you are in London!
Thanks also to Sir Ian Livingstone for giving his time so generously for me to pick his brains about how he writes his epic Fighting Fantasy books.
I am lucky to have a wonderful group of friends who have shared this journey (and many others) with me. Thank you to Caroline Turner, who among other things introduced me to Charlotte Robertson and Jenny Heller at the fabulous Robertson Murray Literary Agency. Thank you to Rachel Lampard, who reads the Booker Prize short list with me every year, and has been so kind and supportive over the last few years. Thank you to Alex Bell, whom I met when we were very pregnant with our first babies, and our families have been close ever since. Alex, you’re a rock! I’m sorry I couldn’t sneak the words supercalifragilisticexpialidocious, hippopotomonstrosesquipedalian, floccinaucinihilipilification, honorificabilitudinitatibus, contraremonstrance, and epistemophilia into the book like you dared me to. Or could I? And thank you, too, to my wonderful book club, the Ladies Wot Read. We’ve been meeting every month since 2006 and seen one another through good and bad times with love and support (and occasionally we also discuss the book). Alex, Claire, Claire, Colette, Emma, Hadassah, Lucy, and Rachel: thank you.
I have the great good fortune to have grown up in a house filled with both books and ideas. My dad, Martin, trained me and my sister, Mary, up very well as independent researchers by sending us to a dictionary every time we asked the meaning of a word. Mary put up with my many foibles, and she didn’t mind coming with her little sister to the geological museum during my rocks-and-minerals phase, or talking with me on long car journeys about four-dimensional shapes during my … well, that phase is still ongoing, to be fair. My mum, Pat, who died in 2002 of multiple sclerosis, was always there for me when I was young, supplying cuddles, soothing away my (many) worries, and of course asking me interesting mathematical questions when I was bored. She went with me to lectures by the then–Gresham Professor of Geometry Christopher Zeeman. I wish she could have known that one day it would be her little girl up there. I think of you every day, Mum. Thank you.
My brilliant, beautiful daughters, Millie and Emma, bring so much joy into my life. (They have also taught me the importance of being at peace with chaos.) They’ve had so much to deal with in the past few years, and have coped amazingly. You can’t write a book without time, and they have given me that time with a good grace.
Finally, and most important, my husband, Mark. I find it hard to put into words how much he has done for me. He has always given me unconditional support for everything I have wanted to do, and this book is no exception. I’m the family worrier, and he’s the chief morale officer. He talks me down from my periodic “why on earth did I think I could do this” freak-outs. He makes me a nice cup of tea when he can sense I need one. I know he will always be there for me, and I for him. He’s the best husband and father it’s possible to be. This book wouldn’t exist without him.
Notes
1: One, Two, Buckle My Shoe
1. The zeros are represented by ten-letter words, in case you were wondering! If you want to compose a bit of pilish of your own, the first forty digits are 3.141592653589793238462643383279502884197.
2. Pound says that “an ‘image’ is that which presents an intellectual and emotional complex in an instant of time.… It is this presentation of such a “complex” instantaneously which gives that sense of sudden liberation; that sense of freedom from time limits and space limits; that sense of sudden growth, which we experience in the presence of the greatest works of art” (“A Few Don’ts by an Imagist,” Poetry, Chicago, March 1913). He explained that just as in poetry, the same mathematical expression can often be interpreted on several different levels.
3. For a comprehensive academic treatment, try The Poetics of Japanese Verse—Imagery, Structure, Meter, by Koji Kawamoto (University of Tokyo Press, 2000). I’d also recommend Abigail Friedman’s The Haiku Apprentice: Memoirs of Writing Poetry in Japan (Stone Bridge Press, 2006), a charming account of her experiences learning to write haiku while working as an American diplomat in Tokyo. In terms of online resources, an excellent place to start is the website www.graceguts.com, run by the poet and haiku expert Michael Dylan Welch.
4. A full set of all fifty-two Genji-ko diagrams, as well as some from The Arte of English Poesie, is presented in the essay “Two Thousand Years of Combinatorics” by the mathematician and computer scientist Donald Knuth, which appears in Combinatorics: Ancient & Modern, edited by Robin Wilson and John J. Watkins and published by Oxford University Press in 2013. He believes, like me, that the best way for humans to communicate, whether mathematics or anything else, is through story. This extends to his philosophy of computer programming, which he says would be much improved if we considered programs to be works of literature. He also wrote a novel in 1974. Surreal Numbers: How Two Ex-students Turned On to Pure Mathematics and Found Total Happiness is, as perhaps the title indicates, rather of its time. But it deserves a mention in this book because it is, to my knowledge, the only novel to introduce a piece of mathematics research—the invention of new kinds of numbers by the mathematician John Conway—before it was published anywhere else.
5. Copyright for this important 2021 poem rests with the author, Emma Hart, aged ten at the time of composition. It is reproduced here with her gracious permission.
6. There are several translations of the Temple Hymns, but this one, by Sarah Glaz, is my favorite. Glaz is a respected mathematician and poet whose published books include both an academic textbook on abstract algebra and a book of poetry, Ode to Numbers (Antrim House, 2017). The title takes its name from a poem by the Chilean poet Pablo Neruda.
2: The Geometry of Narrative
1. From a public lecture given by Vonnegut in 2004 at Case Western Reserve University. You can watch it online at https://youtu.be/4_RUgnC1lm8.
2. The quote is from Lockwood’s 2021 novel, No One Is Talking About This.
3. Towles was interviewed for the BBC Radio 4 Bookclub on April 8, 2021. At the time of writing, the episode is available on the BBC iPlayer at https://www.bbc.co.uk/programmes/m000tvgy.
4. The spiraling effect is converging around a point that turns out to be exactly two-thirds of the way along the square and one-third of the way up (if you’re a mathematician you might enjoy proving this).
5. Perec made this remark in his article “Four Figures for Life: A User’s Manual,” which appears in English translation in the anthology Oulipo Compendium (Atlas Press, 2005). It is noted there that the girl in question appears on pages 231 and 318 in the English edition.
3: A Workshop for Potential Literature
1. There is a translation by Ian Monk of Les Revenentes with the title The Exeter Text: Jewels, Secrets, Sex. It comes out with a lipogrammatic difficulty level of though again this is not a fair comparison once you take into account the superadded challenge of translation.
4: Let Me Count the Ways
1. Not everyone approved of the Fighting Fantasy books. A church group published an eight-page pamphlet with dire warnings about the dangers of reading them, saying that because you are interacting with ghouls and demons, you might get possessed by the Devil: “A worried housewife in deepest suburbia phoned her local radio station and said that having read one of our books her child levitated.” This didn’t seem to put people off. “Kids are thinking—what, for £1.50 we can fly? I’ll have some of that!” Teachers, on the other hand, were delighted that these books were actually getting kids reading. It’s reported that they increased literacy by 20 percent, and it’s certainly good for the vocabulary—“Hey, Dad, what’s a sarcophagus?”
2. If you’d like to see another example of a reverse poem, I highly recommend Brian Bilston’s “Refugees,” which he has made available online.
3. Nesting a narrative like this is sometimes known as metalepsis, by the way, for any lovers of ancient Greek out there. There’s an example of many-layered metalepsis in another of the stories from Lost in the Funhouse. In “Menelaiad,” there are a full seven nested stories. Menelaus (king of Sparta) struggles to find his way through the labyrinth of his own narrative: “When will I reach my goal through its cloaks of story?” he asks in desperation.
4. Coe’s biography of B. S. Johnson is excellent—it’s the source of much of the biographical information I include here and is well worth a read. Jonathan Coe, Like a Fiery Elephant (Picador, 2004).
5. I can’t say “sonnets” because I’m showing off with an e-free sentence.
5: Fairy-Tale Figures
1. Suppose we start a “say what you see” sequence at 42 (after all, according to The Hitchhiker’s Guide to the Galaxy, 42 is the answer to “Life, the Universe, and Everything”). We’d get a sequence starting 42, 1412, 11141112, 31143112. The brilliant mathematician John Conway, subject of a wonderful 2015 biography by the Canadian author Siobhan Roberts, studied “say what you see” sequences and found they have some truly remarkable properties, which are worth googling if you ever want your mind blown by how much amazing math can come from a little puzzle.
2. I’m certain that there are, but that’s just a hunch—nobody has a mathematical proof yet.
3. Bonus alternative version for mathematicians: There are 10 kinds of people in the world. Those who understand binary, those who don’t, and those who weren’t expecting this joke to be in base 3.
4. The essay is “The Number Three in American Culture,” in Every Man His Way: Readings in Cultural Anthropology (Prentice-Hall, 1968). By all accounts, Dundes, an American folklorist, was not afraid of controversy—he even received death threats after he wrote an article called “Into the Endzone for a Touchdown,” positing a homoerotic subtext in the language and rituals of American football.
6: Ahab’s Arithmetic
1. I go into a bit more detail in my paper “Ahab’s Arithmetic: The Mathematics of Moby-Dick,” Journal of Humanistic Mathematics 11, no. 1 (January 2021): 4–32, https://scholarship.claremont.edu/jhm/vol11/iss1/3, DOI: 10.5642/jhummath.202101.03.
2. Blaise Pascal is maybe best known outside mathematics for what’s now known as Pascal’s wager, which essentially says that humans, in our behavior, are betting for or against the existence of God. There are four possibilities: you believe and God exists; you believe and God doesn’t exist; you don’t believe but God exists; and you don’t believe and God doesn’t exist. If you believe and God exists, then great (assuming you behave accordingly). Off you go to Heaven for all eternity. If you believe and you are wrong—there is no God—then you lose out on perhaps some pleasures during your finite life, perhaps people laugh at you, you have to get up early to go to church, and so on. But your losses are finite. On the other hand, suppose you don’t believe. If there is no God, then again, you’re okay. But if there is a God, then you will go to Hell for all eternity, so your losses are infinite. Even if you think the probability that God exists is tiny, there is still a nonzero probability. Anything nonzero multiplied by infinity is infinity. Therefore, if you act purely rationally, says Pascal, you should act as if God exists and try to believe in God, because the expected gains of believing are infinite (however low the probability of God’s existence), whereas the expected losses of not believing are also infinite.
3. George Eliot had strong views about the education of women, and The Mill on the Floss (1860) hints at them. Brother and sister Maggie and Tom Tulliver have very different educational experiences. Euclid is wasted on Tom, who doesn’t get along with geometry at all, but Maggie, who could have gained great pleasure from it, is not given the opportunity. Later on, she begins teaching herself, from Tom’s Euclid and some of his other schoolbooks. She “began to nibble at the thick-rinded fruit of the tree of knowledge, filling her vacant hours with Latin, geometry and the forms of syllogism, and feeling a gleam of triumph now and then that her understanding was quite equal to these peculiarly masculine studies.”
