Author: Kit Yates
Details: 352pp; £20.00
It’s 8pm on a balmy evening in March. I can barely contain my wildly spiralling thoughts as I watch a spellbinding lecture from Dr Hannah Fry, part of her acceptance of the Zeeman Medal for which I (as well as many others) wrote a glowing nomination.
Fry is talking about mathematics with her usual grace and humour, but the topic she has settled on has me particularly riveted. I wave my hand at her as she closes. She greets me by name, thrillingly.
“I was at a lecture by Paul Earnest last week about ethics in mathematics,” I begin. "He suggested that we should have better training for mathematicians, a national organisation, much more thought and awareness around the topic. What do you think?”
In his new book, The Maths of Life and Death, Kit Yates writes: “We should treat claims sceptically and ask for more information… Maths and statistics can be difficult to understand, even for trained mathematicians; this is why we have experts in those areas. If needs be, ask for help from a professional, a Poincaré [a famous mathematician], who can lend an expert opinion. Any mathematician worth their salt will be happy to oblige.”
Maths and liminal spaces
This crisp, clear and compelling book is about the liminal spaces between expertise in mathematics and hardline decision-making, taking you on a powerful journey about truth and belief and what maths actually is, out in the wild.
I doubt you’ll find many who disagree with the first part of that statement. Yates does an extremely good job of explaining, with a beautiful, interlacing narrative, all kinds of mathematical and statistical ideas in the text. I’ve read a huge number of books on popular mathematics and I really enjoyed this one – it breathed new life into old ideas and shed fresh light on topics I had only partially understood in the past.
But the second part?
Put yourself, if you will, in the place of a professional mathematician for a moment. Banish the boring first thoughts of Einsteinian wild hair and white maleness. You can still be you, or you can be a Fields Medallist from Iran (Maryam Mirzakhani) or an articulate and forthright mathematical icon from Essex (Rachel Riley) or a 19th-century rebellious “original mathematical investigator, perhaps of first-rate eminence” (Ada Lovelace). Someone asks you to check some numbers, some patterns, some equations for them. No problem. Then they let slip that this is for a criminal trial, or a nuclear bomb, or a chromosome test. Would you still do it? What if you were never told the context of the maths in question?
That same Fry who won the Zeeman Medal this year (I may have mentioned it) was quoted in a recent article: “We need a Hippocratic oath in the same way it exists for medicine… In medicine, you learn about ethics from day one. In mathematics, it’s a bolt-on at best. It has to be there from day one and at the forefront of your mind in every step you take.”
Her response to my question covered her own worries about being asked to do mathematics without being told the political, social or medical context – something that had happened to colleagues. She agreed that ethics needed to be a key consideration for mathematicians, and that asking for context and recognising one’s right to refuse projects on ethical grounds was something to be encouraged and engendered in young mathematicians.
Ethics in mathematics
Yates, to give him his due, certainly does not treat ethics as a “bolt-on”, but spends the space of this book exploring the intersection between mathematics and (often life-changing) decision-making.
He does not shy away from the big questions, tackling issues such as breast-cancer screening, Aids, infant death, space travel, nuclear war and police brutality, and highlighting real stories to illustrate the sometimes catastrophic mathematical errors that have been made in many of these areas. It is clear that he, like Fry, also wishes to highlight ethical blindspots and to prompt readers to consider the work of mathematicians not as apolitical, neutral and cold, but as having very real-world and often very messy consequences.
Mathematicians, Yates tells us, determine who gets NHS funding for drugs and who dies without them; who is convicted for crimes and who walks free; who is told they have cancer when they don’t; and who is told they are not pregnant when they are. This is not a coincidence: mathematics so often intersects with these crucial decision points because it’s our only method of slicing our world into ways that make sense to everybody – and yet so often it makes sense to almost nobody.
The key message of this book – that, even if mathematics makes sense to you, the consequences of it may be terribly and tragically hard to make meaning from – is rich and powerful and yet not drawn out half as strongly as I would like.
This book hits all the bases of interesting and jaw-dropping popular maths and yet doesn’t quite tell the human stories with enough depth, sensitivity and – I’ll say it – love. If the central theme is the very humanity of mathematics – its profoundly resonant relevance and how ironic that is to a world full of people who profess to stand apart from it – then I would have taken a greater risk with the storytelling and dropped the flat, neutral tone altogether.
For example, Yates tells the story of Sally Clark, the woman wrongfully imprisoned for murder, on the basis that losing two children to cot death was (as testified by an expert who got it wrong on several counts) “a one-in-73-million event”. He tells it well, and thoroughly, but without emotion. I think this is the wrong judgement call in a world where mathematicians are so often accused of heartlessness and rationality for all the wrong reasons and none of the right ones.
Am I a “bad” mathematician to weep at that story, with its heartbreaking trajectory and terrible conclusion? Am I sentimental for wishing Yates had dwelled a little longer on the tragedy of the Hiroshima explosions? Is it folly to suggest that a softer telling of the Ariana Grande bombing might have been preferable? Possibly.
Balancing honesty and truth
I acknowledge the paradox of finding the balance between telling stories with honesty and “truth” and telling them with a generous side of authorial sensitivity; navigating between the twin straits of fact and opinion is the most difficult issue facing writers in our time, and I don’t think Yates missteps significantly. (He also loosens up as the book progresses, and addresses these issues head-on.)
Another point Fry makes well is that so many mathematicians who are now being asked to work on problems of this magnitude are “young white boys”. Without better representation, the breadth of the input and therefore to some extend the quality of our decisions will be only as narrow as the pool of experts we have bothered to invest in. The author of this book cares about these issues and is interested in them, but not enough emphasis on them in the book left me slightly disappointed.
That said, I am a harsh critic on these matters because I have been utterly and passionately immersed in them for some time. I would wholeheartedly recommend this book, in particular to those who teach mathematics at any stage (the maths contained in it goes up to a reasonably hard level, but is so astonishingly well explained you may not even notice). Its value – and I hope the author would agree – is not in being the last word on the matter, but the beginning of an important and fruitful conversation about ethics in mathematics, which should absolutely be happening at school level from the very start.
When early years students begin to count and record data, how can we help them to ask what gets counted and why? When primary students share out and divide, how can they consider questions of what is “fair” and “equal” in the circumstances?
When secondary-level students use hypothesis tests, how can they question as well as use standard algorithms for accepting or rejecting ideas?
If you can find the time, I would do as my English teacher always drilled me to do and read around the subject. In particular, I would read this book in conjunction with Caroline Criado-Perez’s Invisible Women, Weapons of Math Destruction: How big data increases inequality and threatens democracy by Cathy O’Neil, and, of course, Hannah Fry’s Hello World.
Lucy Rycroft-Smith produces the Mathmatips podcast for Tes
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