In Praise of Mathematics (or Exodus)


First broadcast on BBC Radio 4, A POINT OF VIEW

Last month I introduced my 5 year old godson to some well-known workbooks, a bundle of four covering English, Verbal Reasoning, Non-Verbal Reasoning and Mathematics. I leafed through them all before dismissing the Mathematics book as boring and settled on the Non-Verbal Reasoning book, which in any case corresponded much more to what I thought of as mathematics.

Novelists like me are often asked who’d had the greatest influence on their writing; my answer has always been my college tutor. As an undergraduate, zI was lucky to have been taught almost entirely through my undergraduate degree by one of Britain’s leading mathematicians, Dame Frances Kirwan, a Fellow of the Royal Society. Mathematics taught me to think clearly; it taught me to sift the relevant from the irrelevant; and it taught me to search for assumptions I might be making. These three skills have been essential to my practice of writing.

Sir David Spiegelhalter, the Cambridge statistician and professor of the public understanding of risk, recently wrote a piece explaining how a newspaper headline might unduly have alarmed some people. “Study shows 29% of the 42 people who have died after catching the new strain had BOTH vaccinations” ran the headline. Spiegelhalter explained that as the rate of double jabs rises high, we should actually expect the proportion of hospitalized who’ve had two shots to rise. Imagine, if you will, that everyone were double vaccinated. Then, given that the vaccine while marvelous is nonetheless imperfect, some people will still be hospitalized, even if they will be far fewer in number. Yet they will all—100% of them—have been double jabbed. Spiegelhalter is addressing something called the Base Rate Fallacy, a misreading of data by failing to regard it in its correct context.

I have to admit to a little smile when I see such closely reasoned pieces as Spiegelhalter’s placed in the opinions section of a newspaper. They feel like someone saying: Hey, if you’re telling me this is a right angle triangle and its two shortest sides are of length 3 and 4 cms, then let me tell you that the longest side is 5cms. Should we regard that as an opinion, when it is rigorously true and anyone can verify it by careful reasoning, just as Pythagoras might have done? The claim is true in a way that opinion can never be true. And it’s certainly far more reliable than any news report from the corridors of Whitehall or the White House.

Spiegelhalter isn’t invoking authority to sell his claims. Equally, my brilliant former teacher, Frances Kirwan, might now sport a dame honorific along with the FRS post nominals but none of these confers any authority on her as a mathematician: her claims stand and fall by reasoning alone.

In another recent op-ed, by way of contrast, another commentator fell headlong into the same base rate fallacy, when arguing that men don’t read enough books written by women. Among various data cited was one that only 19% of readers of Margaret Atwood, author of The Handmaid’s Tale, were men. However, as had been widely reported previously in the same newspaper, only one in five fiction books are bought by men. Men simply don’t read fiction, in comparison with women. The fact is, 19% is pretty much the proportion of Atwood readers you’d expect to be men. If more than 20% of purchasers of Atwood’s work were men, we would be asking why women don’t buy Atwood’s novels.

A former court of appeal judge—Lord Justice Chadwick, himself a mathematics graduate—once described mathematics to me as an education in thinking without the encumbrance of facts. It’s certainly true that a mathematics education involves the reception of relatively few facts. My entire undergraduate education involved fewer than 20 books, a number that looks comical against the voluminous reading undertaken by a good student of the humanities or social sciences. But a mathematics textbook is slow going because you’re being asked to follow reasoning. Mathematical reasoning is not necessarily easy for Homo sapiens. Only in the last few hundred years has mathematics found people with enough free time to advance the subject greatly and others to apply it and transform our societies. 

Bill Gates famously said “If your culture doesn’t like geeks, you’re in real trouble.” If Gates is right, it’s all the more important to ask if geeks in turn like our culture.

Engaging directly in the public space—that is, politics, journalism, entertainment and the arts—has always been the province of the few. Not everyone has access. Many lack the social capital that is all too often the price of entry. 

But what I think should concern us all is a new division emerging in the last 20 years, one less about access than exodus, the story of a section of society turning away from the public space, people who are the preeminent economic change makers of the past three decades. I think about this a lot when I contemplate the future my godson will come into.

The internet is routinely blamed for surfacing everything base or idiotic, by enabling the likes of conspiracy theorists, the bigoted and pedophiles to gather and traffic their delinquency. But what is less widely understood, because it is little discussed, is how the web has facilitated the abandonment of the public space by those who tire of pre-internet or what’s often called the legacy media, a media that assumes too little of its readers’ capacity to reason. A vast online network of analysis and commentary is now available to readers seeking richer analysis, taking as given its readers’ familiarity with mathematical nomenclature and stomach for extended reasoning. Of course, the legacy media has little to gain in calling attention to this parallel universe. There are great writers such as Zeynep Tufekci, a sociologist working on matters concerned with the internet, who in the past year has repurposed her wide powers towards explaining Covid-related issues to readers of her newsletters, including mathematical models of the spread of the disease. Her global readership, dwarfing that of many national columnists, includes those driving the stampeding capitalist economy we seem to have hitched our lives to.

Such readers, we know, are cut off from the lives of most of us—a junior banker’s starting salary today puts her in the top 2% of earners. But they are cut off not only by wealth. Cash rich, time poor, and mathematically adept, they have little truck with the public space, where the discussions about the roots of the 2008 financial crisis, the epidemiology of Covid, or the logistical aspects of military drawdown in Afghanistan—all of these are shorn of the involved reasoning that is necessary to gain functional understanding of what’s going on. How can a simple discussion of artificial intelligence and its dangers be of use to busy people servicing the public appetite for AI applications, when that discussion can’t even provide a functional understanding of AI’s limitations and capabilities? “Make your explanations as simple as possible, but no simpler,” Einstein famously cautioned.

As a younger man, I was motivated by a desire to contribute to the betterment of the lives of others, which took me across the world to work as an anti-corruption lawyer and activist. But the world my godson will grow into, I have come to believe, will be much more individualist, self-centered and competitive than the one of my youth. Today, even young people with the privileges of a good education and of being born to parents who can help with the deposit on a mortgage—even they can’t get onto the property ladder, that having somehow become a stepping stone to financial security. Tomorrow’s world will be shaped still more by finance, tech, science, and the minds of the mathematically disposed. What then am I to hope for my godson? Does he take his chances with a job outside finance, tech, science and engineering? Or do I help him acquire the prospect of security by encouraging his mathematical acumen?

Or maybe, just maybe, he’ll get lucky and find himself in a world where the public space is able to talk about tech, finance, and science in sufficiently sophisticated ways to make this ruthless modern economy accountable to us all. But I’m not betting on it.