There will be precious few children in Europe who have not visited a cathedral by the age of ten. From Notre Dame to Naples, there are over 600 across the continent, tangible reminders of national histories, the indiscriminate power of the church, and the ability of architecture to lift our spirits.
As a young boy, I was awestruck by the efforts that must have gone into constructing these monuments. At a time when most people couldn’t read, when harvest yields meant life or death when medicine was little more than superstition… here were our forefathers, building these intricate structures with the most basic of tools. How did they do it? How did they know it would all line up and not fall down?
Cathedrals began my fascination with mathematics
Medieval masons didn’t use abstract equations, nor did they work to the detailed plans we would expect today. What they did have, though, was a deep understanding of practical geometry. Using simple tools such as set squares, dividers, and plumb lines, they could calculate the forces involved in complex features like vaulted roofs; column supports, and flying buttresses. Indeed, so powerful were the ratios they discovered that even God was sometimes depicted as a geometer in Christian iconography.
Decades on from my childhood visits, I remain astonished at the skills of these craftsmen and can’t help but think that their down-to-earth application of mathematics has something to teach us today. It is frankly a shameful disrespect to their legacy that despite centuries of progress, we struggle to embed basic numeracy even in college graduates. Here in the US only one-third of the population rates as having intermediate math skills, and fewer than 10% are classed as numerically proficient.
Mathematics Matters
And this observation matters. Not so much for the construction of buildings or the development of integrated systems – we don’t need everyone to have those skills. But rather, for a shared understanding of issues that affect us all: for sound finances and planning, for decisions that determine the future of enterprises; for policies that lay the foundations of our public services and healthcare; for the fight against pseudo-science and the deplorable army of social media charlatans; for the understanding of basic concepts of statistics.
Data can be Misrepresented
Today, there are whole industries that thrive on a deliberately misleading presentation of data, promoting all manner of quackery, from transformative beauty products to miracle diets and sure-fire financial investments. They are aided by negligent or insufficiently critical media more interested in clickbait headlines than robust analysis. The standard of financial journalism, for example, is almost criminally poor. But all of this pales into insignificance compared to the politicians who would whip up hate and mindless populism on the back of spurious numbers presented as facts.
Regrettably, the challenge of improving numeracy is not confined to the socially disadvantaged. Over my career, I’ve worked with many brilliant and inspiring people. But I’ve also been in Board rooms with board members and colleagues who lacked the basic understanding of concepts that are necessary to interpret, correlate and extrapolate data.
Granted, my academic training was in statistics and operations research, so no doubt I may be more alert and attentive to these shortcomings. And I should also be clear that good business is about more than mere numbers. Nonetheless, surely, we can, and we, in fact, must do a lot better.
Data and Mathematics are Fundamental to Understanding Problems
During the recent pandemic, we all became armchair epidemiologists, but how many of us truly understood what the data was actually telling us? I am not sure I did in every regard. Was it any surprise that manipulators and charlatans then exploited the gaps to influence opinions? Much the same is true of the climate change debate, of anti-vaccination crusaders, of immigration, taxation, and welfare, of government spending, and we can go on and on. It is an irony that as we move rapidly to a world that’s likely to be shaped by Artificial Intelligence, we need more than ever to have a greater understanding of the underlying basics. It is these that help to give us the analytical (and indeed often moral) compass we need when confronted with otherwise overwhelming information.
On my recent visit to the UK, Prime Minister Rishi Sunak launched a campaign to improve mathematics teaching. Then followed an article in the London Times by one of its leading columnists who bravely admitted to having such poor numeracy skills that she struggled to calculate her change when shopping. Her case is not atypical, nor is her ability to improve (which she did) through better instruction and practical application. I hope the UK campaign succeeds and that, more broadly, governments across the democratic nations are able to address the regression of numerical literacy that’s ultimately of our own making and a big part of the reason for the populist demagoguery and the resulting democratic deficit.
Returning to the cathedrals I began with, it’s often said that those who built them were laboring for future generations. I wonder, though, what those master craftsmen would make of our world today. I’m sure they’d be as in awe of us as we are of them, recognizing that so much has changed for the better. But I’m certain too that they would be astonished by our casual loss of what was once a bedrock of everyday knowledge. And that if they set their dividers and squares to many of our analytical foundations, they would find them in need of some urgent underpinning.