The Football takes readers on an entertaining and fact-filled exploration of the mathematical secrets of the most popular spherical object on the planet. The football is familiar to billions of fans across the globe, but how many really look at it? Do footballs all have the same shape? Spoiler: not exactly. How does their shape affect how they play? With Étienne Ghys as our guide, we discover why ballistics, friction, and air flow are key to scoring goals—and why the football is a mathematical problem that engineers are still trying to solve.
You are a mathematician, yet you wrote a book about the football. Are you a football fan, or maybe a player?
Étienne Ghys: Not at all! Like many people, I sometimes watch matches on television, especially during the World Cup. But my motivation has nothing to do with a passion for the sport. What truly fascinates me is geometry.
The world around us is full of geometric objects, even if we rarely notice them: the horizon is a straight line, walls are vertical, water is level, doors and windows are rectangles. The Sun and the Moon appear as discs, but in reality they are spheres. And footballs too are spheres—symbols of perfection since antiquity. To do geometry is to learn how to observe, to reason, and also to draw. Geometry and drawing belong together. As Lodovico Cigoli wrote to Galileo in 1611:
“A mathematician, however great, not possessing the art of drawing, will be but half a mathematician, and also a man without eyes.”
So your book is written for specialists in geometry?
EG: Not at all. I wanted to write for a broad audience. My aim was to show that mathematics is not as abstract as people often believe. By simply looking around us, we find countless objects that mathematics can help us understand better. Take the classical football: everyone thinks they know it, but if you ask people how many black and white panels it has, most cannot answer.
In what sense is the football a mathematical object?
EG: The traditional football, with its black pentagons and white hexagons, is a celebrated mathematical form, known since Plato and Archimedes. It is one of the most iconic examples of symmetry. In the book I explain this, not through heavy technical detail but with many illustrations. And I also wanted to highlight that there is not just one kind of football. Every World Cup introduces new designs, some of which are geometrically stunning.
But isn’t a football just round, nothing more?
EG: Not quite. Look a little closer. When I lived in Brazil, the official ball for the 2014 World Cup—the Brazuca—was unveiled on television. I turned to my wife and said, “Incredible, this ball is a cube.” She thought I was out of my mind… but I was right. The Brazuca is made of six pieces, not quite squares but with gently curved edges, assembled exactly like the faces of a cube. In the book I explain this—or rather, I show it—through drawings.
You stress the connection between geometry and drawing. Why?
EG: Because they are inseparable. I once asked a group of children, aged 10 to 14, to draw a football. Their sketches were fascinating, though rarely accurate. Even counting the black and white panels is not easy. Afterwards I showed them different models of footballs, and together we compared their shapes, their strengths, and their flaws. It was both a geometry lesson and a drawing workshop.
Psychologists have noted something similar. If a problem is presented as a “geometry exercise,” boys often perform better. If the very same problem is introduced as a “drawing exercise,” it is the girls who tend to excel. In an era when too few girls choose scientific careers, such findings give us reason to reflect on hidden biases in the way mathematics is taught.
Finally—do you have a favorite football club?
EG: That is a tricky question, mostly because I know so little about football! In Brazil, one had to choose between Flamengo and Fluminense, a choice with more social than sporting meaning. In France, having lived many years in Lyon, I feel a natural loyalty to Olympique Lyonnais—even if the club has had its ups and downs.
About the Author
Étienne Ghys is CNRS director of research emeritus at the École normale supérieure de Lyon and permanent secretary of the French Academy of Sciences. Inaugural recipient of the prestigious Clay Award for Dissemination of Mathematical Knowledge, he writes a popular mathematics column for Le Monde.