The Beauty of Chalk

In A Mathematician’s Apology, G. H. Hardy writes, “The mathematician’s patterns, like the painter’s or the poet’s, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.” Anyone who finds these words utterly baffling – maybe anyone who battled with long division or quadratic equations at school – should have a look at Jessica Wynne’s Do Not Erase: Mathematicians and Their Chalkboards.

Wynne, a professor at the Fashion Institute of Technology in New York, traveled across North and South America and into Europe to photograph mathematicians’ chalkboards. Nothing more. Not the classrooms in which those chalkboards were found or even the mathematicians who worked on them. Just the chalkboards and the mathematics that filled them. It might seem a niche project but the results are surprisingly beautiful. There really is no place in the world for ugly mathematics.

However, Wynne’s photographs tell only half the story. Accompanying each picture is a short meditation by the mathematicians whose work is seen on the chalkboards. These meditations focus not only on the mathematics, much of which is extremely high level, but also on the sheer physicality of the mathematicians’ work. We tend to think of mathematics as the most cerebral of disciplines, but in this book, we discover how mathematics involves the body just like any other craft.

Sahar Khan’s blackboard at Columbia University. Photograph by Jessica Wynne, courtesy of Edwynn Houk Gallery

But why chalkboards? Wouldn’t whiteboards do the job just as well? Aren’t chalkboards redundant in our high-tech world? Not according to Philippe Michel, who holds the chair of analytic number theory at the École Polytechnique Fédérale de Lausanne in Switzerland. Michel sets the tone for the whole book by explaining that “the very first thing I did when I arrived in my office in Lausanne ten years ago was to ask that the ugly whiteboard, with its smelly red pen, be replaced by a true chalkboard.” Chalkboards are easier on the eye than whiteboards, and while writing with chalk is slower than with a “smelly pen,” in this case slower may be better because it allows the reader time to process. Repeatedly, the mathematicians in this book expatiate on their love of chalkboards: “I couldn’t live without them,” says Benson Farb, professor of mathematics at the University of Chicago. It’s “an old friend,” says Gilles Courtois, director of research at CNRS, Institut de Mathématique de Jussieu. Étienne Ghys even convinced his wife to allow him to hang a chalkboard in their bedroom, though he did eventually agree to remove it when the amount of chalk dust on the sheets became unmanageable.

Since mathematics is as much process as product, the physical tools of the trade are of paramount importance, as Tadashi Tokieda, a professor of mathematics at Stanford University, explains:

We mathematicians like to watch mathematics being done with chalk on a board for the same reason that people like to listen to music note by note, in real time. Science, at least mathematics, is made of information plus experience. Our age is addicted to transmitting more and more information, blaring climax (result) after climax. For us, that’s not enough: we also want to experience, indeed to relive personally, how the result has come to be. Only in this way can we create science – and on the side, experience joy.

Beauty and joy. These unexpected words sing out from page after page of Wynne’s book. So, perhaps it’s no surprise when the language of dance also emerges out of the mathematical maelstrom. Mathematics is a collaborative discipline, but it’s not so easy to dance round a computer screen or keyboard. Here’s Benson Farb again: “A computer doesn’t help much with 40,000 dimensions, but on a blackboard, I can work up a schematic of the situation, explaining it in real time to a student or collaborator. She can jump up and start writing on the board during my explanation, amending my computations, noting possible problems, unwrapping some equation into a flurry of computations of her own.” At the chalkboard, the collaborators move into intensely creative work: “Doing this dance at the blackboard with someone is an intense, frustrating, energizing, and sometimes moving experience. It’s the kind of connection with the mind of another human being that is rare in everyday life.”

Writing with chalk on a blackboard allows your audience to learn with you, to see the development of your argument, maybe even to appreciate its beauty.

But maybe you’re still skeptical about the value of the chalkboard outside the rarified conditions of mathematical institutes. Maybe in the real world we need smartboards and PowerPoint. Not at all, says Wilfrid Gangbo of the University of California, Los Angeles. “The chalkboard is the ideal tool for helping others follow your ideas. When you are writing explanations on a chalkboard or a whiteboard, you write at a slower pace than if you are showing previously typed explanations. This makes it easier for someone encountering new concepts to follow along, taking some of the pressure off them.” The trouble with PowerPoint is that either speakers rattle through information that their audience hasn’t had a chance to digest, or they read what’s there on the screen already. Confusion or tedium: there’s rarely a middle way. But writing with chalk on a blackboard (or a greenboard) allows your audience to learn with you, to see the development of your argument, maybe even to appreciate its beauty.

The educational world, quite as much as every other sector of society, has fallen prey to the vice of technological determinism. The latest must be the best. No matter the cost (in monetary or human terms) the newest technology demands to be bought. Jessica Wynne reminds us that there is another way, that some of the finest minds in the most prestigious institutions on the planet think differently. Beauty, physicality, and the slow dance of chalkboard mathematics all have their place in the modern world.

In 1930 G. H. Hardy wrote an article for Oxford Magazine arguing for the founding of a purpose-built mathematical institute: “Why should a professor have to grovel before a college bursar when he wants a room and a decent blackboard?” he asked. After reading Do Not Erase, I asked myself the same question. Knowing what the reply would be if I really were to take my request to the bursar, I bought myself some Hagoromo chalk – “the Rolls Royce of chalk” – and carried my old chalkboard into school. If anyone asks, I tell them it’s my new interactive smartboard.