Artists have brushes and canvases, carpenters have hammers and wood; for mathematicians, the tools of the trade have long been a blackboard and a thin cylinder of chalk (preferably Hagoromo, the cult Japanese brand famous in the profession for its durability and lack of dust).

â€œThe paintings are their homes, their laboratories, their private spaces for reflection,â€ writes photographer Jessica Wynne in the introduction to *Do not erase: mathematicians and their blackboards* (Princeton University Press, 2021). The book features 110 images of chalk surveys conducted by mathematicians around the world – several affiliates of UChicago, as these pages show – along with their thoughts on chalkboards as a medium.

The project was started by married mathematicians from UCicago **Friend wilkinson** and **Benson farb**, Wynne’s neighbors every summer on Cape Cod. One afternoon, Wynne watched Farb at the dining room table take notes on paper (any port in a storm) and ponder symbols, drawings, and equations she couldn’t. discern the meaning. Not understanding the notes made them more intriguing, like a glimpse into a secret world.

The memory came back to her as she examined a series of photos she had taken in Jaipur, India, of Hindi lessons on chalkboards at a local school. In his eyes, the images had the same elegant and impenetrable quality as Farb’s calculations.

Wynne began writing to mathematicians at institutions near his home in New York City, requesting permission to photograph their paintings. They could share new or completed projects; his only rule was no whiteboards or glass.

The mathematicians’ own research remained a mystery to Wynne, but she came to see a connection between their work and hers. â€œThey have an increased aesthetic awareness, distinct styles and ways of using chalk, just like a visual artist,â€ she writes in *Do not erase*. “Some of the formulas are intensely chaotic, with explosive energy, while others feel neat, calm, serene and carefully considered.”

For all of these individual differences, she was also struck by deep similarities when she took photos in the United States, Europe and South America: Mathematics is the same everywhere, a common language pointing to universal truth. .

*Do not erase* attracted more attendees than she expected, and Wynne found that she rarely had to explain to her subjects why she was interested. â€œMathematicians have universally understood this,â€ she says. “Their reaction was, basically, ‘Of course math is good.'”

## Friend wilkinson

**Professor of Mathematics, University of Chicago**

â€œOn this chalkboard is a central argument in an article I wrote with Keith Burns (professor of mathematics, Northwestern University) about a mechanism of chaotic dynamics. It represents a sequence of shapes that, in a specific sense, are equivalent to each other, starting with a spherical ball and ending with what is called a julienne, named for its resemblance to a minced vegetable. We are proud of this paper; as Keith likes to say, one good article has a really new idea, and this one has two. Â»(See photo above.)

## Benson farb

**Professor of Mathematics, University of Chicago**

â€œThe main tool most of us use to communicate our ideas is the board. … A computer doesn’t help much with 40,000 dimensions, but on a blackboard I can draw a diagram of the situation, explain it in real time to a student or a collaborator. She can jump in and start writing on the board while I explain, altering my calculations, noting possible problems, breaking down some equations into a flurry of calculations of her own. Doing this dance on the board with someone is an intense, frustrating, energizing and sometimes moving experience.

## Paul Apisa, SM’14, PhD’18

**Donald J. Lewis Assistant Research Professor, University of Michigan**

â€œThere are two axioms that I would like to reject and which I imagine few people will oppose: first, mathematics can be complicated; and second, humans think slowly – or, to make the second axiom less grandiose, I think slowly.

â€¦ A virtue of chalk, and of the discourses that use it, is that it slows down a speaker’s Icarian desire to communicate too much, regardless of the comprehension capacity of the listeners. But perhaps the most important virtue of chalk is that it allows bad drawings. … it forces you to draw cartoons that only capture the essential features of a complex system and forces you to think about what exactly those features are.

## Ana Balibanu, SM’13, PhD’17

**Benjamin Peirce Fellow, Harvard University**

â€œThis painting has a schematic outline of a project on a family of geometric objects called Hessenberg varieties. An individual Hessenberg variety can be very complicated, even impenetrable. Instead, we need to consider all the possible Hessenberg varieties together and understand the relationships between them. Their geometry then becomes more precise through their interaction. The diagrams on the board illustrate these interactions. … Lists are speculation about where the results might go. (Looking back, some of them are true and some are not.) The painting is a snapshot of an exciting moment in the project – there are many uncertainties, but also many possibilities.

## AndrÃ© NÃ©ves

**Professor of Mathematics, University of Chicago **

â€œThe work on this chalkboard was developed in part with my collaborator, Fernando CodÃ¡ Marques, at a Thanksgiving dinner in Palo Alto in 2011. My wife and three year old daughter and our newborn baby enjoyed the party. while Fernando and I were obsessed with the Willmore Conjecture, a well-known problem that comes up with what should be the â€œoptimalâ€ shape among all donut shapes. Surveyors love to think about these kinds of questions.

## Simion Filip, SM’12, PhD’16

**Associate Professor of Mathematics, University of Chicago**

â€œThe chalkboard is an active space, ready to change and ready to carry any thought. It does not have the restrictive linear quality of written text, and it allows the user to organize the material according to its natural spatial characteristics. Compared to writing on a page, the chalkboard invites larger gestures and larger symbols. The larger physical space makes it psychologically satisfying to work on a blackboard.

## Clark Butler, SM’14, PhD’18

**Veblen Research Instructor, Princeton University**

â€œThe blackboard pictured here was created during discussions with Jairo Bochi, a mathematician working at the Pontifical Catholic University of Chile. The left side presents a motivating discussion for the problem we are considering. The right side is a set of equations governing the phenomenon we are studying. The middle is a visualization we created that shows these equations in motion. We have noticed that it looks like the pages of a book that we turn around its spine. â€¦ I think non-mathematicians would be surprised at how concrete our thinking is and how many analogies we draw with everyday objects and experiences.