Mathematicians’ chalk experiments captured as art in photographer Jessica Wynne’s new book

Friend wilkinson

Professor of Mathematics, University of Chicago

“On 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. ”

Benson farb

Professor of Mathematics, University of Chicago

“The board is the primary tool most of us use to communicate our ideas. … 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. Doing this dance on the chalkboard 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

“There 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.

… A virtue of chalk, and the discourses that use it, is that it curbs a speaker’s Icarian desire to communicate too much, regardless of the listeners’ ability to understand. 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 characteristics of a complex system and forces you to think about what exactly those characteristics are.

Ana Balibanu, SM’13, PhD’17

Benjamin Peirce Fellow, Harvard University

“This 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.

André Néves

Professor of Mathematics, University of Chicago

“The work on this chalkboard was developed in part with my collaborator, Fernando Codá Marques, at a Thanksgiving dinner in Palo Alto in 2011. My wife and our three-year-old daughter-to-be and our newborn baby enjoyed the partying while Fernando and I were obsessed with the Willmore Guess, a well-known problem that comes up with what should be the “optimal” 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

“The 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

“The 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 are wrapped around its spine. … I think non-mathematicians would be surprised at how concrete our thinking is and how many analogies we draw with everyday objects and experiences.

—This story was first published by University of Chicago Magazine.

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