As a mathematics student, I spend a lot of time in front of a traditional blackboard watching equation after equation be written and erased, written and erased. While the equations I encounter this way are used to rigorously communicate mathematical concepts to a group of students, they can also be mesmerizing just to look at. In lecture, I often find myself suddenly captivated (distracted?) by the script as it appears in front of me–chalk gliding across the chalkboard as it traces out the curvilinear script of greek letters and other mathematical symbols, sometimes lazily, other times with such fervor it suddenly snaps, waking me from my daze and bringing me back to the classroom.
Over the years, I’ve also noticed that each professor will fill the blackboards in their own unique way. Some choose to place only a single concept at the center of each board before moving on to the next, and others fill each one with scrawling text and diagrams. Much like a writer, each professor curates their exposition according to his or her own taste. What appears on the board are the symbols and surrounding prose that each mathematician has deemed essential to understanding.
When I learned of the exhibit Concinnitas: Prints by Physicists and Mathematicians at Nancy Hoffman Gallery, I was excited to see if this elusive aesthetic could be captured and communicated successfully to an audience of non-mathematicians. Is it possible to really give people who haven’t spent years of study a glimpse of this mathematical aesthetic?
This exhibition is part of the larger Concinnitas Project curated by Daniel Rockmore, a professor of computer science at Dartmouth. The portfolio contains ten prints based on the mathematical drawings of highly-esteemed physicists and mathematicians. Each contributor was asked to produce what they consider to be the “most beautiful mathematical expression.” Their creations were then published as aquatints, white print on black background, reminiscent of the blackboard. The complete collection of works on display can be viewed in the Concinnitas Portfolio.
The list of contributors is impressive: Michael Atiyah, Enrico Bombieri, Simon Donaldson, Freeman Dyson, Murray Gell-Mann, Richard Karp, Peter Lax, David Mumford, Stephen Smale, and Steven Weinberg (links provided to mathematicians and physicists I recognize). While the list is comprised only of men, this is hardly the fault of the curator as so far there has only been a single female winner of a Fields medal to date, and many of these contributors have either Nobel prizes or Fields medals.
Also included in the project is the Concinnitas Studio, where anyone can submit their own equation representing mathematical beauty. While sparse at the time of this post, I’m looking forward to seeing the list fill out with additional equations and mathematical ideas.
When I rounded the corner and entered the middle exhibition room of the gallery, I was pleasantly surprised by what I saw. Given that the works were carried out by ten different individuals, I had worried that there might be that usual group show feel: a hodge-podge of works that normally wouldn’t appear all in the same room all cuddled up next to each other, or perhaps fighting each other for space on the walls. Instead, the prints are uniform in size and presentation, though the orientation varied depending on how each ‘artist’ chose to depict his mathemtical concept.
The space felt uncluttered, allowing me to walk freely from one mathematical concept to the next, unhindered by distractions. Most of the pieces themselves were sparse in presentation, displaying clearly a central concept or idea in mathematics, even if the symbols themselves remained undefined and incomprehensible to all but a few mathematically-inclined individuals who happened to enter the exhibition space. Next to each work was an ‘artist’s statement’ made by the physicist or mathematician who chose the equation. Even with the descriptions, mathematics is such a vast field that a mathematics Ph.D. student such as myself found many of the equations impenetrable even with the accompanying explanation.
But this didn’t bother me. I got to feel that same way I do in the classroom of a prestigious mathematics department, in awe of the great minds that stand at the board in front of me, writing equation after equation. It was exciting to me that this exhibit gave others a glimpse of this same experience.
Concinnitas gives a sense of a bird’s eye view of mathematics. All of these disparate topics depicted succinctly in the same room give the viewer a chance at gazing upon a vast range of mathematics all at once. Viewing the entire portfolio, we see singular equations, a collection of equations grouped under a heading, graphical structures, and topological drawings. Some equations contain numbers while others only symbols, curvilinear in their elegance or a forest of greek letters.
Even if one does not understand the exact meaning of the symbols, there is something about the tangible nature of the prints that is accessible. Perhaps the number of symbols required to communicate the idea gives some insight into its complexity. That some require a diagram and cannot be summarized by a simple equation betrays the elusivity of the nature of an open problem in mathematics. Some prints contain headings written by the mathematician which I argue detracts from the beauty; others I spoke to seemed to feel that this gave a context and more immediate context for the mathematics.
While it’s impossible for me to step outside of my understanding of mathematics and to see these works as purely aesthetic, what I do know is that I walked away from this exhibit feeling as if I had viewed true works of art. Conceptual art, yes, but the execution of the project was such that it felt like art nonetheless. Not illustration of mathematical ideas, not an artist’s interpretation of a mathematical concept, but unadulterated mathematics as art.