Feeling GROVI: Research at the intersection of design, art and mathematics

Article by Francis Oliver

Mathematicians and visual artists seem like ready partners — both playfully think about space and symmetry. But how do they bring this shared vision into focus? Two University of Georgia faculty members found a way through a free yet elegant exploration of design, transforming multi-dimensional twists and knots into compelling objects and works of art.

Designer and artist Moon Jung Jang met mathematician David Gay through the UGA Arts Collaborative, a research incubator that encourages collaboration across the arts and sciences, and between the university and the Athens community. Since 2017, the two professors have engaged in design workshops, co-taught an interdisciplinary course, and curated a student exhibition weaving mathematics and design.

In 2020, UGA awarded Gay and Jang with the Creative Teaching Award, recognizing their “excellence in developing and implementing creative teaching methods to improve student learning.” Their innovative pedagogy culminated most recently in GROVI (Geometry, Research, Outreach and Visualization Initiative). GROVI (pronounced “groovy”), an umbrella for a variety of creative projects that will involve students and faculty in math and design, is funded by a recently-awarded five-year National Science Foundation grant for the Geometry and Topology group.

Jang’s research in parsing visual languages for multiple and transforming narratives fits closely with the knotted diagrams of Gay’s research in the field of topology.

“I have been interested in the simultaneous, multiple existences of something, contradictory ideas about unseen things, and their information in everyday life,” said Jang, associate professor of graphic design at the Lamar Dodd School of Art. “Finding patterns of objects and anticipating their behaviors are the keys to building visual narrative systems. Dave is a storyteller who discovers narratives of objects, imagining their potential transformations in topology. Our collaborations aim to uncover memorable expressions to reach more audiences.”

Topology, a branch of mathematics that explores continuous deformation of space — say, a rubber band stretching and twisting — has inherently aesthetic qualities. The language of topology describes properties that remain the same between distinct spaces using schematics and drawings. Physicists, data scientists, neuroscientists, and many other specialists apply the results of topology to understand complex, interwoven phenomena.

“I work in a field loosely called Geometric Topology, where we engage some kind of fundamentally visual, spatial reasoning and inspiration. A pretty picture alone does not result in a theorem, but having that pretty picture makes the theorem feel much more elegant and impactful,” said Gay, professor in the department of mathematics. “How then do you communicate that inspiration in a way that also carries all the mathematical rigor necessary? I’ve learned from working with Moon and her students in design that this process can actually be made intentional and thought about in a fairly coherent way. There is a whole world of problem solving in the visual design communication context that mirrors and elegantly reinforces the problem solving I do in proving theorems.”

To a casual viewer, the drawings that a topologist scribbles on a chalkboard or in a published article to make a mathematical argument are a foreign language yet somehow more approachable than a sequence of equations. Jang and students in graphic design at the School of Art have enlisted a variety of materials — from laser-cut wood to metal type on triangle-shaped pages of a book — to interpret these abstract objects and learn what makes their twists and curvature beautiful and profound.

The latest activation of this collaboration debuted in November at the UGA McBay Science Library in the exhibition Spacing Out: Art and Topology Pop-up Museum. Coordinated by the UGA Department of Mathematics in tandem with the UGA Arts Collaborative, the show features fabric arts, 3D animations, and more. Works on view include two glazed ceramic pieces — one a sphere with a knot at its apex, the other composed of two flat planes knotted at their intersection — presented as the same topological object: a Seifert Surface. Another series of cartoonishly large fabric knots in turquoises, yellows, and purples in a glass display case present a sequence of basic knots cataloged in the field of knot theory. In a drawer below, a series of small folded zines, i.e., a self-published magazine, titled “Notes on Topology: Unraveling Topology” are free for the taking, with instructions on building a Möbius strip with a half-twist (tracing the band by finger will reveal that the inside and the outside are the same continuous surface).

Organized by mathematics doctoral students Alexander Tepper and Han Lou and Professor Gay, with assistance from art students and alumni, Spacing Out is part of an ongoing effort to advance visualizations of intriguing geometric phenomena.

UGA graphic design student Charlize Carlisle led the final exhibition design of Spacing Out. “Working with Dr. Gay, Alex and Han allowed me to gain various perspectives on the exhibition’s pieces,” said Carlisle. “Their passionate motivation helps observers learn and appreciate topology. From a design perspective, selecting various elements that are cohesive is fulfilling and lends the project a strong hands-on element.”

Over the next five years, GROVI will support various working groups of mathematics and arts students and faculty to reflect on design principles and the principles of rhetoric to “collaborate procedurally.” Whether they produce objects for display to invite fresh perspectives and understandings of topology or conduct material experiments to discover new art techniques like adding a half-twist to a plank of wood, GROVI will support both design and mathematics research by exploring how thoughtful shifts in approach can make all the difference.

“There are barriers to engaging with abstract mathematics for people outside the field and there are not many avenues for those with casual interest to engage,” said Tepper. “Mathematicians by and large want to share, and these artists bring craftsmanship, material expertise, and mindfulness of visual communication. The process of ideation, prototyping, and refinement by artists in the development of these objects is similar to a mathematician’s process. The objects they have contributed reach out across the room and invite people to admire, wonder, and just space out for a bit.”

Spacing Out: Art and Topology Pop-up Museum was on view at the UGA McBay Science Library November 1-December 1, 2024 as a part of the UGA Spotlight on the Arts Festival. A portion of the work will remain on view through February 2025.

For more information or to participate in the GROVI project, contact David Gay at dgay@uga.edu