Design + Mathematics: Math Outreach Design Lab

An image from a model created in an active learning course co-taught by mathematics professor David Gay and associate professor of graphic design Moon Jung Jang appeared as the cover of the October 23 issue of the Proceedings of the National Academy of Sciences.

The model in the illustration was created by 3 math majors and one graphic design major, working collaboratively in the course "Math Outreach Design Lab.” The story of how the course came about provides a great example of the collegial atmosphere between art and STEM faculty on campus, especially as UGA hosts the Alliance for the Arts in Research Universities national conference for the first time.

Gay explained that the collaboration goes back two years to when he was invited to be the "mathematician in residence” by Ideas for Creative Exploration director Mark Callahan, who encouraged Gay and Jang to meet and talk at ICE.

“I relished my Friday mornings in the art school talking to Moon and Mark and whoever else came by and drawing topology pictures (knots, surfaces, schematics of 4-dimensional objects),” Gay said.

Soon after, math department associate head for undergraduate affairs Jason Cantarella asked Gay to pilot an experiential learning course. “I immediately thought of a course in which students make physical objects that could be used in a math outreach context, the idea being that in the making process they would learn some math, solve some hard problems, and think carefully about math in a larger context.”

“Working with Moon, we came up with the collaborative course idea, since I knew that by myself I couldn't get the high-level design outcomes I really wanted. We ran one Saturday afternoon pilot project that spring (with support from ICE), and then we had a pretty good picture of what we wanted to do.”

"Unsolved: Math + De-sign” was an inter-disciplinary workshop in April 2017 for math, art, and design research, with the goal of making a product to be used in math outreach contexts. The idea was to engage the public in thinking about unsolved problems in mathematics, such that participants could take part in problem-solving to discover the intersection between math and design. 

“The workshop really made us move forward and led us to the collaborative course,” Jang said.

The collaborative course was titled "Mathematics Outreach Design Lab." Jang and Gay wrote the syllabus together and developed the course as they went through the semester.

The course stressed the importance of making prototypes in design practices, and students made different kinds of prototypes at every meeting: Drawings defining the math problems, questioning and answering in group settings, understanding visual sequences and building them with paper, developing the prototypes with different materials, testing, refining designs and finalizing designs, and making them with actual materials or printing the designs, and finally presenting the outcomes. 

“During the semester, Dave and I contacted the Athens Library to schedule an exhibition with the design outcomes from the course because one of the objectives was to reach out to the public. We wanted to share the outcomes with the local people and children at the library,” Jang said. However, when scheduling proved too difficult, the show was ultimately held at C-U-B-E, the experimental design lab and gallery at the art school. 

The cover illustration is based on one of many outcomes of the course; the theme of the course ended up being focused around knot theory in dimensions three and four, which was directly relevant to the theme of this PNAS special issue. 

The actual model is closely based on Figure 1 in a paper by UGA mathematics post doc Jeffrey Meier, and Alex Zupan (U. North Dakota); the two took an idea coming from Gay’s research with Rob Kirby (UC Berkeley) and generalizing it to the setting of surfaces in 4-dimensional space. “This nexus of ideas (mine and Kirby's on "trisecting" 4-dimensional spaces, and Meier and Zupan's on trisecting surfaces inside 4-dimensional space) has sparked a small industry of math research over the last few years, leading to a workshop at the American Institute of Mathematics in Palo Alto in the spring of 2016, and that workshop led in turn to this special feature of the PNAS - all the trisections papers in the PNAS feature come from work done at that workshop,” Gay said.

“As the special feature was nearing completion, PNAS asked us for a cover image, and the initial reaction amongst the various authors was to take one of the illustrations from one of the papers, fairly typical computer-drawn topology illustrations - that could have been pretty good but I thought, why not a photograph of this beautiful model our students made? So the other authors and the PNAS production staff liked the idea, and then the hard work of making the photograph happened - really Moon gets the bulk of the credit for that - the devil is in the details - I could take a decent picture but not a beautiful picture perfectly framed and lighted. Moon had the brilliant last-minute insight of inverting all the colors, after looking at all these other flashy microbiology oriented PNAS covers with dark backgrounds and fluorescent molecules or strange organisms, and so on - in the end the math almost looks like it comes out of a biology lab!”

Image courtesy of David Gay, Moon Jang, and Dayna Tang