Illustration of golden ratio

Illustration: Benjamin K. Shown

In 1990 I was in the middle of a traditional academic career, teaching philosophy and logic at San José State University, when I received a call from a friend that changed my life. The Western Association of Schools and Colleges, the folks who accredit West Coast institutions, had just visited the California College of Arts and Crafts (now CCA) and informed them that since they granted the BFA degree, every student was required to take a mathematics course. Would I be interested in becoming the CCAC “math guy”?

When I interviewed with the Dean, he told me I had two responsibilities: (1) Make sure the course(s) had enough mathematical content to satisfy WASC, and (2) Make sure the courses were interesting enough so that my students didn’t occupy the President’s office. As a big believer in the McLuhan dictum that “Those who try to draw a distinction between education and entertainment know nothing about either,” I figured I could handle (2). As for (1), WASC never complained; occasionally a student did, but I guess not at the Presidential level. Here’s how I did it.

First, I set out to convince my students that, at their essential cores, mathematics and art are engaged in the same vital, important, intellectual activity—interpreting the fundamental nature of both the universe and our place within it. Second, since it would have been inappropriate and impossible to teach a traditional algebra, geometry or calculus class, I tried to help my students understand how mathematicians approach problems, the types of questions they ask and how such strategies might be applied to artistic endeavors. The capstone course requirement was always an individual project relating art and mathematics that was shared with the entire class.

Artists and mathematicians are entwined in a complex, five-stage relationship:

01 Shared Tools

Every form of human activity uses mathematics as a tool—for counting, measuring, modeling. Try stretching a canvas, annealing glass or designing a building without some pretty sophisticated mathematics. Similarly, mathematicians engage in visualizations (non-Euclidean spaces, topological transformations, higher dimensions) that seem as much art as mathematics.

02 Mathematical Foundations

Like the hard sciences, the foundations of many of the fundamental concepts of art (e.g., perspective, proportion, symmetry) are mathematically based. Frank Gehry seems as much an applied mathematician as an award-winning architect.

03 Mathematical Inspiration

There are no limits to what any artist may choose to depict, so it should not be surprising to discover that many artists have found inspiration in mathematical concepts and ideas: Phidias, Leonardo, Dürer, Kandinsky, Escher and Le Corbusier not only created works inspired by mathematics, they also wrote treatises explaining the role of science and mathematics to the arts. Today, those in the Cyber-Arts movement, with their interest in chaos theory, fractals and computers, are sometimes hardly distinguishable from the mathematicians working on those very subjects.

04 Epistemology

Artists and mathematicians are both problem solvers in search of beautiful, truthful, elegant solutions. As they seek their solutions, artists and mathematicians may both profitably ask themselves:

What are the ground rules? What limits do they enforce? What if I change something? How can I sort, organize, group and visualize information? Is there a pattern? Will the trend continue? What are the maximum and minimum extents of the problem? The solution? What are the possibilities? Am I missing something? What strategies are available? Is there a different way to approach the problem? How are resources employed? What if I build a model and then understand how it grows to scale?

Given their applications of similar epistemic processes and goals, artists and mathematicians may be uniquely suited to judge the quality of each other’s work.

05 Metaphysics

Does the work of mathematicians tell us more about the inner workings of our own minds or the outer workings of the universe? Similarly, should artists be credited with inventing totally new ways of seeing or merely with discovering already preexisting modalities? Such questions may have no final answers. But this much is clear: Mathematicians and artists are engaged in the ultimate act of imagination—creating something out of nothing.

Finally, we need to do more than simply understand the affinity these two disciplines have for each other. We need to incorporate their modus vivendi into our own lives. For how else are we to define the good life, and live it with grace, if we leave the creative act and appreciation of beauty to specialists?