Start with Art

By Eve Torrence

Eve Torrence holding her sculpture Blizzard Three.
Photo Courtesy of Randolph-Macon College.

If music and math have so much in common, why do so many people love music but hate math? This is a paradox that mathematics should exploit as a way to improve our image with the public. Dare we have the courage to be loved? Schoolchildren study both math and music. Both involve learning abstract notation and practicing applying that notation. Both require hard work for success. But music is often a special weekly treat that children are excited to explore, while math can become daily rudgery. This is, of course, not universally true for every student or every classroom. And I do not mean to diminish the great progress that has been made in mathematics education. Yet we could do much more to improve the image of mathematics as beautiful and worthy of enjoyment.

Music can be appreciated on many levels. Even infants seem to enjoy music. Why not mathematics? Perhaps our approach is wrong. We don’t make children learn music composition before they ever hear a tune. Why can’t we introduce students to a beautiful piece of mathematics at a young age?

The growth in the field of mathematical art may be a step in the right direction. Here is a way to express the beauty of mathematics in a way that is accessible to everyone. It is the perfect visual balance to music’s auditory appeal. With modern technology, we can produce images and objects that demonstrate complex concepts in ways that had been impossible. If you have never seen the Exhibit of Mathematical Art at the Joint Mathematics Meetings, your mathematical education is incomplete. Luckily the computer age not only makes many of these pieces possible, but it also makes them possible to view at bridgesmathart.org/bridges-galleries/art-exhibits.

Mathematicians know that mathematics is a creative subject, but other people laugh at this idea. How can there possibly be creativity in mathematics? Most people are never exposed to this concept, let alone see a demonstration of it. Yet everyone knows that music is a creative endeavor, even if he or she has never studied an instrument and cannot read music. The time has come to open up access for all to the creative world of mathematics.

Not everyone has the opportunity or desire to learn about hyperbolic geometry, but everyone can enjoy Start with Art AFTERMATH Escher’s Circle Limit prints. We should accept this as legitimate math appreciation. The difficulty of our subject is not a valid excuse for our sometimes-elitist attitude toward its enjoyment. Those who want to explore the concepts exhibited in a piece can delve into the topic as deeply as they wish. Not everyone needs to understand music theory to appreciate Bach. Not everyone needs to understand circle packing to appreciate what Robert Lang can accomplish in origami (see http://bit.ly/1TWQrQK).

But anyone can appreciate that Lang’s work is an extraordinary accomplishment made possible through his knowledge and application of mathematics. And seeing Lang’s work has drawn many students into studying the mathematics behind his art. How many students might be drawn to studying mathematics if we could change the way they think of our subject?

We need to expose the public to the fact that mathematics is not simply arithmetic and polynomial factorization. The arts are a way to shed light on the diversity, creativity, and progress of modern mathematics. Every schoolchild should have the chance to see mathematical art. Perhaps someday mathematics, like music, will be thought of as a subject for lifelong interest and enjoyment. It is never too late to learn to play the piano—or study field theory.

Eve Torrence is a professor of mathematics at Randolph-Macon College and past president of Pi Mu Epsilon. She loves the symmetric beauty of polyhedra and sharing mathematics through her sculptures. Email: etorrenc@rmc.edu