Beauty in Numbers: Stephen Ornes on ‘Math Art’

Math and science writer Stephen Ornes, winner of a AAAS Kavli Science Journalism Award in 2015, has always found beauty in mathematical concepts. “The mental exercise of going through Euclid’s proof of the infinitude of the primes felt as exhilarating as listening to Beethoven's Ninth,” he says.

In his new book, “Math Art: Truth, Beauty, and Equations,” published in April by Sterling, Ornes introduces us to art in which mathematics is expressed in paintings, sculpture, weavings, quilts and other media. The artists he chose to write about created their art based on mathematical ideas.

“Many of the artists describe their process as being more akin to discovery than invention,” Ornes writes in the introduction to his book. “They feel, at some level, that they're giving material form to something big and deep and eternal, ideas and connections that existed before their thoughts took them there.”

In the following Q&A, Ornes discusses his evolution into, and fascination with, the world of mathematically inspired art.

You studied English and physics in college. Like the math artists in your book, were you in a sense someone who chose not to choose between English and the humanities on one hand and math and science on the other?

Yes, definitely. I wrote a lot of fiction and plays during college and in the years after, but they often revolved around ideas from classical and quantum physics. Characters could appear in two places at once, for example, or take on different appearances. Some would follow narrative arcs that were deterministic and predictable in some sense. I think those stories may have helped me process the counterintuitive ideas I had to learn in my physics classes.

Did you have career plans when you were in college, and in grad school when you were studying applied math?

Not really. When people saw what I was studying, they often assumed that I wanted to write textbooks, but that was never appealing to me. I was always writing something and enjoyed studying literature, but physics was endlessly fascinating. Right after school, I taught — first at a charter school in Dallas and then at the International School of Barcelona. After graduate school in math, I went back to teaching math, in Connecticut, and loved it. 

When did you decide to become a writer?

It was less of a decision than a compulsion. I’ve been writing stories and essays my whole life, but I couldn’t figure out how to write for a living until a friend pointed out that someone had to write the stories I read in Discover and Scientific American and the specials on public television. Why not me? 

How did you get interested in the intersection of math and art?

When I studied math in grad school, I thrilled at the elegance of some proofs and definitely felt a kind of emotional excitement at understanding how they fit together. It seemed aesthetic, but in a very abstract way.

I think the first writing I did on math and art was a really short review about Bathsheba Grossman about 12 years ago. She’s a pioneer in 3-D printing, and was using the technology to create these beguiling, textured sculptures of shapes with spectacular symmetries. I’d never seen anything like it. Since then, I’ve been lucky to find editors who are interested in the intersection and let me write about it.

What sort of audience did you write the book for, and how do you think a general audience will relate to it?

The math curious. The ones who look for patterns. The ones who have always seen some semblance of order and rhythm and beauty behind the certainty and logical pleasure of math problems. As I was writing, I was so buoyed by excitement that I just thought, who wouldn't be thrilled about math art? 

I do think it will appeal to a general audience if they give it a chance. My hope is that my excitement and enthusiasm about what these artists are doing is clear enough that anyone can get excited about the topic, even if just for a few pages. I’ve heard from mathematicians, digital artists, and math teachers that the book makes them feel validated in their love for math. I also hope the book can speak to people who struggled with math as it's usually taught. I hope it offers another access point to appreciate math.

Is the connection between math and art something that children should learn as they start studying math?

Absolutely, I think it’s something that kids can respond to even without knowing equations or proofs or anything. [Math artist] George Hart really believes this — he said something to the effect that kindergarteners are natural mathematicians. They’re delighted by symmetry, are naturally curious, and get excited when they look for patterns. Mathematics is in a way the quest to see and understand fundamental patterns. There’s no reason math has to be introduced only as the class where you memorize multiplication tables or the names of shapes. 

What intrigued you the most as you did research for the book?

The diversity of stories and perspectives. It became clear that even though I was including these artists under the broad umbrella of “mathematical art,” their styles, stories, inspirations, and mathematical perspectives were delightfully individual.

What drove your selection of artists for the book?

I started with a master list of people I already knew about, then solicited suggestions from artists and mathematicians. Then I whittled the list down to include as many mathematical subfields as I could, and to include works that I had some emotional response to. I didn't include pieces that were only visualizing some math idea; I wanted to include pieces with an added aesthetic consideration, where the artist seemed to have something to say — maybe not in words, maybe in geometry — about the math. I'm not an art critic. I only wanted to write about pieces to which I had an emotional response. 

In your book, you refer to Dürer, da Vinci and the Greeks, pointing out that they used mathematics to explore ideas about anatomical beauty. You also of course mention Escher. Could you tell me how the post-Escher math art you chose to write about is new and different?

The works I chose are different because they’re driven explicitly by ideas in math. Escher gave visual form to these paradoxical ideas about impossible worlds made possible. He wasn't driven by the ideas of math — he later discovered the way in which his works were mathematical in spirit. But he wasn’t a mathematician. Many of the artists in my book talk about their connection with Escher’s art, but what they’re doing, for the most part, is more intentionally focused on representing these heady ideas.

Were you always so taken with the beauty of certain mathematical concepts?

Yes, definitely. I mentioned Euclid’s proof of the infinitude of the primes as one example. It’s just so clean, and so intuitive. I also love the fact that even though the Pythagorean Theorem was proved thousands of years ago, mathematicians continued to come up with new proofs. Hundreds of proofs. I also see a kind of elegance, challenge, and beauty in unproved statements, like the Goldbach Conjecture, which says that every even integer larger than two is the sum of two prime numbers. It’s so easy to state, but it shows the limitation of what we know. There’s beauty in not knowing — a kind of temptation and itch that needs to be scratched, too, but also a kind of beauty.

What were the most surprising or unexpected examples of math-driven art that you came across?

The weaving patterns introduced by Ada Dietz caught me completely off-guard. She’s one of the only artists in the book who’s not still alive today, but her work just seemed too fascinating not to include. She expanded algebraic expressions, and then used those expanded expressions to determine settings on her loom. The patterns are unlike any other woven things I’ve seen. Her work is a great example of how handwork can be so closely and intimately tied to interesting ideas in math.

You have said that art inspired by math is a growing field. Why now?

Galleries across the country are hosting more math art exhibitions every year; and math artists are publishing monographs and books of their work. In addition, I’ve seen growing interest in combining math with poetry, and with dance, and other arts. I’m not sure why now, but I’m glad it's happening. Maybe it’s because all these artists are finding each other, and establishing community, and offering support to younger, emerging artists as well. Maybe they have time to indulge these ideas. Or maybe the time is ripe for these ideas to finally come together.

[Associated image: Courtesy of Bathsheba Grossman]