Frank A. Farris, associate professor of mathematics and computer science at Santa Clara University, is a mathematical artist and author of the upcoming book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. His talk on Thursday, titled “Seeing Symmetry: A Talk About a Mathematical Art Show,” discussed the mathematical concepts behind art.

What interests you about the intersection of mathematics and art?

That’s a hard question. What I found is that my study in mathematics led me to situations where I was wanting to produce illustrative diagrams. And it was only very gradually, over a course of really almost 20 years, that I realized that there was artistic potential in these mathematical diagrams. And then with that came a massive desire to make them — the diagrams — as beautiful as I could, and so that brought me to wanting to produce visual art. So for me it very much started with an interest in certain mathematical things, and then that drew me.

I’ve always been interested in visual art. My mother was a watercolorist, and so I feel that I have some background in it, but I never thought of myself as a person who might produce visual art. So this has been a very interesting journey.

What are the main concepts of mathematical art? What makes it aesthetically pleasing?

I can’t answer about mathematical art in general, but I do have something that I like to say about my own art … A lot of computer-generated art looks like a computer made it, whereas my art has a certain organic feel to it. So a phrase that I use to describe my own work is, I call it “symmetric yet organic.” Because often when we see things with symmetry, they might look to us like rigid crystals or patterns with a very harsh rhythm, and my work has a more gentle rhythm to it, because it’s made from waves. It’s made from mathematical things called wave functions.

Is mathematical art a relatively new practice, or is there a lot of historical background behind it?

In the past there have tended to be artists that used a lot of mathematics in their art … It’s well-known how Italian Renaissance artists needed to use mathematics when they desired to make a building look exactly right in perspective. Albrecht Dürer is a German example who just used so much mathematics to make his work look precise, the way the world does. Then, in the 20th century, M.C. Escher was an artist who learned from a mathematician to put mathematics in his art. But those are more situations of artists using mathematics to advance their craft, and it does seem to me relatively recently that there have been mathematicians that realize that their ideas can inspire works of art, and so it’s created greater collaboration. There’s an annual conference called the Bridges conference. … They describe themselves as wanting to draw together mathematicians with artists of many different kinds, not just visual artists, to explore connections. It’s, I would say, a growing field.

Do you think this kind of popularity and mathematical art’s relatively recent conception influences people’s perceptions of math?

Yes. There’s a new museum of mathematics in New York City, and they’re very aware of the value in producing displays that attract people’s interest to mathematics. So I think that a lot of people are aware of the aesthetics. We really want to draw people into mathematics to show them that it’s a human activity and … show people who are potentially interested in mathematics that this is something approachable and interesting and fun. Visual beauty can be a way to attract people. I think it’s only one of many ways, but the mathematical community has a great desire to welcome other people into our enterprise. We want to be seen as welcoming, and to intro[duce] participation of different kinds of people who maybe haven’t traditionally thought, “Oh, yeah, I could be a mathematician.” I hope my work serves to attract people to [an] interest in mathematics.

Do you think that art which doesn’t have an expressed interest in mathematics expresses mathematical concepts?

Yeah, there’s really so much variety. It’s a really big question, but there have been artists who I think almost unconsciously are addressing mathematical ideas. Think of some of the minimalists of the middle of the 20th century … I guess another thing is that any art that is meant to represent. So like that painting there, it’s a representative idea [in which] the artist, whether they knew it or not, was intending that your eye should be at certain point in relation to that painting. There’s this interesting computation in mathematics where you can look at a picture and do a computation, and figure out where you should put your eye in order to have it look its best. So that’s a way that, in any art that’s representative, there’s some math you can do on it to help you understand it better. [It’s a] funny little thing.