James F. Clark Professor of Mathematics Robert (Bob) Bosch, OC ’85, is fascinated by the interactions between mathematics and art. He currently uses optimization techniques to create pictures, portraits, and other works of art. Bosch is the author of Opt Art: From Mathematical Optimization to Visual Design, an illustrated introduction to the art of linear optimization.

This interview has been edited for length and clarity.

What drew you to teaching math? 

I was always interested in something to do with creativity. In my junior year at Oberlin, I took a class that really resonated with me. It was a class that’s now called Optimization, my specialty. I realized at the time that there’s a mathematical field that aligns well with the way I think. If I go out in the car and I have errands to run, I naturally ask myself, “In what order do I make these stops?” There’s a whole branch of math that is studying these types of things that I kind of naturally am interested in. That was a transformative moment.

I then went to grad school and did very theoretical things, but then I came back to Oberlin to teach. I was continually thinking, “How can I convince my students that this branch of mathematics that I love is so great?” I thought, one way to convince them that it’s terrific is to show that it’s applicable in so many areas, including areas that you wouldn’t think it would be possible to apply it in, like designing artwork. 

Can you tell me about how you decided to start using math to make art? 

I was really inspired by this Bell Labs engineer named Ken Knowlton. He was making mosaics out of complete sets of dominoes. Fast forward to when I’m teaching here, I was browsing through the stacks at Mudd and found this book that had a Ken Knowlton domino mosaic on the back cover. At that moment, I said, I know how to do this. It wasn’t the same way that Ken Knowlton did it, but it was using the type of math that I had studied in grad school. I tried it myself and became obsessed with it. You continue to tinker with your ideas: if I do it a slightly different way, how’s it going to turn out if I make this change? After a little bit of time, I’m starting to consistently put out things that I think look good. I can share them with more people than I could before. 

I could talk to anyone and share with them my love of math. You could get people who were not even interested in math to see that math could be used for things that they didn’t imagine. I was invited by people at Spelman College to do a domino mosaic of one of the retired faculty members, a woman named Etta Zuber Falconer. She had taught there for 37 years, so I designed this big domino mosaic made out of 37 complete sets of dominoes. I unveiled the plans there and gave a talk, and later the students there built it out of actual dominoes. 

Then the guy who hosted me said, “Well, would you be willing to come and speak to my child’s fourth grade class tomorrow?” And I did. I essentially gave the same talk, but I didn’t get into all the mathematical details. I took out all the equations and all the intense mathematical content and shared the pictures. I had a great conversation with these fourth-graders. Later that day, I went and spoke at Georgia Tech to a group of grad students. Same pictures, just put back the equations and talk in more detail about the math. It’s just been fun to be able to share my passion for this stuff with wildly different groups of people.

How do you decide what you want to create next, and how does it progress from there?

I’ve been doing this for 25 years now. The first project was the domino mosaics, but I’ve branched out into other things. Basically, I’ll have some idea for some interesting way to take a familiar image and approximate it in some kind of mathematical way. Some examples are Andy Warhol’s Campbell’s Soup Cans and the Celtic Knot — both single line drawings. I found a source image. I then approximated that source image with 25,000 black dots on a white background. You need to write software to do what artists call stippling. I view these 25,000 dots as locations for the giant Meals on Wheels delivery program and then use software to figure out the best possible route that I can find. If I make it so that the total length of that path is as short as possible, the resulting single line drawing will look, hopefully, very much like what you start off with.

 My favorite pieces are ones where I assert through the continuous line drawing that two or more people are connected. There’s an old family photo of me and my dad. My dad died just after I was six years old. There’s a photo that was taken when I was five. We’re on a seesaw, opposite ends. It’s a single line that goes through me, goes through the seesaw, goes through him, and because all these intricate tours are essentially distorted circles, and because circles for thousands of years in various cultures have been used to symbolize eternity and connectedness, I view that piece as asserting that my dad and I are still connected. So I think it has some real emotional depth to it. 

I’ve done pieces for people in town who’ve lost a loved one. I’ve done pieces as wedding gifts. When I’m pairing two people and drawing them with one line, I’m asserting that they’re connected, or a group of people are connected. 

Tell me about the knight’s tour method of creating art.

In chess, you have the piece that’s the knight, who moves in the most unusual way of any of the chess pieces. The question that people have been interested in for over a thousand years is, if you put a knight somewhere on a chessboard, can you make it so that they visit each square of the board once and then return back to where they started? I come in every two years and share whatever knight’s tour images that I’ve made. Each is a 5×5 array of knight’s tours, and each of the component tours are sometimes in rotated or reflected form. I’m fascinated by how these kinds of patterns emerge. Even though they’re made out of straight lines, you get these curvy patterns popping up. How does that happen? It’s a mystery, and I find it endlessly fascinating. There’s probably more of these tours than there are stars in the entire universe. It’s impossible for a human being to see each and every one, even if we lived hundreds of thousands of millions of years. So how do you develop software to find the best ones? And what do you even mean by best? These are the types of questions that interest me. It’s an obsession.

Is there anything else you would like to say today for students; for anyone interested in math or art? 

I’m a big fan of interdisciplinary work. Think hard about what it is that you could take here at Oberlin that you won’t ever have a chance to study again. One piece of advice I give to my advisees is talk to your friends and ask them, is there any professor here who you would say that every student should take a class with? Try to take a class with them. There’s so many amazing faculty here.