Q: When you merge math and art in your work, which comes first?
They go hand in hand. The graphical user interfaces I program are investigative tools for me. They’re my experimental apparatus. They sometimes help me discover new mathematical results by helping me organize the information, keep track of data and mathematical constructions. Sometimes the things I discover using the programs lead to papers, while the program itself ends up being separate from the actual publication — just a sort of demonstration of the math.
This is something I’ve always done. I just always had this style. I like things with bright, flashy colors and interesting patterns. I try to make programs to efficiently answer the math questions I have, and I want the design of the interface to reflect the underlying mathematical structure. As a bonus, these interfaces sometimes produce beautiful pictures. The nature of the programs depends on what I’m working on. For example, different subfields of mathematics lend themselves more naturally to visual things.
Q: As both a mathematician and an artist, what are some similarities you see between the two fields?
It's an interesting question and I was thinking about this a lot recently because of the gallery exhibit. For one, both generate many types of images, albeit through different means. Many mathematicians use algorithms and equations. An artist has many different methods, of course. I talked in depth with the owner of the gallery about how another commonality is the repetitive motion you see in both. Artists will retrace things over and over again and make sketches and explore things before the final piece comes out. Mathematicians are like that, too. They'll draw the same picture over and over again and gradually mutate it. Practitioners from both disciplines seem to go through this iterative drawing process.
Of course, there’s also a common theme of creativity. On the art side, the creativity part is pretty obvious, but people often think of math as being set in stone — there are just these equations, and they're either right or they're wrong. That’s true, in a sense, but the way you discover the truth is often through creative attempts that involve a level of choice and risk similar to what you see in art.
Q: Speaking of the exhibit, can you share details about the pieces you created for display?
Over the years, these computer programs I’ve written end up having an extensive visual interface. For the show I made videos of the interfaces in action. I ended up making about 18 of them, and the exhibit shows about a dozen. One of them looks like an Alka-Seltzer. It is a bunch of dots in the middle and they diffuse out, filling up a region. This one was just for fun, meaning it isn’t so closely related to my research but I liked the mixture of chaos and order shown in the video: