Stephen Ornes has always found mathematics attractive. The journalist has written articles about the discipline, but lately he has focused on the startling visual attractions created by artists who follow mathematical rules of group theory or rotations. Ornes gave Scientific American readers a gallery of such images and sculptures in “Art by the Numbers” in the August 2018 issue. Now he is back with a larger collection in his new book titled Math Art: Truth, Beauty, and Equations (Sterling Publishing, 2019). In it he explores dozens of artworks that stem from principles behind the number pi, the puzzle of the Traveling Salesman Problem, esoteric geometry, and more. Recently Ornes spoke to Scientific American about the aesthetics of math and some of his favorite pieces in the book.

[An edited transcript of the interview follows.]

Art and math do not usually occur in the same sentence. How did you make the connection?

Years ago I was interviewing Bathsheba Grossman, an artist who uses three-dimensional printing to make mathematical sculptures out of metal. She was working with surfaces that minimize area—they can be modeled by soap films. One of her favorites was a Seifert surface, which is “locked” in place by an ancient, interlinked form called Borromean rings, which you can see in the logo of the International Mathematical Union. She has also created 3-D projections of four-dimensional shapes. I was fascinated listening to her talk. Then I learned about the annual Bridges conference on math and the arts, and that there are beautiful interactions between these fields.

How did you pick art for the book?

I wanted to look at art that had its origins in math concepts. There is an artist called Dorothea Rockburne who combines set theory with paper and chipboard and crude oil in many pieces; I included one called Scalar. Her works embody math but they succeed as art because they challenge you to consider things in a new and different way. I think math-driven works are different from works like Jackson Pollock paintings that can be interpreted mathematically to show fractals, or paintings and sculptures and buildings that show the golden ratio. In the works I wrote about in the book, math is part of them from the beginning.

Why do you like the art using the Travelling Salesman Problem?

That’s by Robert Bosch, who teaches at Oberlin College. He is obsessed with optimization. The Travelling Salesman is an optimization problem: He has to get to X number of cities and end where he started, so what is the fastest or shortest route without doubling up? Bosch wanted to show his students any field was open to optimization, and to prove it he picked the least likely: visual arts. He recreated da Vinci’s Mona Lisa as a collection of dots and then traced a continuous line that connects them on the shortest path, and never crosses. When you look at it closely you can see the line divides all space into an inside and an outside. It solves a math problem but it is clearly aesthetic, too. It pushes you to think about something in a novel way, and so it stands on its own as a work of art, I think.

Crockett Johnson, who wrote Harold and the Purple Crayon, gets a big section in the book. Why?

I loved the Crockett Johnson paintings about geometry. One of them is titled Proof of the Pythagorean Theorem. The theorem, about the relationship between three sides of a right triangle, is something we all have to check off by ninth grade. Johnson’s work evokes this familiar idea of proof and trustworthiness, and it’s solemn in that way. But it’s also a celebration with colored boxes and angles. It has its own beauty. He takes what you thought you knew about the theorem and puts it in a whole new context.

Was there anything amazing you left out?

I wish you could see Henry Segerman’s virtual reality projects, like the hypercube, which is usually drawn to look like a cube within a cube. His artworks often involve 4-D space. I show some details of an installation he worked on called Monkey See, Monkey Do in the book, but he did an augmented reality presentation of it at a Bridges conference where viewers could explore 4-D symmetries. These high dimension figures are all depicted as arrangements of monkeys. To include that in the book, we’d probably need an app and some goggles.