A&#160;children’s book about mathematics could use anything to illustrate patterns and prime numbers — cars, buildings, pieces of fruit. Richard Schwartz, professor of mathematics, decided to use monsters. Richard Lewis talked with Schwartz about his new children’s book, <em>You Can Count on Monsters.</em>

What was your inspiration for the book?

I made a very crude initial draft of the book around eight years ago, when my daughter Lucy turned 5. She was a very precocious kid and I thought it would be a great present for her fifth birthday. Initially, there were just 20 pictures, drawn in black and white. Later on, I got the idea to make the pictures fancier and in color. For a while I dropped the book idea and organized the new color pictures into a poster. Last year my wife reminded me about the original book and suggested that I turn the poster back into a book.

What do you hope a child (or an adult) will learn from your book?

The main thing I hope that someone gets from the book is the sheer pleasure of looking at and then grasping mathematical patterns. Ever since I was a kid, I’ve found both numbers and shapes fascinating. Even though I do math professionally now, I mainly take pleasure in the simple things about it. Sometimes it bothers me that something as beautiful as math is seen as dry and impenetrable. I’d like for people to get some pleasure from an especially beautiful piece of mathematics — primes and factoring — in the same way that nonmusicians get pleasure from music.

How did you come up with monsters as the conduit to explain math?

When I initially made the book for Lucy, I just wanted to have something that she needed to puzzle out. In fact, in the original version, the only difference between the primes and the composites was that the primes were all smiling and the composites were all frowning. So the question was: Why are some of the monsters smiling? Later on, I dropped the smile/frown idea and just concentrated on making interesting monsters and monster-combos. I can’t remember exactly when the whole idea of factoring the composite pictures came to me. Maybe I was running out of ideas for individual monsters!

How do those monsters explain prime numbers and factoring?

I don’t think that the monsters explain prime numbers and factoring per se. It’s more that they are organized according to a pattern that is controlled by prime numbers and factoring. In that sense, the pictures could be of anything — cars, buildings, different kinds of fruits, etc. The idea is that the patterns related to prime numbers and factoring are somehow guiding the drawings.

When did you draw the illustrations? How did you learn to illustrate?

Well, that’s sort of funny. I was never any good at art when I was a kid — or at least thought I wasn’t. I remember trying to draw things like beach or mountain scenes and the result was always atrocious. Later on, I once tried to make some sketches of my wife when we were on vacation in Paris, but I turned her into a cave woman. But we mathematicians often use a drawing program called xfig to illustrate our papers. Xfig lets you draw simple shapes like polygons and circles and then color them in. It turned out that I was strangely good at xfig. All my drawings are composed of these simple xfig units. So the whole book was done with this drawing program. I just repurposed it.

Your book dissolves, or marries, hard science, like math, and art. How do you view the relationship of science and art?

I think of science and art as being two main branches of human creativity, with science tending to be more controlled and powerful and art being more whimsical and wild. I think of my own work in mathematics as being about halfway between the two subjects. (A lot of mathematicians will say that math is halfway between art and science.) What I try to do in my research is to find things of beauty — I mean theoretical or “ideal” objects like perfect spheres. The artistic part is knowing what to look for and trying to bring out the beautiful features of what I’ve found. The scientific part is investigating the thing and using the tools of experiment and logic to actually prove that these objects have the properties I’m claiming that they have.