Richard Evan Schwartz has written math books for a range of audiences: for university students, researchers, and several for children. His distinctive approach brings a touch of childlike freedom to his high-level research monographs, and mathematical depth to his whimsical children’s books.
(Added Note: Richard Schwartz has just received an honorable mention at the 2017 Prose Awards for Gallery of the Infinite. He has previously received the 2015 MSRI Mathical Book for Kids from Tots To Teens Award for Really Big Numbers.)
Here are Schwartz’s responses to a list of questions we posed by email.
What made you decide to write the book?
In the case of my first book, “You Can Count on Monsters”, I wrote the first version specifically to teach my then 6-year-old daughter Lucy about prime numbers and factoring. 
I wrote later versions of that first book because I thought that other children would like them as well. I wrote my second book, “Really Big Numbers” because I wanted to share my fascination with really huge numbers. Even though there are many counting books in the literature, there are none which explore the kind of insanely huge numbers that mathematicians occasionally think about. I thought that kids might like to see this.
Was there a gap in the literature you were trying to fill?
Yes, this is definitely true, especially of my last two picture books, “Gallery of the Infinite” and “Life on the Infinite Farm”. These books attempt to explain some concepts of infinity to audiences of various ages. I don’t think that there is anything like it available. In these cases, I wanted to write something really novel.
How did 
you decide on the format and style of the book?
I think that my limited artistic range dictated the format for me. I like to draw pictures using the computer drawing programs xfig and inkscape. I used those programs to illustrate my books because I was comfortable with them. For a long time, I had been obsessed with trying to find an illustrator who could illustrate my books, and this actually held me back for quite some time. I kept waiting for this magical person to come along who could bring my ideas to life. It was extremely difficult for me even to get in touch with illustrators, let alone find one who would be a good fit, and so eventually I just improved my own drawing to the point where (more or less) I could do it myself.
What did you focus on the most when writing?
I think that my focus varies depending on the stage of the writing. In the beginning, I focus on the overall shape of the book, the big picture. Once I have a good idea of the scope of the project, I focus on trying to produce as many pictures as fast as I can. I find that my projects often die if I can’t get going fast enough in the beginning, so I like to get up a big head of steam.
Once the project gets going, I don’t have too much problem with motivation and focus. What keeps me going is the strong desire to see the finished project. Once the ideas are (to my mind) fully formed, I can’t wait to get them all out on the page. On the other hand, it is often very hard for me to start a new project. In that case, I find that it is very hard to force myself to work. I have to get an idea I’m really excited about, and those don’t come along so often.
After I have something rough banged out, or at least many pages done, I focus quite a bit on revision and improvement. I try to make the pictures as clean and simple as possible, the color schemes harmonious and beautiful, and the writing sharp and graceful and interesting. At the very end, I focus almost entirely on eliminating typos and glitches.
What were the positives and negatives of the experience?
The most positive part of the experience is when someone sends me email or otherwise tells me that they have enjoyed the book. I have gotten a fair amount of email like this for my first two books, and it really makes me happy. I am delighted when some little kid says that he or she loves my books. Another positive part is when I actually get to hold the final product in my hands. For as long as I can remember, I wanted to write books. Often when I am holding one of my books, my mind goes back to those dark days in middle school or high school when I was slogging through boring work and dreaming of doing something bigger.
The most negative part of the experience is when I find out about a mistake in the published version. Like many mathematicians, I hate making mistakes. This doesn’t happen too often in the picture books, but I have found many little mistakes — mostly typos or notation errors — in my published works and this really sickens me. Another negative experience is getting bad or luke-warm reviews of my books online, especially if they complain about the artwork. One of my unpublished books, “Life on the Infinite Farm” somehow got onto tumblr, and about 20,000 people looked at it. There were lots of comments to the effect that the book was horrifying or monstrous or otherwise terrible, and these made me pretty unhappy.
Probably the most surprising thing is that my book, “You Can Count on Monsters” shot to number 1 on amazon.com after Keith Devlin reviewed it on NPR. It only stayed number 1 for about a weekend, but still it was a totally surreal experience.
Was your writing influenced by other books? Which ones?
I’m not sure how much other books have directly influenced my writing, but there are certainly many books I admire and try to live up to when I write. For comics and animation, I love the beautifully and simply animated television series “Justice League”. My drawing style is a lot like “Justice League”, but of course not nearly as good. For mathematical exposition, I love the book “Journey through Genius”. My books aren’t exactly like
“Journey through Genius”, but I love the great expository style of that book, as well as the great choice of topics. I also love the bright, primary-colored geometric sculptures of Calder. My drawing style is somewhat like Calder’s sculpture style but, again, not nearly as good.
Did you find ways to get feedback while writing your book or was it a solitary effort?
The writing process for me is mostly a solitary process, except that sometimes I will ask my wife or daughters (who are all good artists) for critiques of the pictures I have drawn. I am generally open to their criticism, and will implement suggestions they make. Usually the suggestions are of the form, “You drew the arms too big” or “That red and green don’t go together well.” Once the book is mostly written, and all the main ideas are in place, I send it out to friends and colleagues, asking 
for comments. I am generally very grateful for criticism and happy to implement suggestions I get.
What advice would you give to new authors?
I would say that the most important thing is just to jump in and WRITE IT! A lot of times people dither around with a good idea and never quite get around to bringing it to fruition. I used to listen to my dad talk for years about this great board game he was going to develop — it really was a good idea — but he just never got around to doing it.
Another piece of advice is that you shouldn’t solicit too much feedback early on. If you hear from lots of people before you get going very far on your idea, you will be daunted by all the different kinds things you hear. You may feel as if you have to satisfy all kinds of constraints and expectations. It is better to just write a bunch of stuff on your own first and then see what people think of an idea that is already well in progress.
On the other hand, do solicit a lot of feedback eventually. Once you have written a large part of your book, by all means solicit lots of feedback. I have found that other people’s suggestions have made my books much better. A lot of times you develop blind spots in isolation, and think that something will be clear to other people just because it is clear in your mind. By finding out what people actually experience when reading your book, you can adjust things so that they make sense to the outside world.
One last thing: protect your time and try to block out large free periods. Most people (including me) have a lot of demands on their time, but it is important to compartmentalize these tasks so that you are not working on trivia all day long. I try to concentrate the daily tasks so that I do them in short bursts, leaving myself free time. For instance, I set aside certain days for refereeing a paper or writing letters of recommendation or meeting with students, and I will do everything on those special days.
What kind of feedback did you get after the book came out?
I’ve gotten all kinds of feedback. Here are some examples
— Occasionally people have asked me to lecture about the books, or (on a very small scale) participate in book signings.
— I got one of the 2015 Mathical Prizes for my book “Really Big Numbers”. That involved me going down to an award ceremony in Washington D.C.
–I get a fair amount of emails about the books, from parents of children who like them. I like this feedback the best.
— I’ve had a few people tell me that they’re used the book as part of lectures or teaching presentations.
— I once got an email from an art school telling me that they were using my book, “You Can Count on Monsters” as the basis for an art project.
— A Korean computer scientist developed a video game based on “You can Count on Monsters”.