G4G is pleased to announce that **Professor Doris Schattschneider** of Moravian College will present in Atlanta in April 2018 on these two Martin Gardner related topics: “Math and M.C. Escher’s Art” (at a public lecture), and “The Story of Marjorie Rice” (**at the G4G13 conference**). Both are fascinating tales involving Martin Gardner’s celebrated “Mathematical Games” column in *Scientific American*. For the first, we will learn of how Martin’s 1961 column on a new geometry book by H.S.M. Coxeter introduced readers to Escher’s symmetry drawings, and how the cover of that *Scientific American* caused Escher to write a correction to the editor. For the second, a reader of Martin’s column with no math training was inspired to do some original research which lead to investigations that are still ongoing. We were delighted to chat with Professor Doris Schattschneider about her upcoming Atlanta talks on these topics.

# Interview

#### 1. Escher wrote to Martin in early 1961 to express his appreciation for the *Annotated Alice*. A few months later Martin wrote about Escher’s art, and *Scientific American* used a colorized version of an Escher print on their cover, captioned Mathematical Mosaic. Sadly, Escher died in 1972 just as his work was “going viral” to use a modern term. Do you believe the *Scientific American* cover played a significant role in Escher’s rising profile?

The April 1961 *Sci**entific American* cover accompanied **Martin Gardner**‘s column “Mathematical Games” that was primarily about HSM Coxeter’s new geometry book that was a huge departure from standard geometry books, and included the topic of symmetry, along with two of Escher’s tessellations for demonstration. Gardner reproduced these two tessellations in that column. Coxeter (and many other mathematicians, including Penrose) had seen an exhibit of Escher’s work that was arranged in conjunction with the 1954 ICM in Amsterdam. While **the Scientific American cover** (which, by the way, not only was

**colorized without Escher’s permission**, but also wrongly described by the editors who said the two flocks of birds were reflections of each other) might have had some influence, the popularity of Escher’s work no doubt was popularized by the availability of large authorized reprints of his work that were published in the early 60s. Pirated reproductions also proliferated.

#### 2. How did you first encounter Escher’s mathematically inspired work? How did it fit into your own mathematical training and research?

Escher’s work was not part of my mathematical training—my research field was algebraic groups. When I came to Moravian College in 1968 (from teaching at the University of Illinois, Chicago), there was a “January term” of 3-4 weeks in which faculty were to teach intensive courses of their own choosing, but not a regular catalog course. I designed a course on the mathematics of decorative art, and with no literature (at least that was readable by undergraduates), I researched the topic myself and wrote daily notes for class. The students used Caroline Macgillavry’s book of analysis of periodic designs that included 40 of Escher’s tessellations, along with a Dover book of Arabic designs to analyze periodic symmetry. From that point on, I learned more about Escher’s work and also added more to the January term course each time I taught it. In 1976 I traveled to Holland with my family and visited Caroline Macgillavry and also spent several days at the Gemeentemuseum in the Hague photographing all of Escher’s symmetry drawings and some other materials.

#### 3. Do we know how much mathematics Escher came to know and understand by the end of this life?

Escher had a deep intuitive and visual understanding of geometric relationships. He did not “know” or “understand” in the usual sense much beyond high school mathematics— he failed math in high school. Although he gleaned enough about geometric relationships in the Poincare model of the hyperbolic plane (from a single figure in a reprint that Coxeter sent him) to produce his four “Circle Limit” prints, he understood nothing of Coxeter’s explanations and notations about hyperbolic tessellations.

#### 4. Did he ever visit the USA or meet Martin?

He was scheduled to visit and lecture at MIT in 1968 after visiting his son George in Canada, but got ill and had to cancel. The lecture notes and slides were sent to Arthur Loeb and Loeb gave the lecture. I believe that Escher never met Martin, but he did have some correspondence with him.

#### 5. Which mathematicians did correspond with him, as many did with Martin?

The only mathematicians I am sure corresponded with him are Coxeter, Penrose, and Loeb. There were some others who wrote letters to ask to visit him or to express gratitude for his work. He also had correspondence with several scientists.

#### 6. What is Escher’s legacy now, 45 years after his death?

Escher’s work has never been appreciated by the “academy” of the art world, but remains popular with the public as attested to by the crowds that come to exhibitions of his work. There are many contemporary artists who are inspired by his work (see *MC Escher’s Legacy*, Springer).

#### 7. Can study of Escher’s works inspire the young and not so young to learn mathematics?

I’m not sure—but most elementary geometry books and elementary classrooms now include some study of symmetry and tessellations. Perhaps this does inspire some to learn math (but what math??). I’ve witnessed youngsters light up at making a successful tessellation when all they have done mathematically before is fail at computation and symbol arranging.

#### 8. Another talk you will give at G4G13 in Atlanta is about a San Diego homemaker named Marjorie Rice (1923-2017), who read some Martin Gardner columns and decided to take on a challenge he posed.

Simply told, it is a story of a very unlikely “mathematician” who made major contributions to an old mathematical problem.

#### 9. Is is true that we now know that no more such pentagonal tilings are left to be discovered?

There are an infinite number of pentagonal tilings, and many left to be discovered. There are, however only 15 types of *convex* pentagons known to tile the plane. Whether or not there are no further types to be discovered, as has been claimed by Michael Rao, the jury is out.