When Scientific American Made M. C. Escher Famous
Between 1957 and 1986 Martin Gardner wrote the Mathematical Games column for this magazine, with a total of 297 installments. During that time he became the world’s most prolific and best-known popularizer of recreational mathematics. His fans still revere him as a kind of sorcerer who conjured up an endless feast of puzzles, games and riddles built on mathematical ideas that often turned on counterintuitive twists. He may have lived as he wrote: after visiting Gardner’s office, in the attic of the writer’s home, the late mathematician John Horton Conway remarked that “it was filled with puzzles, games, mechanical toys, scientific curiosities, and a host of other intriguing objects, exactly like a wizard’s den.”
In his April 1961 column, Gardner introduced U.S. audiences to Dutch artist M. C. Escher, a meticulous craftsman who took great delight in defying expectations and breaking rules. He created mind-bending worlds where impossible things happen: Animals crawl out of the page, staircases rise to meet themselves and form infinite closed loops where one can climb forever, gravity pulls in multiple directions, and waterfalls cascade into the same pools that produced them.
Gardner’s column was not directly about Escher. It was a rave review of Introduction to Geometry by University of Toronto geometer H.S.M. Coxeter, which explored areas where older textbooks had feared to tread, such as non-Euclidean geometries. Coxeter had used Escher’s works to illustrate the book.
It was a natural pairing: For all of his blatant disregard for convention and authority, Escher embraced the laws of symmetry in geometry. In math-speak, “symmetry groups” refers to the collection of ways one can slide, reflect or rotate an object so that its final appearance is the same as its starting one. Escher often invoked translations, mirror reflections and repetition of forms.