October 18, 2013

Martin Gardner and Mathematics, Magic, and Mystery

One of my fonder memories of growing up in an isolated town in northwestern Ontario in the 1950s was my delight when the mail brought fresh issues of Humpty Dumpty's Magazine and Children's Digest. What I didn't appreciate until long afterward was that Martin Gardner was a key contributor to the early success of these magazines.

For Humpty Dumpty, Gardner was responsible for writing stories about the adventures of Humpty Dumpty Junior and poems of moral advice from Humpty senior to his son.

"For eight happy years, most of the time working at home, I wrote Junior and the poem, and also provided each of the year's ten issues (summer months were skipped) with the magazine's activity features of the sort that destroyed pages," Gardner writes in his posthumously published autobiography Undiluted Hocus-Pocus (Princeton University Press, 2013).

For example, Gardner notes, you folded a page to change a picture, held it up to the light to see something on the back of a page, or moved a strip back and forth through slots.

Gardner also contributed to Children's Digest, writing both articles and filler material such as puzzles and brainteasers.

Among his many other writing activities, Gardner produced a series of articles on mathematical magic for the journal Scripta Mathematica, edited by Jekuthiel Ginsburg of Yeshiva University. These articles were later fashioned (with much additional material) into the book Mathematics, Magic, and Mystery, published in 1956 and still in print as a Dover paperback.

In the preface, Gardner writes: "So far as I am aware, the chapters to follow represent the first attempt to survey the entire field of modern mathematical magic. Most of the material has been drawn from the literature of conjuring, and from personal contacts with amateur and professional magicians rather than from the literature of mathematical recreations. It is the magician, not the mathematician, who has been the most prolific in creating mathematical tricks during the past half-century."

Around the same time, Gardner was introduced to a fascinating mathematical toy called a hexaflexagon. After learning as much as he could about flexagons, he submitted an article on the topic to Scientific American, and it was published in the December 1956 issue. The magazine had earlier published a Gardner article on logic machines.

Gardner's article on flexagons attracted widespread interest and led directly to his monthly "Mathematical Games" column in Scientific American, starting with an article on a curious type of magic square. By coincidence, Gardner notes in Undiluted Hocus-Pocus, the name that Scientific American chose for his column had the same initial letters as his name.

"One of the pleasures in writing the column was that it introduced me to many top mathematicians, which of course I was not," Gardner modestly insists. "Their contributions to my column were far superior to anything I could write, and were a major reason for the column's growing popularity."

Indeed, many mathematicians owe their start to Gardner's columns, and his writing was certainly an inspiration to me (see "Martin Gardner’s Generosity" and "Martin Gardner’s Mรถbius Surprise").

October 21, 2013, is the 99th anniversary of Gardner’s birth, and many Gardner enthusiasts are commemorating the anniversary in a variety of ways (see "Celebration of Mind"). The MAA-sponsored event in Washington, D.C. features a presentation by mathemagician Art Benjamin.

The title of Gardner's book Mathematics, Magic, and Mystery also happens to be the theme chosen by the Joint Policy Board for Mathematics (JPBM) for Mathematics Awareness Month in 2014, just in time for the 100th anniversary of Gardner’s birth. Watch for more news and announcements about the exciting activities planned for April 2014.

Two recent books, both written by mathematicians, expand considerably on Gardner's original mathematical magic writings: Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks by Persi Diaconis and Ron Graham (Princeton University Press, 2012) and Mathematical Card Magic: Fifty-Two New Effects by Colm Mulcahy (A K Peters/CRC Press, 2013).

In his foreword to Magical Mathematics, Gardner writes: "If you are not familiar with the strange, semisecret world of modern conjuring you may be surprised to know that there are thousands of entertaining tricks with cards, dice, coins, and other objects that require no sleight of hand. They work because they are based on mathematical principles."