Magical Mathematics - A Tribute to Martin GardnerPerhaps no one has done more to make the world aware of mathematics than Martin Gardner...
Who are the people who write about mathematics in the clearest way? One might expect that such people are trained mathematicians - those who have majored in mathematics and gone on to get a doctorate in mathematics. While there are many wonderfully talented expositors of mathematics who are graduate school trained mathematicians, it turns out that one of the greatest expositor of mathematics, for me perhaps the greatest, was Martin Gardner. Gardner in a sense "became" a mathematician but did not "train" to do so.
Martin Gardner in 1932 (Courtesy of Wikipedia)
Many mathematicians see their subject as magical - having unexpected surprises and delights. However, all too often the magic of mathematics is lost on those who have not chosen mathematics or a related subject as a career. Perhaps no one has done more to bridge the gap between the sometimes lukewarm public view of mathematics and internal views of mathematics as a magical subject than Martin Gardner. Here I would like to provide a tribute to Martin Gardner for his efforts to popularize mathematics, as well as to his success in convincing many people of the beauty, applicability, joys and magic of mathematics. And I am not alone--this month mathematics pays tribute to him with "Mathematics, Magic, & Mystery," the theme for Mathematics Awareness Month (April) 2014. Perhaps no one has done more to make the world aware of mathematics than Martin Gardner.
Who was Martin Gardner?
Martin Gardner was born October 21, 1914 in Tulsa, Oklahoma. and died on May 22, 2010 not that far from where he was born, in Norman, Oklahoma. During his long life he lived in and traveled to many places but wherever he was, he seemed to carry his pen with him. What were the forces that molded this author of over 60 hardcover books?
(Photo of Martin Gardner)
Gardner's columns and books
What put Gardner on the mathematical map was his association with Scientific American magazine, which had started publication in 1845. In December, 1956 Gardner wrote an article for Scientific American about an intriguing family of geometrical objects known as flexagons.
Diagrams illustrating a flexagon (Courtesy of Wikipedia)
Two positions of a flexagon (Courtesy of Wikipedia)
(Photograph of Arthur Stone, courtesy of Stuart Anderson)
Photo of Jeremiah (Jerry) Lyons, Martin Gardner, and Thomas Banchoff (Courtesy of Tom Banchoff)
(Photo of John Horton Conway)
(Photo of Ronald Graham)
(Photo of Donald Knuth)
The range of wonderful problems, examples, and theorems that Gardner treated over the years is enormous. They include ideas from geometry, algebra, number theory, graph theory, topology, and knot theory, to name but a few. Characteristically, his columns were self-contained and were light on the mathematical notation that makes many people have a distaste for mathematics. Not having any easy way to pick among many gems, I am choosing a few that show some magical or intuitive aspects, and one that shows Gardner's playfulness.
We have mentioned that Gardner was born on October 21. He shared October 21st as a birthday with a variety of people who are perhaps better known than he: Benjamin Netanyahu, Kim Khardashian, Dizzy Gillespie and Malcolm Arnold. However, for those within mathematics who were born and died on this day, Gardner may hold his own in recognizability.
For 10 people, there is about a 12 percent chance that at least 2 of them will have the same birthday.
P(X|Y) = P(X and Y both occur)/P(Y). (*)
A map requiring 5 colors?
Martin Gardner had a playful streak and often had columns which had whimsical goals. In his Scientific American column of April 1975 he showed a plane map which purportedly required 5 colors to color the faces. The rule is that if two regions share an edge they should get different colors.
(Plane map requiring 5 colors?)
Image courtesy of Wolfram
(Photo of Percy Heawood)
(4-coloring by Stan Wagon of Gardner's April Fools' map)
Image courtesy of Wolfram
Joseph Malkewitch (sic) meets Martin Gardner
I was in the audience to hear Martin Gardner but I never met him in person. However, in a variety of ways our paths crossed. Gardner first came to my attention when as a teen on a trip to Florida, an automobile accident stranded me and my parents in Winter Haven, Florida, while our car was being repaired. My "lifesaver" for this period was a local library within walking distance of where we were staying, which was where I got my first introduction to Scientific American magazine and the columns of Martin Gardner. On returning to NY I started a subscription to Scientific American, and my subscription has never lapsed. Eventually, when I had large enough living quarters I started to acquire Gardner's books. HIs books were initially easier to consult than trying to go back to his Scientific American columns. However, there was also the fact that when his Scientific American columns appeared in book form, Gardner updated information about the mathematics in the columns with additional details about what was new about the problem since it had initially been published. One wonderful aspect of Gardner's Scientific American columns was that he and an "army" of appreciative, motivated and talented people (including some who were professional mathematicians) thought about the questions that he raised. In some cases his columns dealt with issues which, at the time he wrote about them, were not fully understood. So his books allowed him the opportunity to "update" columns with new ideas and results when the columns were collected for reprinting.
(Patch of tiles which consists of equilateral triangles and squares)
I was very pleased when Martin Gardner picked up on this problem and used it in his book Knotted Doughnuts and the later compendium Colossal Book of Short Puzzles and Problems. However, Joseph Malkewitch is really me! (Vould I lie to you?)
Carrying on the Gardner tradition
Gardner fans were disappointed when Gardner no longer continued to write his column for Scientific American. The magazine tried to find a "replacement" for Gardner by having various authors and columns that tried to capture the spirit of Mathematical Games. Eventually, however, Scientific American resigned itself to the fact that Gardner really could not be "replaced!" Happily Gardner continued to provide inspiration for fans with his books (see a partial list in the references).
(Photograph of Martin Gardner by Colm Mulcahy)
A list of some of Martin Gardner's books:
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