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Martin Gardner in the Twenty-First Century

Michael Henle and Brian Hopkins, editors
Mathematical Association of America
Publication Date: 
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Darren Glass
, on

Martin Gardner is probably as close as any author covered by MAA Reviews could come to needing no introduction. So rather than spend my own energy trying to write one, let me quote from a few other reviews of his works that have been written on this site over the years:

  • “Martin Gardner is a national treasure, someone whose contribution to mathematics has been immense.”
  • “Ask almost any mathematician who grew up during the 1960s or 1970s, and they’ll tell you about the enormous influence Martin Gardner’s Mathematical Games column had on them.”
  • “[Gardner] has enlightened, educated and delighted readers around the world during many decades as a prolific contributor to many publications”
  • “It is hard to exaggerate the importance and influence of these books. You must have them! Buy one for yourself, and buy many to give away.”
  • “It is an indisputable fact that Martin Gardner has done more to excite people about mathematics than anyone else. In fact, he is so far ahead of everyone else in that category that he would need a powerful telescope just to see the crowd bunched in second place.”
  • “All mathematicians owe a debt to Martin Gardner and can learn from reading what he wrote.”
  • “Some of us purchase Martin Gardner’s books without even looking at their titles because the author’s name is a full warranty of a good investment of time and money.”
  • “Martin Gardner’s joy is infectious and when the infection is insight, you will never forget it. Aha!”

Given that there are now several generations of mathematicians and friends of mathematics who write this effusively about Gardner’s writings and claim him as a major influence, it is no surprise that when he passed away in 2010, the mathematical community was deeply affected. This has manifested itself in several ways, including the ever-growing set of lectures and meetings held each October to commemorate Gardner’s birthday under the banner of Celebration of Mind. Given Gardner’s many contributions to the Mathematical Association of America over the years, it was no surprise that the various journals of the MAA published several articles and whole issues in tribute to Gardner. Recently, Michael Henle and Brian Hopkins have compiled a number of these articles in addition to several articles written by Gardner himself, and released them in a nice collection entitled Martin Gardner in the Twenty-First Century.

The book collects a total of forty-one articles from American Mathematical Monthly, Mathematics Magazine, College Mathematics Journal, and Math Horizons. Eight of these pieces were penned by Martin Gardner and the others are written by names that will be familiar to regular readers of the MAA publications including Art Benjamin, Neil Sloane, sarah-marie belcastro, Fred & James Henle, Ian Stewart, Avi Fraenkel, Jason Rosenhouse to name a few.

[This is probably the best time for a Full Disclosure: my own article from the CMJ Martin Gardner tribute issue is also included in this collection, a fact of which I was not aware until I received the review copy of the book. I hope the reader of this review will trust me when I say that my positive feelings about the book are in spite of my article’s presence and not because of it, and understand that I am not receiving any financial compensation no matter how well the book sells.]

One of Martin Gardner’s strengths was his wide-ranging interests: magic, mathematics, puzzles, pseudoscience and many other topics. While the articles in this collection naturally all fit under the general heading of “mathematics” they do a good job of reflecting the wide range of interests Gardner had even in this world. There is a section dedicated to “Geometry” which includes articles on the asymmetric propeller and some applications of mathematics for a dance troupe. Another section has articles about “Number Theory and Graph Theory” including one about how arithmetic would work if we didn’t know how to “carry” and another discussing a game theoretic approach to the Four Color Theorem. One section contains five articles on “Flexagons and Catalan Numbers” and there is a section entitled “Making Things Fit,” which includes articles about L-trominos, polyominos, squaring the plane, magic hexagrams, and knight’s tours.

The section on “Further Puzzles and Games” includes topics with such intriguing names as Cups and Downs, Congo Bongo, Bulgarian Solitaire, and RATWYT. The section on “Cards and Probability” includes an article Gardner wrote about modeling various mathematical phenomena using playing cards and another article which purports to “determine the likelihood that the author’s students were underwhelmed” by a magic trick. There are also articles dealing with variations on well-known problems such as the Monty Hall Problem, the Secretary Problem, and the famous property of Lake Wobegon that all children are above average. A final section collects papers dealing with “Other Aspects of Martin Gardner”, including a book review Gardner wrote of the (in this reviewer’s opinion) very fun novel PopCo by Scarlett Thomas. It also includes the last piece Gardner ever submitted to the MAA, a short story entitled “Superstrings and Thelma” that appeared in Math Horizons that touches on the question of whether string theory should count as pseudoscience… in a humorous way.

Just as with Gardner’s Mathematical Games columns, most of the articles in this volume are at a level that an undergraduate student could follow and enjoy, with a handful of articles at a higher level and a handful that would be accessible to bright middle school students. In short, there is something for just about everyone in this collection (especially if by “everyone” I mean “everyone who would read an MAA book review”). At the same time, I imagine there are few readers who will find every article in this book to their liking — for the life of me, I have never been able to understand the fascination many people have with hexaflexagons and despite some good writing this book did not convince me otherwise — but the joy of an anthology is the ability to skip around and only focus on the parts that are to one’s own liking.

Even three years later I periodically realize that we will never get to read another new book by Martin Gardner and I find myself saddened. The depth of thought and quality of exposition that Gardner achieved even in his lesser works is greater than I, or most other people, will ever reach. The articles in Martin Gardner in the Twenty-First Century do a good job of capturing the spirit of Gardner, and make for great reading. Is it the same thing as a new collection of Gardner articles? No, and if you go into it looking for that you will probably be disappointed. But if your tastes run in similar directions to Gardner’s and you enjoy good writing recreational mathematics, you will certainly find something in this collection to your tastes.

Darren Glass is an Associate Professor of Mathematics at Gettysburg College, and one of the best mathematical experiences he has had was speaking at a Gathering For Gardner conference a few years ago. He would be happy to ramble about how great it was or any number of other topics, and can be reached at

I. Geometry
II. Number Theory and Graph Theory
III. Flexagons and Catalan Numbers
IV. Making Things Fit
V. Further Puzzles and Games
VI. Cards and Probability
VII. Other Aspects of Martin Gardner
About the Editors