# Martin Gardner

### Quick Info

Born
21 October 1914
Tulsa, Oklahoma, USA
Died
22 May 2010
Norman, Oklahoma, USA

Summary
Martin Gardner was an American popular mathematics and science writer who had a long-running column on mathematical recreations in Scientific American.

### Biography

Martin Gardner's father was a geologist, with a Ph.D. in geology, who dug for fossils for the Smithsonian Institution before starting up his own very small oil company. While he was still working for the Smithsonian Institution, he often took his young son Martin on his digs. Martin's mother was a primary school teacher in Lexington before her marriage but, once the children were born, she stayed at home to look after them - she did, however, keep up her hobby of painting. Martin was the oldest of his parents' three children having a younger brother Jim and sister Judith. The family were well-off, the oil business being highly lucrative, and they even had their own tennis court by the time Martin was old enough to begin playing. Before he entered primary school, Martin had learnt to read [2]:-
My mother read 'The Wizard of Oz' to me when I was a little boy, and I looked over her shoulder as she read it. I learned how to read that way.
Today Gardner is famed for mathematical puzzles, many would say that he is the most famous modern writer of mathematical puzzles in the world, and this interest in puzzles came early in his life when his father gave him a copy of Sam Loyd's Cyclopedia of Puzzles. One of his early interests was magic and this led to his first publication New Color Divination in The Sphinx, a magic magazine, in May 1930 when he was still a high school student. His achievements at high school were mixed [2]:-
I was very good at math in high school. In fact, it and physics were the only subjects in which I got good grades. I was bored to death by the other classes. I flunked a class in Latin and had to take it over. I just don't have a good ear for languages.
In particular, his high school mathematics teacher, Pauline Baker, gave him a love for deductive reasoning while he thought that his physics teacher, M E Hurst, was most inspiring teacher in the school. After graduating from high school, Gardner wanted to study physics at the California Institute of Technology. However, the entrance requirements were two years at College so Gardner went to the University of Chicago with the intention of moving to Cal. Tech. after two years. However, he became fascinated with philosophy and stayed at Chicago to major in that subject. He graduated from Chicago with a B.A. in 1936 but this was a difficult time to get a job since it was the height of the Depression [2]:-
I had various jobs. I worked as a caseworker for the Chicago Relief Administration. I had to visit 140 families regularly in what was called the Black Belt. I also had several odd jobs: waiter, soda jerk, etc.
He also worked for a while as a reporter for the Tulsa Tribune but his last job before the United States entered World War II in December 1941 was as a public relations officer at the University of Chicago. He enlisted in the Navy and spent a year at Madison, Wisconsin, working at a radio training school before spending three years on the USS Pope, a destroyer escorting convoys across the Atlantic. When the war ended he returned to Chicago and sold his first short story to Esquire Magazine. Realising he could support himself by writing, he did not go back to his public relations job (although this would have been possible). At this time, however, he was still greatly interested in philosophy and made use of the G.I. Bill to spend a year taking graduate courses at the University of Chicago, in particular one on the philosophy of science given by Rudolph Carnap. As well as writing for Esquire Magazine he also wrote for the children's magazine Humpty Dumpty.

Gardner moved to New York in 1947 and continued to earn a living contributing articles and becoming an editor of Humpty Dumpty. He married Charlotte Greenwald in 1952; they had two sons, Jim and Tom. In the same year of 1952 he published his first book In the Name of Science which was republished as a paperback in 1956 under the title Fads and Fallacies in the Name of Science. Another of his books Mathematics, Magic and Mystery was published in 1956. Gardner writes in the Preface:-
The classic reference work of W W Rouse Ball, namely 'Mathematical Recreations and Essays', contains many early examples of mathematical conjuring. ... The present book represents the first attempt to survey the entire field of modern mathematical magic. ... Its principles can be grasped quickly, without training in higher mathematics.
In December 1956 he had his first article, which was on hexaflexagons, published by Scientific American. The publisher liked the article a lot and asked Gardner if he thought a regular column would be possible. Quickly Gradner agreed to produce 'Mathematical Games', resigned from his editorial role with Humpty Dumpty and had his first column in the January 1957 issue of Scientific American. From that point on he produced the monthly 'Mathematical Games' column for twenty-five years.

His books have also had a huge impact on popularising mathematics. He has written over sixty hardback books as well as numerous pamphlets of around 50 pages. We certainly do not want to even list the titles of over sixty works so we will give a selection: Logic Machines and Diagrams (1958); The Annotated Alice (1960); Relativity for the Million (1962); The Ambidextrous Universe: Mirror Asymmetry and Time-Reversed Worlds (1964); Mathematical Carnival: A New Round-up of Tantalizers and Puzzles from "Scientific American" (1975); The Incredible Dr Matrix (1976); Aha! Insight (1978); Science: Good, Bad, and Bogus (1981); Aha! Gotcha: Paradoxes to Puzzle and Delight (1982); The Whys of a Philosophical Scrivener (1983); Codes, Ciphers and Secret Writing (1984); Entertaining Mathematical Puzzles (1986); Time Travel and Other Mathematical Bewilderments (1987); Perplexing Puzzles and Tantalizing Teasers (1988); Fractal Music, Hypercards and More (1991); My Best Mathematical and Logic Puzzles (1994); Classic Brainteasers (1995); Calculus Made Easy (1998); A Gardner's Workout: Training the Mind and Entertaining the Spirit (2001); Mathematical Puzzle Tales (2001); and Bamboozlers (2008).

In 1981, to celebrate Gardner's sixty-fifth birthday, the book The Mathematical Gardner was published. The editor, David A Klarner, writes in the Preface:-
This volume is dedicated to Martin Gardner for his 65th birthday, 21 October 1979. His relationship to the mathematical community makes him unique: Gardner's monthly column in 'Scientific American' has been appearing for more than two decades. These columns together with some of his books (not all of them limited to mathematics) have presented a popular account of some of the recent developments in modern mathematics. More than just a reporter or popularizer, his correspondence with his readers makes him a 'mathematical Gardener'. This phrase describes his cultivation and propagation of ideas - an activity exemplified by Doris Schattschneider's article in this volume, 'In praise of amateurs'. Very few people in the general population who are capable of understanding and enjoying the beauty of mathematics actually get the opportunity to do so. Martin Gardner's writing has contributed enormously to improve the accessibility of the subject. The authors of this book together with a larger group of fans praise and thank him.
For many years the Gardner family lived on Euclid Avenue (everyone remarks on the apt address) in Hastings-on-Hudson, New York, but in 1979 they moved to Hendersonville, North Carolina. At this time Gerdner was sixty-five years old and considered that it was time to retire. He continued to produce the 'Mathematical Games' column in Scientific American until 1981 when he retired from that role. However, he remained extremely active in producing books, in fact his main motivation in giving up the column was to give him more time to devote to writing books. In 2000, his wife Charlotte died and two years later he moved to Norman, Oklahoma to be near his son Jim who was Professor of Education at the University of Oklahoma.

The columns he wrote for Scientific American have been published as fifteen books. Let us quote Gardner's own words in the Preface to A Gardner's Workout: Training the Mind and Entertaining the Spirit (2001):-
For 25 years I had the honour and pleasure of writing the 'Mathematical Games' column in 'Scientific American'. All those columns have now been reprinted, with updating, in fifteen volumes, starting [in 1959] and ending with [The last recreations, 1997]. Since I stopped writing the column I have from time to time contributed articles and book reviews about mathematics to both academic journals and popular magazines. Forty-one of these pieces are gathered here. The most controversial is the final review in which I criticize a current teaching fad known as the 'new new math'. By the time this book is published I would guess and hope that new new math is being abandoned almost as rapidly as the old new math faded. I could be wrong. In any case, it may be decades before our public education is able to attract competent teachers who have learned how to teach math to pre-college students without putting them to sleep. There are, of course, many teachers who deserve nothing but praise. It is to them I have dedicated this book.
The American Mathematical Society awarded Gardner the Leroy P Steele prize at the summer meeting in Salt Lake City in 1987 [1]:-
... for his many books and articles on mathematics and particularly for his column "Mathematical Games" in 'Scientific American'.
The citation continues [1]:-
Martin Gardner has introduced generations of readers to the intellectual excitement, the wonder, the variety, and the sheer fun of mathematics and mathematical ways of thought. With Dr Matrix and his other friends, he has exposed spurious thinking and misuse of mathematics in areas from numerology to economics. Martin Gardner has captured the attention of his readers, obtained their active involvement, and stretched their minds to an extent which is the envy of all of us who teach.
In his response, Gardner said [1]:-
Had I not developed a strong interest in philosophy when I was an undergraduate at the University of Chicago, I might have majored in mathematics, become a professional, and perhaps made some contributions to the field. As it happens, I had no formal training in mathematics, only an amateur's passion for its marvels, and admiration and awe for its leaders. I think of myself as like a person who loves classical music, but whose talents never advanced beyond playing simple tunes on a musical saw. There is no better way to teach oneself mathematics than to write about it. Every column I completed for 'Scientific American' was a learning experience that gave me intense pleasure. If I have been able to convey to others something of the fascination of mathematics, it is because I did not know enough to write about it on a technical level. ... To be given the Steele Prize is the greatest honour I can imagine myself receiving.
Let us end by noting that Gardner has produced a number of mathematical papers, written with leading mathematicians. He said [3]:-
I enjoy mathematics so much because it has a strange kind of unearthly beauty. There is a strong feeling of pleasure, hard to describe, in thinking through an elegant proof, and even greater pleasure in discovering a proof not previously known. On a low level I have experienced such a pleasure four times.
(1) I discovered the minimum number of acute triangles into which a square can be dissected. (Coxeter includes the dissection in his classic, 'Introduction to Geometry'.)
(2) I found a minimal network of Steiner trees that join all the corners of a chessboard.
(3) I constructed a bicolour proof that every serial isogon of 90 degrees - a polygon with all right angles, and sides in 1, 2, 3... sequence - must have a number of sides that is a multiple of 8.
(4) I devised a novel way to diagram the propositional calculus.
The results Gardner mentions here under (2) appear in the paper "Fan Chung, Martin Gardner and Ron Graham, Steiner trees on a checkerboard, Math. Mag. 62 (1989)". Ding Zhu Du writes:-
This is a very interesting article. It tells us what kind of Steiner minimum tree a checkerboard should have. The proof is left to the reader as an open problem. The Steiner minimum tree is the shortest network interconnecting the given points. A checkerboard of order $n$ is the set of $n^{2}$ points which form an $n \times n$ rectangular array. The connection pattern of the Steiner minimum tree for a checkerboard is quite complicated. However, the authors describe it very clearly with many nice pictures. It is amazing that the proof seems so hard. Every case except $n = 2$ or 3 is only conjectured. Hopefully, a sequence of efforts will result from this article.
The result Gardner mentions under (3) appears in "Lee Sallows, Martin Gardner, Richard Guy and Donald Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991)". The authors write:-
In 1988 Sallows devised a computer program to search a unit-square grid for closed paths with the following properties. The path starts along a lattice line with a segment of unit length, turns 90 degrees in either direction, continues for 2 units, turns again in either direction, continues for 3 units, and so on. In other words, the segments of the path are in serial order $1, 2, 3, .. N$, with a right angle turn at the end of each segment. A path of $N$ segments - the number is of course the same as the number of turns or corners - is said to be a path of order $N$. If the path returns to its starting point, making a right-angle with its first segment, we call it a serial isogon of 90 degrees. We prove that, for any 90-degree serial isogon, $N$ must be a multiple of 8.
Three papers by Gardner which appear in The College Mathematical Journal are Modeling mathematics with playing cards (2000), Some new results on magic hexagrams (2000), and L-tromino tiling of mutilated chessboards (2009).

Gardner has received a number of honours for his remarkable contributions including an honorary doctorate from Bucknell University in 1978 and the American Institute of Physics science writer of the year award for 1983.

### References (show)

1. 1987 Steele prizes awarded at the summer meeting in Salt Lake City, Notices Amer. Math. Soc. 34 (6) (1987), 875-878.
2. D Albers and M Gardner, On the Way to 'Mathematical Games': Part I of an Interview with Martin Gardner, The College Mathematics Journal 36 (3) (2005), 178-190.
3. D Albers and M Gardner, 'Mathematical Games' and Beyond: Part II of an Interview with Martin Gardner, The College Mathematics Journal 36 (4) (2005), 301-314.
4. M J Castello, Martin Gardner - The Dean of American Puzzlers, in The Greatest Puzzles of All Time (Courier Dover Publications, 1996), 114-123.
5. K Frazier, A Mind at Play: An Interview with Martin Gardner, Skeptical Inquirer 22 (2) (March/April 1998).
6. I Hargittai, A great communicator of mathematics and other games: a conversation with Martin Gardner, Math. Intelligencer 19 (4) (1997), 36-40.
7. Interview with Martin Gardner, Notices Amer. Math. Soc. 52 (6) (2005), 602-611.
8. D Lister, Martin Gardner and Paperfolding. http://www.britishorigami.info/academic/lister/martin_gardner.php
9. C Mulcahy, Martin Gardner's Magic Spells, Mathematical Association of America (October 2006). http://www.maa.org/columns/colm/cardcolm200610.html
10. J Tierney, For Decades, Puzzling People With Mathematics, The New York Times (19 October 2009).
11. J van de Craats, Of, for and about Martin Gardner (Dutch), Nieuw Arch. Wisk. (4) 2 (2) (1984), 311-316.