Martin Gardner's Collections of "Mathematical Games" Columns

Martin Gardner wrote a monthly column on the subject of recreational mathematics for Scientific American. It began with an article on hexaflexagons which ran in the December 1956 issue. The editor suggested he write a regular feature, and the January 1957 issue contained the first column, called "Mathematical Games".

Martin Gardner continued to write a monthly "Mathematical Games" column until the 1980s, at which point his column began appearing only irregularly. (New columns appeared briefly during this time by such writers as Douglas Hofstadter and A. K. Dewdney.) The May 1986 issue saw the publication of the final installment of "Mathematical Games".

All of his columns have been collected into books. In addition to the original text (modulo corrections), the books contain updated information, and occasionally an extra chapter. Many yet-unanswered questions in the columns are answered in the addenda, after readers were inspired to tackle the problems.

Did you ever play with hexaflexagons? Or pentominoes? Or a Soma cube? Ever watched Conway's Game of Life on a computer? Maybe you've heard of the RSA cipher? If so, it may surprise you to realize that all these things owe their popularity to having been mentioned in one of Martin Gardner's columns.

The book collections are a bit inconsistent in their availability, having been in the hands of a number of different publishers. As a book collector, I have thus had to use a many sources to put together the information in this list.

(Items marked with <*> are books that are in my personal collection. Where the book is a hardback, it also indicates that the book is a first edition.)

# 1

The Scientific American Book of Mathematical Puzzles & Diversions

subtitled "Paradoxes and Paperfolding, Moebius Variations and Mnemonics, Fallacies, Brain-Teasers, Magic Squares, Topological Curiosities, Probability and Parlor Tricks, and a variety of ancient and new games and problems, from Polyominoes, Nim, and the Tower of Hanoi to Four-Dimensional Ticktacktoe. Together with mathematical commentaries by Mr. Gardner and addenda from readers of Scientific American. Plus bibliograhics and, of course, solutions."

# 2

The 2nd Scientific American Book of Mathematical Puzzles & Diversions

subtitled "A new selection: from Origami to Recreational Logic, from Digital Roots and Dudeney Puzzles to the Diabolic Square, from the Golden Ratio to the Generalized Ham Sandwich Theorem. All with mathematical commentaries by Mr. Gardner, ripostes from the readers of Scientific American, references for further reading and, of course, solutions."

# 3

Martin Gardner's New Mathematical Diversions from Scientific American

# 4

The Dr. Matrix Collections

# 4.0

The Numerology of Dr. Matrix

subtitled "The fabulous feats and adventures in Number Theory, Sleight of Word, and Numerological Analysis (Literary, Biblical, Political, Philosophical, and Psychonumeranalytical) of that incredible Master Mind first introduced, in the pages of Scientific American, by Martin Gardner"

Includes the first 8 Dr. Matrix columns.

# 4.1

The Incredible Dr. Matrix

Includes another 9½ Dr. Matrix columns.

# 4.2

The Magic Numbers of Dr. Matrix

Includes all Dr. Matrix columns (except one, published much later in collection #13).

# 5

The Unexpected Hanging
And Other Mathematical Diversions

# 6

Martin Gardner's Sixth Book of Mathematical Games from Scientific American

# 7

Mathematical Carnival

subtitled "From Penny Puzzles, Card Shuffles and Tricks of Lightning Calculators to Roller Coaster Rides into the Fourth Dimension. A new round-up of Tantalizers from Scientific American, with elegant Mathematical Commentaries (and Afterthoughts) by Mr. Gardner, Backtalk from readers, and 115 Pictures and Diagrams"

# 8

Mathematical Magic Show

subtitled "More Puzzles, Games, Diversions, Illusions and Other Mathematical Sleight-of-Mind from SCIENTIFIC AMERICAN With Repartee from Readers, Afterthoughts from the Author and 133 Drawings & Diagrams"

# 9

Mathematical Circus

subtitled "More Games, Puzzles, Paradoxes, and Other Mathematical Entertainments from SCIENTIFIC AMERICAN -- With Thoughts from Readers, Afterthoughts from the Author, and 105 Drawings and Diagrams"

# 10

Wheels, Life, and Other Mathematical Amusements

# 11

Knotted Doughnuts and Other Mathematical Entertainments

# 12

Time Travel and Other Mathematical Bewilderments

# 13

Penrose Tile to Trapdoor Ciphers
... And the Return of Dr. Matrix

# 14

Fractal Music, Hypercards, and More ...
Mathematical Recreations from Scientific American Magazine

# 15

The Last Recreations
Hydras, Eggs, and Other Mathematical Mystifications

This list is not quite yet complete. Additions and corrections are welcome. Send me email at <>.

Finally, here is an excellent resource -- an index to the full set of collections:

Brian Raiter