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."
- Simon & Schuster (New York), 1959. <*>
No ISBN (?).
Hardback.
- Simon & Schuster (New York), 1963.
ISBN 0671245597.
Paperback.
- University of Chicago Press, 1988. <*>
Under the title Hexaflexagons and Other Mathematical
Diversions: The First Scientific American Book of Puzzles and
Games.
ISBN 0226282546.
Paperback.
With an updated biblography, a new introduction, and a new
13-page postscript.
# 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."
- Simon & Schuster (New York), 1961. <*>
ISBN 0671245597.
Hardback.
- Simon & Schuster (New York), 1967 (?).
Paperback.
ISBN 0671636537.
- University of Chicago Press, 1987. <*>
ISBN 0226282538.
Paperback.
With a brief 2-page postscript added (bibliography not updated).
# 3
Martin Gardner's New Mathematical Diversions from Scientific American
- Simon & Schuster (New York), 1966. <*>
ISBN 0671452401.
Hardback.
- Simon & Schuster (New York), 1971.
ISBN 0671209132.
Paperback.
- University of Chicago Press, 1983. <*>
ISBN 0226282473.
Paperback.
(No updates/additions.)
- Mathematical Association of America (Wash DC), 1995. <*>
Under the title New Mathematical Diversions.
ISBN 0883855178.
Paperback.
With an updated bibliography and a new 12-page postscript.
# 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.
- Simon & Schuster (New York), Dec 1967. <*>
No ISBN (?).
Hardback.
·
# 4.1
The Incredible Dr. Matrix
Includes another 9½ Dr. Matrix columns.
- Charles Scribner's Sons (New York), 1976. <*>
ISBN 068414669X.
Hardback.
·
# 4.2
The Magic Numbers of Dr. Matrix
Includes all Dr. Matrix columns (except one, published much later in
collection #13).
- Prometheus Books (Buffalo), 1985. <*>
ISBN 0879752815.
Hardback.
- Prometheus Books (Buffalo), 1985. <*>
ISBN 0879752823.
Paperback.
- Dorset Press, 1990.
ISBN ???.
Hardback.
# 5
The Unexpected Hanging
And Other Mathematical Diversions
- Simon & Schuster (New York), 1969. <*>
ISBN 0671200739.
Hardback.
- Fireside / Simon & Schuster (New York), 1969.
ISBN 067121425X.
Paperback.
- Simon & Schuster (New York), 1986. <*>
ISBN 0671628194.
Paperback.
- University of Chicago Press, 1991. <*>
ISBN 0226282562.
Paperback.
With an updated bibliography and a new 6-page postscript.
# 6
Martin Gardner's Sixth Book of Mathematical Games from Scientific
American
- W H Freeman (San Francisco), 1971. <*>
ISBN 0716709449.
Hardback.
- University of Chicago Press, 1983. <*>
ISBN 0226282503.
Paperback.
Under the title Martin Gardner's Sixth Book of Mathematical
Diversions from Scientific American.
(No updates/additions.)
# 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"
- Borzoi / Alfred A Knopf (New York), Oct 1975. <*>
ISBN 0394494067.
Hardback.
- Vintage Books / Random House (New York), 1977(?). <*>
ISBN 039472349X.
Paperback.
- Mathematical Association of America (Wash DC), 1989. <*>
ISBN 0883854481.
Paperback.
With an updated bibliography, a new 14-page postscript, a new
preface, and a 3-page foreword by John Conway.
# 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"
- Borzoi / Alfred A Knopf (New York), Sep 1977. <*>
ISBN 0394408225.
Hardback.
- Vintage Books / Random House (New York), Sep 1978. <*>
ISBN 0394726235.
Paperback.
- Mathematical Association of America (Wash DC), 1989. <*>
ISBN 0883854481.
Paperback.
With an updated bibliography, a new 16-page postscript, and a
2-page foreword by Ronald L. Graham and Persi Diaconis.
# 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"
- Borzoi / Alfred A Knopf (New York), Sep 1979. <*>
ISBN 0394502078.
Hardback.
- Vintage Books / Random House (New York), Apr 1981. <*>
ISBN 0394747127.
Paperback.
- Mathematical Association of America (Wash DC), 1992. <*>
ISBN 0883855062.
Paperback.
With an updated bibliography, a new 6-page postscript, and a
2-page preface by Don Knuth.
# 10
Wheels, Life, and Other Mathematical Amusements
- W H Freeman (New York), 1983. <*>
ISBN 0716715880.
Hardback.
- W H Freeman (New York), 1983.
ISBN 0716715899.
Paperback.
# 11
Knotted Doughnuts and Other Mathematical Entertainments
- W H Freeman (New York), 1986. <*>
ISBN 0716717948.
Hardback.
- W H Freeman (New York), 1986.
ISBN 0716717999.
Paperback.
# 12
Time Travel and Other Mathematical Bewilderments
- W H Freeman (New York), 1988. <*>
ISBN 071671924X.
Hardback.
- W H Freeman (New York), 1988. <*>
ISBN 0716719258.
Paperback.
# 13
Penrose Tile to Trapdoor Ciphers
... And the Return of Dr. Matrix
- W H Freeman (New York), 1989. <*>
ISBN 071671986X.
Hardback.
- W H Freeman (New York), 1989. <*>
ISBN 0716719878.
Paperback.
- Mathematical Association of America (Wash DC), 1997. <*>
ISBN 0883855216.
Paperback.
With an updated bibliography and a new 7-page postscript.
# 14
Fractal Music, Hypercards, and More ...
Mathematical Recreations from Scientific American Magazine
- W H Freeman (New York), 1992. <*>
ISBN 0716721880.
Hardback.
- W H Freeman (New York), 1992. <*>
ISBN 0716721899.
Paperback.
# 15
The Last Recreations
Hydras, Eggs, and Other Mathematical Mystifications
- Copernicus / Springer-Verlag (New York), 1997. <*>
ISBN 0387949291.
Hardback.
- Copernicus / Springer-Verlag (New York), 2001.
ISBN 0387988831.
Paperback.
This list is not quite yet complete. Additions and corrections are
welcome. Send me email at <breadbox@muppetlabs.com>.
Finally, here is an excellent resource -- an index to the full set of
collections:
http://www.ms.uky.edu/~lee/ma502/gardner5/gardner5.html
Books
Brian Raiter