The great Martin Gardner's "Mathematical Games" columns in Scientific American were assembled, over the years, into fifteen volumes. I put together this simple listing to help me trace which book a remembered essay actually appears in. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001) comprises 50 already collected columns (with updates), taken from every previous collection except The Numerology of Dr. Matrix. My thanks to Douglas Krajnovich for providing information on this book's contents. Columns reappearing in the The Colossal Book of Mathematics are marked with a paragraph sign ¶ in earlier listings below. – David Langford
Title List
- 1. Mathematical Puzzles and Diversions (1959)
- 2. More Mathematical Puzzles and Diversions (1962)
- 3. New Mathematical Diversions from Scientific American (1966)
- 4. The Numerology of Dr. Matrix (1967; exp 1976 The Incredible Dr. Matrix; exp 1985 The Magic Numbers of Dr. Matrix)
- 5. The Unexpected Hanging (1969; UK Further Mathematical Diversions)
- 6. Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American (1971)
- 7. Mathematical Carnival (1975)
- 8. Mathematical Magic Show (1977)
- 9. Mathematical Circus (1979)
- 10. Wheels, Life and Other Mathematical Amusements (1983)
- 11. Knotted Doughnuts and Other Mathematical Entertainments (1986)
- 12. Time Travel and Other Mathematical Bewilderments (1988)
- 13. Penrose Tiles to Trapdoor Ciphers (1989)
- 14. Fractal Music, Hypercards and More (1992)
- 15. The Last Recreations (1997)
- The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001)
Contents Lists
Mathematical Puzzles and Diversions (1959) - Hexaflexagons ¶
- Magic with a Matrix
- Nine Problems
- Ticktacktoe, or Noughts and Crosses
- Probability Paradoxes
- The Icosian Game and the Tower of Hanoi
- Curious Topological Models
- The Game of Hex
- Sam Loyd: America's Greatest Puzzlist
- Mathematical Card Tricks
- Memorizing Numbers
- Nine More Problems
- Polyominoes
- Fallacies
- Nim and Tac Tix
- Left or Right?
- References for Further Reading
More Mathematical Puzzles and Diversions (1962) - The Five Platonic Solids
- Tetraflexagons
- Henry Ernest Dudeney: England's Greatest Puzzlist
- Digital Roots
- Nine Problems
- The Soma Cube ¶
- Recreational Topology
- Phi: The Golden Ratio
- The Monkey and the Coconuts ¶
- Mazes
- Recreational Logic
- Magic Squares
- James Hugh Riley Shows, Inc.
- Nine More Problems
- Eleusis: The Induction Game
- Origami
- Squaring the Square
- Mechanical Puzzles
- Probability and Ambiguity ¶
- References for Further Reading
New Mathematical Diversions from Scientific American (1966) - The Binary System
- Group Theory and Braids
- Eight Problems
- The Games and Puzzles of Lewis Carroll
- Paper Cutting
- Board Games
- Packing Spheres ¶
- The Transcendental Number Pi
- Victor Eigen: Mathemagician
- The Four-Color Map Problem
- Mr. Apollinax Visits New York
- Nine Problems
- Polyominoes and Fault-Free Rectangles
- Euler's Spoilers: The Discovery of an Order-10 Graeco-Latin Square
- The Ellipse
- The 24 Color Squares and the 30 Color Cubes
- H.S.M. Coxeter
- Bridg-it and Other Games
- Nine More Problems
- The Calculus of Finite Differences ¶
The Numerology of Dr. Matrix (columns 1-7, 1967; expanded 1976 with columns 8-18 as The Incredible Dr. Matrix; expanded 1985 with columns 19-22 as The Magic Numbers of Dr. Matrix) - Introduction
- New York
- Los Angeles
- Sing Sing
- Lincoln and Kennedy
- Chicago
- Miami Beach
- Philadelphia
- Pi
- Wordsmith College
- Squaresville
- Left Versus Right
- Fifth Avenue
- The Moon
- Honolulu
- Houston
- Clairvoyance Test
- Pyramid Lake
- The King James Bible
- Calcutta
- Stanford
- Chautauqua
- Istanbul
- Answers and Commentary
The Unexpected Hanging (1969; UK Further Mathematical Diversions) - The Paradox of the Unexpected Hanging ¶
- Knots and Borromean Rings
- The Transcendental Number e
- Geometric Dissections
- Scarne on Gambling
- The Church of the Fourth Dimension ¶
- Eight Problems
- A Matchbox Game-Learning Machine ¶
- Spirals
- Rotations and Reflections ¶
- Peg Solitaire
- Flatlands
- Chicago Magic Conventions
- Tests of Divisibility
- Nine Problems
- The Eight Queens and Other Chessboard Diversions
- A Loop of String
- Curves of Constant Width ¶
- Rep-Tiles: Replicating Figures on the Plane ¶
- Thirty-Seven Catch Questions
- Bibliography
Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American (1971) - The Helix ¶
- Klein Bottles and Other Surfaces ¶
- Combinatorial Theory
- Bouncing Balls in Polygons and Polyhedrons
- Four Unusual Board Games
- The Rigid Square and Eight Other Problems
- Sliding-Block Puzzles
- Parity Checks
- Patterns and Primes
- Graph Theory
- The Ternary System
- The Trip around the Moon and Seven Other Problems
- The Cycloid: Helen of Geometry
- Mathematical Magic Trick
- Word Play
- The Pythagorean Theorem
- Limits of Infinite Series
- Polyiamonds
- Tetrahedrons
- Coleridge's Apples and Eight Other Problems
- The Lattice of Integers
- Infinite Regress ¶
- O'Gara, the Mathematical Mailman
- Op Art
- Extraterrestrial Communication
Mathematical Carnival (1975) - Sprouts and Brussels Sprouts ¶
- Penny Puzzles
- Aleph-Null and Aleph-One ¶
- Hypercubes ¶
- Magic Stars and Polyhedrons
- Calculating Prodigies
- Tricks of Lightning Calculators
- The Art of M.C. Escher ¶
- The Red-Faced Cube and Other Problems
- Card Shuffles
- Mrs Perkins' Quilt and Other Square-Packing Problems
- The Numerology of Dr. Fliess
- Random Numbers
- The Rising Hourglass and Other Physics Puzzles
- Pascal's Triangle
- Jam, Hot and Other Games
- Cooks and Quibble-Cooks
- Piet Hein's Superellipse ¶
- How to Trisect an Angle
- Bibliography
Mathematical Magic Show (1977) - Nothing ¶
- More Ado About Nothing
- Game Theory, Guess It, Foxholes
- Factorial Oddities
- The Cocktail Cherry and Other Problems
- Double Acrostics
- Playing Cards
- Finger Arithmetic
- Möbius Bands
- Ridiculous Questions
- Polyhexes and Polyaboloes
- Perfect, Amicable, Sociable
- Polyominoes and Rectification
- Knights of the Square Table
- The Dragon Curve and Other Problems
- Colored Triangles and Cubes
- Trees
- Dice
- Everything ¶
- Bibliography
Mathematical Circus (1979) - Optical Illusions
- Matches
- Spheres and Hyperspheres ¶
- Patterns of Induction
- Elegant Triangles
- Random Walks and Gambling
- Random Walks on the Plane and in Space
- Boolean Algebra
- Can Machines Think?
- Cyclic Numbers
- Eccentric Chess and Other Problems
- Dominoes
- Fibonacci and Lucas Numbers
- Simplicity ¶
- The Rotating Round Table and Other Problems
- Solar System Oddities
- Mascheroni Constructions
- The Abacus
- Palindromes: Words and Numbers ¶
- Dollar Bills
- Bibliography
Wheels, Life and Other Mathematical Amusements (1983) - Wheels
- Diophantine Analysis and Fermat's Last Theorem
- The Knotted Molecule and Other Problems
- Alephs and Supertasks ¶
- Nontransitive Dice and Other Probability Paradoxes ¶
- Geometrical Fallacies
- The Combinatorics of Paper Folding ¶
- A Set of Quickies
- Ticktacktoe Games
- Plaiting Polyhedrons
- The Game of Halma
- Advertising Premiums
- Salmon on Austin's Dog
- Nim and Hackenbush
- Golomb's Graceful Graphs
- Charles Addams' Skier and Other Problems
- Chess Tasks
- Slither, 3X+1, and Other Curious Questions
- Mathematical Tricks with Cards
- The Game of Life, Part I ¶
- The Game of Life, Part II
- The Game of Life, Part III
Knotted Doughnuts and Other Mathematical Entertainments (1986) - Coincidence
- The Binary Gray Code
- Polycubes
- Bacon's Cipher
- Doughnuts: Linked and Knotted ¶
- The Tour of the Arrows and Other Problems
- Napier's Bones
- Napier's Abacus
- Sim, Chomp and Racetrack
- Elevators
- Crossing Numbers
- Point Sets on the Sphere
- Newcomb's Paradox ¶
- Reflections on Newcomb's Paradox
- Reverse the Fish and Other Problems
- Look-See Proofs
- Worm Paths
- Waring's Problems
- Cram, Bynum and Quadraphage
- The I Ching
- The Laffer Curve
Time Travel and Other Mathematical Bewilderments (1988) - Time Travel ¶
- Hexes and Stars
- Tangrams, Part 1
- Tangrams, Part 2
- Nontransitive Paradoxes ¶
- Combinatorial Card Problems
- Melody-Making Machines ¶
- Anamorphic Art
- The Rubber Rope and Other Problems
- Six Sensational Discoveries ¶
- The Császár Polyhedron
- Dodgem and Other Simple Games
- Tiling with Convex Polygons
- Tiling with Polyominoes, Polyiamonds, and Polyhexes
- Curious Maps
- The Sixth Symbol and Other Problems
- Magic Squares and Cubes
- Block Packing
- Induction and Probability ¶
- Catalan Numbers
- Fun with a Pocket Calculator
- Tree-Plant Problems
Penrose Tiles to Trapdoor Ciphers (1989) - Penrose Tiling ¶
- Penrose Tiling II
- Mandelbrot's Fractals
- Conway's Surreal Numbers ¶
- Back from the Klondike and Other Problems
- The Oulipo
- The Oulipo II
- Wythoff's Nim
- Pool-Ball Triangles and Other Problems
- Mathematical Induction and Colored Hats
- Negative Numbers
- Cutting Shapes into N Congruent Parts
- Trapdoor Ciphers
- Trapdoor Ciphers II
- Hyperbolas
- The New Eleusis ¶
- Ramsey Theory ¶
- From Burrs to Berrocal
- Sicherman Dice, the Kruskal Count and Other Curiosities
- Raymond Smullyan's Logic Puzzles
- The Return of Dr. Matrix
Fractal Music, Hypercards and More (1992) - White, Brown and Fractal Music ¶
- The Tinkly Temple Bells
- Mathematical Zoo ¶
- Charles Sanders Peirce
- Twisted Prismatic Rings
- The Thirty Color Cubes
- Egyptian Fractions
- Minimal Sculpture
- Minimal Sculpture II
- Tangent Circles
- The Rotating Table and Other Problems
- Does Time Ever Stop? Can the Past Be Altered? ¶
- Generalized Ticktacktoe ¶
- Psychic Wonders and Probability
- Mathematical Chess Problems
- Douglas Hofstader's Gödel, Escher, Bach ¶
- Imaginary Numbers
- Pi and Poetry: Some Accidental Patterns
- More on Poetry
- Packing Squares
- Chaitin's Omega
The Last Recreations (1997) - The Wonders of a Planiverse ¶
- Bulgarian Solitaire and Other Seemingly Endless Tasks ¶
- Fun with Eggs, Part I
- Fun with Eggs, Part II
- The Topology of Knots ¶
- M-Pire Maps
- Directed Graphs and Cannibals
- Dinner Guests, Schoolgirls, and Handcuffed Prisoners
- The Monster and Other Sporadic Groups
- Taxicab Geometry
- The Power of the Pigeonhole
- Strong Laws of Small Primes
- Checker Recreations, Part I
- Checker Recreations, Part II
- Modulo Arithmetic and Hummer's Wicked Witch
- Lavinia Seeks a Room and Other Problems
- The Symmetry Creations of Scott Kim ¶
- Parabolas
- Non-Euclidean Geometry ¶
- Voting Mathematics
- A Toroidal Paradox and Other Problems
- Minimal Steiner Trees
- Trivalent Graphs, Snarks, and Boojums
The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems (2001) - The Monkey and the Coconuts
- The Calculus of Finite Differences
- Palindromes: Words and Numbers
- Curves of Constant Width
- Rep-Tiles: Replicating Figures on the Plane
- Piet Hein's Superellipse
- Penrose Tiling
- The Wonders of a Planiverse
- The Helix
- Packing Spheres
- Spheres and Hyperspheres
- The Church of the Fourth Dimension
- Hypercubes
- Non-Euclidean Geometry
- Rotations and Reflections
- The Symmetry Creations of Scott Kim
- The Art of M.C. Escher
- Klein Bottles and Other Surfaces
- The Topology of Knots
- Doughnuts: Linked and Knotted
- Probability and Ambiguity
- Nontransitive Dice and Other Probability Paradoxes
- Nontransitive Paradoxes
- Infinite Regress
- Aleph-Null and Aleph-One
- Alephs and Supertasks
- White, Brown and Fractal Music
- Conway's Surreal Numbers
- Hexaflexagons
- The Soma Cube
- The Game of Life, Part I
- The Combinatorics of Paper Folding
- Ramsey Theory
- Bulgarian Solitaire and Other Seemingly Endless Tasks
- A Matchbox Game-Learning Machine
- Sprouts and Brussels Sprouts
- Generalized Ticktacktoe
- The New Eleusis
- Time Travel
- Does Time Ever Stop? Can the Past Be Altered?
- Induction and Probability
- Simplicity
- The Paradox of the Unexpected Hanging
- Newcomb's Paradox
- Nothing
- Everything
- Melody-Making Machines
- Mathematical Zoo
- Douglas Hofstader's Gödel, Escher, Bach
- Six Sensational Discoveries