Martin Gardner column to book mapping — Scientific American article order

Peter Rowlett, November 2023

Mathematical Games

Martin Gardner wrote 288 'Mathematical Games' columns in Scientific American from Jan 1957 to Dec 1980, and 9 more in 1981, 1983 and 1986. From 1959 to 1997 Gardner collected his columns into 15 books, editing and adding to these as articles became chapters. There is one Scientific American article collected in the books that was not 'Mathematical Games', and one 'Mathematical Games' article not found in the books.

Article titles are not used as chapter titles in the books, so it is not straightforward to translate a reference to one of his articles to the corresponding book chapter, or vice versa. This website provides a mapping between Scientific American articles and these 15 books.

Other useful lists

I am aware of a list of books and their chapters by David Langford and a list of topics and which book chapter they are discussed in by Carl W. Lee. Wikipedia has a list of books collecting the columns and a list of his Mathematical Games columns.

Background information

There are different versions of the books available, and I have used the editions I happen to have copies of. You can see a list of books used for this project.

As the list of articles and chapters below was developed, I kept notes on where the information came from. You can view the development archive, which includes notes for each article on why I think what I think. Corrections are welcome, please contact me.

Martin Gardner Scientific American articles and books

The list here is 297 Scientific American articles in publishing order. You can also view a list of all 310 book chapters and which article they are drawn from: list of all book chapters.

YearMonthArticle titleBookChapter
1956DecFlexagons [not Mathematical Games]1. Mathematical Puzzles and Diversions1. Hexaflexagons
1957JanA new kind of magic square with remarkable properties1. Mathematical Puzzles and Diversions2. Magic with a Matrix
1957FebAn assortment of maddening puzzles1. Mathematical Puzzles and Diversions3. Nine Problems
1957MarSome old and new versions of ticktacktoe1. Mathematical Puzzles and Diversions4. Ticktactoe, or Noughts and Crosses
1957AprParadoxes dealing with birthdays, playing cards, coins, crows and red-haired typists1. Mathematical Puzzles and Diversions5. Probability Paradoxes
1957MayAbout the remarkable similarity between the Icosian Game and the Tower of Hanoi1. Mathematical Puzzles and Diversions6. The Icosian Game and the Tower of Hanoi
1957JunCurious figures descended from the Moebius band, which has only one side and one edge1. Mathematical Puzzles and Diversions7. Curious Topological Models
1957JulConcerning the game of Hex, which may be played on the tiles of the bathroom floor1. Mathematical Puzzles and Diversions8. The Game of Hex
1957AugThe life and work of Sam Loyd, a mighty inventor of puzzles1. Mathematical Puzzles and Diversions9. Sam Loyd: America’s Greatest Puzzlist
1957SepConcerning various card tricks with a mathematical message1. Mathematical Puzzles and Diversions10. Mathematical Card Tricks
1957OctHow to remember numbers by mnemonic devices such as cuff links and red zebras1. Mathematical Puzzles and Diversions11. Memorizing Numbers
1957NovNine titillating puzzles1. Mathematical Puzzles and Diversions12. Nine More Problems
1957DecMore about complex dominoes1. Mathematical Puzzles and Diversions13. Polyominoes
1958JanA collection of tantalizing fallacies of mathematics1. Mathematical Puzzles and Diversions14. Fallacies
1958FebConcerning the game of Nim and its mathematical analysis1. Mathematical Puzzles and Diversions15. Nim and Tic Tax
1958MarAbout left- and right-handedness, mirror images and kindred matters1. Mathematical Puzzles and Diversions16. Left or Right?
1958AprConcerning the celebrated puzzle of five sailors, a monkey and a pile of coconuts2. More Mathematical Puzzles and Diversions9. The Monkey and the Coconuts
1958MayAbout tetraflexagons and tetraflexagation2. More Mathematical Puzzles and Diversions2. Tetraflexagons
1958JunAbout Henry Ernest Dudeney, a brilliant creator of puzzles2. More Mathematical Puzzles and Diversions3. Henry Ernest Dudeney:: England’s Greatest Puzzlist
1958JulSome diverting tricks which involve the concept of numerical congruence2. More Mathematical Puzzles and Diversions4. Digital Roots
1958AugA third collection of "brain-teasers"2. More Mathematical Puzzles and Diversions5. Nine Problems
1958SepA game in which standard pieces composed of cubes are assembled into larger forms2. More Mathematical Puzzles and Diversions6. The Soma Cube
1958OctFour mathematical diversions involving concepts of topology2. More Mathematical Puzzles and Diversions7. Recreational Topology
1958NovHow rectangles, including squares, can be divided into squares of unequal size [cover]2. More Mathematical Puzzles and Diversions17. Squaring the Square
1958DecDiversions which involve the five Platonic solids2. More Mathematical Puzzles and Diversions1. The Five Platonic Solids
1959JanAbout mazes and how they can be traversed2. More Mathematical Puzzles and Diversions10. Mazes
1959Feb"Brain-teasers" that involve formal logic2. More Mathematical Puzzles and Diversions11. Recreational Logic
1959MarConcerning the properties of various magic squares2. More Mathematical Puzzles and Diversions12. Magic Squares
1959AprThe mathematical diversions of a fictitious carnival man2. More Mathematical Puzzles and Diversions13. James Hugh Riley Shows, Inc.
1959MayAnother collection of "brain-teasers"2. More Mathematical Puzzles and Diversions14. Nine More Problems
1959JunAn inductive card game2. More Mathematical Puzzles and Diversions15. Eleusis: The Induction Game
1959JulAbout Origami, the Japanese art of folding objects out of paper2. More Mathematical Puzzles and Diversions16. Origami
1959AugAbout phi, an irrational number that has some remarkable geometrical expressions2. More Mathematical Puzzles and Diversions8. Phi: The Golden Ratio
1959SepConcerning mechanical puzzles, and how an enthusiast has collected 2,000 of them2. More Mathematical Puzzles and Diversions18. Mechanical Puzzles
1959OctProblems involving questions of probability and ambiguity2. More Mathematical Puzzles and Diversions19. Probability and Ambiguity
1959NovHow three modern mathematicians disproved a celebrated conjecture of Leonhard Euler [cover]3. New Mathematical Diversions from Scientific American14. Euler’s Spoilers: The Discovery of an Order-10 Graeco-Latin Square
1959DecDiversions that clarify group theory, particularly by the weaving of braids3. New Mathematical Diversions from Scientific American2. Group Theory and Braids
1960JanA fanciful dialogue about the wonders of numerology4. The Magic Numbers of Dr. Matrix1. New York
1960FebA fifth collection of "brain-teasers"3. New Mathematical Diversions from Scientific American3. Eight Problems
1960MarThe games and puzzles of Lewis Carroll3. New Mathematical Diversions from Scientific American4. The Games and Puzzles of Lewis Carroll
1960AprAbout mathematical games that are played on boards3. New Mathematical Diversions from Scientific American6. Board Games
1960MayReflections on the packing of spheres3. New Mathematical Diversions from Scientific American7. Packing Spheres
1960JunRecreations involving folding and cutting sheets of paper3. New Mathematical Diversions from Scientific American5. Paper Cutting
1960JulIncidental information about the extraordinary number pi3. New Mathematical Diversions from Scientific American8. The Transcendental Number Pi
1960AugAn imaginary dialogue on "mathemagic": tricks based on mathematical principles3. New Mathematical Diversions from Scientific American9. Victor Eigen: Mathemagician
1960SepThe celebrated four-color map problem of topology3. New Mathematical Diversions from Scientific American10. The Four-Color Map Theorem
1960OctA new collection of "brain-teasers"3. New Mathematical Diversions from Scientific American12. Nine Problems
1960NovMore about the shapes that can be made with complex dominoes3. New Mathematical Diversions from Scientific American13. Polyominoes and Fault-Free Rectangles
1960DecSome recreations involving the binary number system3. New Mathematical Diversions from Scientific American1. The Binary System
1961JanIn which the author chats again with Dr. Matrix, numerologist extraordinary4. The Magic Numbers of Dr. Matrix2. Los Angeles
1961FebDiversions that involve one of the classic conic sections: the ellipse3. New Mathematical Diversions from Scientific American15. The Ellipse
1961MarHow to play dominoes in two and three dimensions3. New Mathematical Diversions from Scientific American16. The 24 Color Squares and the 30 Color Cubes
1961AprConcerning the diversions in a new book on geometry [cover]3. New Mathematical Diversions from Scientific American17. H.S.M. Coxeter
1961MayIn which the editor of this department meets the legendary Bertrand Apollinax3. New Mathematical Diversions from Scientific American11. Mr. Apollinax Visits New York
1961JunA new collection of "brain teasers"3. New Mathematical Diversions from Scientific American19. Nine More Problems
1961JulSome diverting mathematical board games3. New Mathematical Diversions from Scientific American18. Bridg-it and Other Games
1961AugSome entertainments that involve the calculus of finite differences3. New Mathematical Diversions from Scientific American20. The Calculus of Finite Differences
1961SepSurfaces with edges linked in the same way as the three rings of a well-known design5. The Unexpected Hanging and Other Mathematical Diversions 2. Knots and Borromean Rings
1961OctDiversions that involve the mathematical constant "e"5. The Unexpected Hanging and Other Mathematical Diversions 3. The Transcendental Number e
1961NovWherein geometrical figures are dissected to make other figures5. The Unexpected Hanging and Other Mathematical Diversions 4. Geometric Dissections
1961DecOn the theory of probability and the practice of gambling5. The Unexpected Hanging and Other Mathematical Diversions 5. Scarne on Gambling
1962JanAn adventure in hyperspace at the Church of the Fourth Dimension5. The Unexpected Hanging and Other Mathematical Diversions 6. The Church of the Fourth Dimension
1962FebA clutch of diverting problems5. The Unexpected Hanging and Other Mathematical Diversions 7. Eight Problems
1962MarHow to build a game-learning machine and teach it to play and win5. The Unexpected Hanging and Other Mathematical Diversions 8. A Matchbox Game-Learning Machine
1962AprAbout three types of spirals and how to construct them5. The Unexpected Hanging and Other Mathematical Diversions 9. Spirals
1962MaySymmetry and asymmetry and the strange world of upside-down art5. The Unexpected Hanging and Other Mathematical Diversions 10. Rotations and Reflections
1962JunThe game of solitaire and some variations and transformations5. The Unexpected Hanging and Other Mathematical Diversions 11. Peg Solitaire
1962JulFiction about life in two dimensions5. The Unexpected Hanging and Other Mathematical Diversions 12. Flatlands
1962AugA variety of diverting tricks collected at a fictitious convention of magicians5. The Unexpected Hanging and Other Mathematical Diversions 13. Chicago Magic Convention
1962SepTests that show whether a large number can be divided by a number from 2 to 125. The Unexpected Hanging and Other Mathematical Diversions 14. Tests of Divisibility
1962OctA collection of puzzles involving numbers, logic, and probability5. The Unexpected Hanging and Other Mathematical Diversions 15. Nine Problems
1962NovSome puzzles based on checkerboards5. The Unexpected Hanging and Other Mathematical Diversions 16. The Eight Queens and Other Chessboard Diversions
1962DecSome simple tricks and manipulations from the ancient lore of string play5. The Unexpected Hanging and Other Mathematical Diversions 17. A Loop of String
1963JanThe author pays his annual visit to Dr. Matrix, the numerologist4. The Magic Numbers of Dr. Matrix3. Sing Sing
1963FebCurves of constant width, one of which makes it possible to drill square holes5. The Unexpected Hanging and Other Mathematical Diversions 18. Curves of Constant Width
1963MarA new paradox, and variations on it, about a man condemned to be hanged5. The Unexpected Hanging and Other Mathematical Diversions 1. The Paradox of the Unexpected Hanging
1963AprA bit of foolishness for April Fools' Day5. The Unexpected Hanging and Other Mathematical Diversions 20. Thirty-Seven Catch Questions
1963MayOn "rep-tiles", polygons that can make larger and smaller copies of themselves5. The Unexpected Hanging and Other Mathematical Diversions 19. Rep-Tiles: Replicating Figures on the Plane
1963JunA discussion of helical structures, from corkscrews to DNA molecules6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American1. The Helix
1963JulTopological diversions, including a bottle with no inside or outside6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American2. Klein Bottles and Other Surfaces
1963AugPermutations and paradoxes in combinatorial mathematics6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American3. Combinatorial Theory
1963SepHow to solve puzzles by graphing the rebounds of a bouncing ball6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American4. Bouncing Balls in Polygons and Polyhedrons
1963OctAbout two new and two old mathematical board games6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American5. Four Unusual Board Games
1963NovA mixed bag of problems6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American6. The Rigid Square and Eight Other Problems
1963DecHow to use the odd-even check for tricks and problem-solving6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American8. Parity Checks
1964JanPresenting the one and only Dr. Matrix, numerologist, in his annual performance4. The Magic Numbers of Dr. Matrix5. Chicago
1964FebThe hypnotic fascination of sliding-block puzzles6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American7. Sliding-Block Puzzles
1964MarThe remarkable lore of the prime numbers [cover]6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American9. Patterns and Primes
1964AprVarious problems based on planar graphs, or sets of "vertices" connected by "edges"6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American10. Graph Theory
1964MayThe tyranny of 10 overthrown with the ternary number system6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American11. The Ternary System
1964JunA collection of short problems and more talk of prime numbers6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American12. The Trip around the Moon and Seven Other Problems
1964JulCurious properties of a cycloid curve6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American13. The Cycloid: Helen of Geometry
1964AugConcerning several magic tricks based on mathematical principles6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American14. Mathematical Magic Tricks
1964SepPuns, palindromes and other word games that partake of the mathematical spirit6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American15. Word Play
1964OctSimple proofs of the Pythagorean theorem, and sundry other matters6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American16. The Pythagorean Theorem
1964NovSome paradoxes and puzzles involving infinite series and the concept of limit6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American17. Limits of Infinite Series
1964DecOn polyiamonds: shapes that are made out of equilateral triangles6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American18. Polyiamonds
1965JanSome comments by Dr. Matrix on symmetries and reversals4. The Magic Numbers of Dr. Matrix6. Miami Beach
1965FebTetrahedrons in nature and architecture, and puzzles involving this simplest polyhedron6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American19. Tetrahedons
1965MarA new group of short problems6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American20. Coleridge’s Apples and Eight Other Problems
1965AprThe infinite regress in philosophy, literature and mathematical proof6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American22. Infinite Regress
1965MayThe lattice of integers considered as an orchard or a billiard table6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American21. The Lattice of Integers
1965JunSome diversions and problems from Mr. O'Gara, the postman6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American23. O’Gara, the Mathematical Mailman
1965JulOn the relation between mathematics and the ordered patterns of Op art [cover]6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American24. Op Art
1965AugThoughts on the task of communication with intelligent organisms on other worlds6. Martin Gardner's Sixth Book of Mathematical Games from Scientific American25. Extraterrestrial Communications
1965SepThe "superellipse": a curve that lies between the ellipse and the rectangle7. Mathematical Carnival18. Piet Hein’s Superellipse
1965OctPentominoes and polyominoes: five games and a sampling of problems8. Mathematical Magic Show13. Polyominoes and Rectification
1965NovA selection of elementary word and number problems7. Mathematical Carnival9. The Red-Faced Cube and Other Problems
1965DecMagic stars, graphs and polyhedrons7. Mathematical Carnival5. Magic Stars and Polyhedrons
1966JanDr. Matrix returns, now in the guise of a neo-Freudian psychonumeranalyst4. The Magic Numbers of Dr. Matrix7. Philadelphia
1966FebRecreational numismatics, or a purse of coin puzzles7. Mathematical Carnival2. Penny Puzzles
1966MarThe hierarchy of infinities and the problems it spawns7. Mathematical Carnival3. Aleph-Null and Aleph-one
1966AprThe eerie mathematical art of Maurits C. Escher7. Mathematical Carnival8. The Art of M. C. Escher
1966MayHow to "cook" a puzzle, or mathematical one-uppery7. Mathematical Carnival17. Cooks and Quibble-Cooks
1966JunThe persistence (and futility) of efforts to trisect the angle7. Mathematical Carnival19. How to Trisect an Angle
1966JulFreud's friend Wilhelm Fliess and his theory of male and female life cycles7. Mathematical Carnival12. The Numerology of Dr. Fliess
1966AugPuzzles that can be solved by reasoning based on elementary physical principles7. Mathematical Carnival14. The Rising Hourglass and Other Physics Puzzles
1966SepThe problem of Mrs. Perkins' quilt7. Mathematical Carnival11. Mrs. Perkins’ Quilt and Other Square-Packing Problems
1966OctCan the shuffling of cards (and other apparently random events) be reversed?7. Mathematical Carnival10. Card Shuffles
1966NovIs it possible to visualize a four-dimensional figure?7. Mathematical Carnival4. Hypercubes
1966DecThe multiple charms of Pascal's triangle7. Mathematical Carnival15. Pascal’s Triangle
1967JanDr. Matrix delivers a talk on acrostics4. The Magic Numbers of Dr. Matrix9. Wordsmith College
1967FebMathematical strategies for two-person contests7. Mathematical Carnival16. Jam, Hot, and Other Games
1967MarAn array of problems that can be solved with elementary mathematical techniques8. Mathematical Magic Show15. The Dragon Curve and Other Problems
1967AprThe amazing feats of professional mental calculators, and some tricks of the trade7. Mathematical Carnival6. Calculating Prodigies
1967MayCube-root extraction and the calendar trick, or how to cheat in mathematics7. Mathematical Carnival7. Tricks of Lightning Calculators
1967JunThe polyhex and the polyabolo, polygonal jigsaw puzzle pieces8. Mathematical Magic Show11. Polyhexes and Polyaboloes
1967JulOf sprouts and Brussels sprouts, games with a topological flavor7. Mathematical Carnival1. Sprouts and Brussels Sprouts
1967AugIn which a computer prints out mammoth polygonal factorials8. Mathematical Magic Show4. Factorial Oddities
1967SepDouble acrostics, stylized Victorian ancestors of today's crossword puzzle8. Mathematical Magic Show6. Double Acrostics
1967OctProblems that are built on the knight's move in chess8. Mathematical Magic Show14. Knights of the Square Table
1967NovA mixed bag of logical and illogical problems to solve8. Mathematical Magic Show5. The Cocktail Cherry and Other Problems
1967DecGame theory is applied (for a change) to games8. Mathematical Magic Show3. Game Theory, Guess It, Foxholes
1968JanThe beauties of the square, as expounded by Dr. Matrix to rehabilitate the hippie4. The Magic Numbers of Dr. Matrix10. Squaresville
1968FebCombinatorial problems involving tree graphs and forests of trees8. Mathematical Magic Show17. Trees
1968MarA short treatise on the useless elegance of perfect numbers and amicable pairs8. Mathematical Magic Show12. Perfect, Amicable, Sociable
1968AprPuzzles and tricks with a dollar bill9. Mathematical Circus20. Dollar Bills
1968MayCircles and spheres, and how they kiss and pack9. Mathematical Circus3. Spheres and Hyperspheres
1968JunCombinatorial possibilities in a pack of shuffled cards8. Mathematical Magic Show7. Playing Cards
1968JulOn the meaning of randomness and some ways of achieving it7. Mathematical Carnival13. Random Numbers
1968AugAn array of puzzles and tricks, with a few traps for the unwary8. Mathematical Magic Show10. Ridiculous Questions
1968SepCounting systems and the relationship between numbers and the real world8. Mathematical Magic Show8. Finger Arithmetic
1968OctMacMahon's color triangles and the joys of fitting them together8. Mathematical Magic Show16. Colored Triangles and Cubes
1968NovOn the ancient lore of dice and the odds against making a point8. Mathematical Magic Show18. Dice
1968DecThe world of the Möbius strip: endless, edgeless and one-sided8. Mathematical Magic Show9. Möbius Bands
1969JanDr. Matrix gives his explanation of why Mr. Nixon was elected President4. The Magic Numbers of Dr. Matrix12. Fifth Avenue
1969FebBoolean algebra, Venn diagrams and the propositional calculus9. Mathematical Circus8. Boolean Algebra
1969MarThe multiple fascinations of the Fibonacci sequence9. Mathematical Circus13. Fibonacci and Lucas Numbers
1969AprAn octet of problems that emphasize gamesmanship, logic and probability9. Mathematical Circus15. The Rotating Round Table and Other Problems
1969MayThe rambling random walk and its gambling equivalent9. Mathematical Circus6. Random Walks and Gambling
1969JunRandom walks, by semidrunk bugs and others, on the square and on the cube9. Mathematical Circus7. Random Walks on the Plane and in Space
1969JulTricks, games and puzzles that employ matches as counters and line segments9. Mathematical Circus2. Matches
1969AugSimplicity as a scientific concept: Does nature keep her accounts on a thumbnail?9. Mathematical Circus14. Simplicity
1969SepGeometric constructions with a compass and a straightedge, and also with a compass alone9. Mathematical Circus17. Mascheroni Constructions
1969OctA numeranalysis by Dr. Matrix of the lunar flight of Apollo 114. The Magic Numbers of Dr. Matrix13. The Moon
1969NovA new pencil-and-paper game based on inductive reasoning [cover]9. Mathematical Circus4. Patterns of Induction
1969DecA handful of combinatorial problems based on dominoes9. Mathematical Circus12. Dominoes
1970JanThe abacus: primitive but effective digital computer9. Mathematical Circus18. The Abacus
1970FebNine new puzzles to solve9. Mathematical Circus11. Eccentric Chess and Other Problems
1970MarCyclic numbers and their properties9. Mathematical Circus10. Cyclic Numbers
1970AprSome mathematical curiosities embedded in the solar system9. Mathematical Circus16. Solar System Oddities
1970MayOf optical illusions, from figures that are undecidable to hot dogs that float9. Mathematical Circus1. Optical Illusions
1970JunElegant triangle theorems not to be found in Euclid9. Mathematical Circus5. Elegant Triangles
1970JulDiophantine analysis and the problem of Fermat's legendary "last theorem"10. Wheels, Life, and Other Mathematical Amusements2. Diophantine Analysis and Fermat's Last Theorem
1970AugBackward run numbers, letters, words and sentences until boggles the mind9. Mathematical Circus19. Palindromes: Words and Numbers
1970SepOn the cyclical curves generated by wheels that roll along wheels10. Wheels, Life, and Other Mathematical Amusements1. Wheels
1970OctThe fantastic combinations of John Conway's new solitaire game "life"10. Wheels, Life, and Other Mathematical Amusements20. The Game of Life, Part I
1970NovA new collection of short problems and the answers to some of "life's"10. Wheels, Life, and Other Mathematical Amusements3. The Knotted Molecule and Other Problems
1970DecThe paradox of the nontransitive dice and the elusive principle of indifference10. Wheels, Life, and Other Mathematical Amusements5. Nontransitive Dice and Other Probability Paradoxes
1971JanLessons from Dr. Matrix in chess and numerology4. The Magic Numbers of Dr. Matrix14. Honolulu
1971FebOn cellular automata, self-reproduction, the Garden of Eden and the game "life" [cover]10. Wheels, Life, and Other Mathematical Amusements21. The Game of Life, Part II
1971MarThe orders of infinity, the topological nature of dimension and "supertasks"10. Wheels, Life, and Other Mathematical Amusements4. Alephs and Supertasks
1971AprGeometric fallacies: hidden errors pave the road to absurd conclusions10. Wheels, Life, and Other Mathematical Amusements6. Geometric Fallacies
1971MayThe combinatorial richness of folding a piece of paper10. Wheels, Life, and Other Mathematical Amusements7. The Combinatorics of Paper Folding
1971JunThe Turing game and the question it presents: Can a computer think?9. Mathematical Circus9. Can Machines Think?
1971JulQuickie problems: not hard, but look out for the curves10. Wheels, Life, and Other Mathematical Amusements8. A Set of Quickies
1971AugTicktacktoe and its complications10. Wheels, Life, and Other Mathematical Amusements9. Ticktacktoe Games
1971SepThe plaiting of Plato's polyhedrons and the asymmetrical yin-yang-lee10. Wheels, Life, and Other Mathematical Amusements10. Plaiting Polyhedrons
1971OctNew puzzles from the game of Halma, the noble ancestor of Chinese checkers10. Wheels, Life, and Other Mathematical Amusements11. The Game of Halma
1971NovAdvertising premiums to beguile the mind: classics by Sam Loyd, master puzzle-poser10. Wheels, Life, and Other Mathematical Amusements12. Advertising Premiums
1971DecFurther encounters with touching cubes, and the paradoxes of Zeno as "supertasks"10. Wheels, Life, and Other Mathematical Amusements13. Salmon on Austin's Dog
1972JanHow to triumph at nim by playing safe, and John Horton Conway's game "Hackenbush"10. Wheels, Life, and Other Mathematical Amusements14. Nim and Hackenbush
1972FebDr. Matrix poses some heteroliteral puzzles while peddling perpetual motion in Houston4. The Magic Numbers of Dr. Matrix15. Houston
1972MarThe graceful graphs of Solomon Golomb, or how to number a graph parsimoniously10. Wheels, Life, and Other Mathematical Amusements15. Golomb’s Graceful Graphs
1972AprA topological problem with a fresh twist, and eight other new recreational puzzles10. Wheels, Life, and Other Mathematical Amusements16. Charles Addams’ Skier and other Problems
1972MayChallenging chess tasks for puzzle buffs and answers to the recreational problems10. Wheels, Life, and Other Mathematical Amusements17. Chess Tasks
1972JunA miscellany of transcendental problems: simple to state but not at all easy to solve10. Wheels, Life, and Other Mathematical Amusements18. Slither, 3X+1, and Other Curious Questions
1972JulAmazing mathematical card tricks that do not require prestidigitation10. Wheels, Life, and Other Mathematical Amusements19. Mathematical Tricks With Cards
1972AugThe curious properties of the Gray code and how it can be used to solve puzzles11. Knotted Doughnuts and Other Mathematical Entertainments2. The Binary Gray Code
1972SepPleasurable problems with polycubes11. Knotted Doughnuts and Other Mathematical Entertainments3. Polycubes
1972OctWhy the long arm of coincidence is usually not as long as it seems11. Knotted Doughnuts and Other Mathematical Entertainments1. Coincidence
1972NovOn the practical uses and bizarre abuses of Sir Francis Bacon's biliteral cipher11. Knotted Doughnuts and Other Mathematical Entertainments4. Bacon’s Cipher
1972DecKnotty problems with a two-hole torus11. Knotted Doughnuts and Other Mathematical Entertainments5. Doughnuts: Linked and Knotted
1973JanSim, Chomp and Race Track: new games for the intellect (and not for Lady Luck)11. Knotted Doughnuts and Other Mathematical Entertainments9. Sim, Chomp and Racetrack
1973FebUp-and-down elevator games and Piet Hein's mechanical puzzles11. Knotted Doughnuts and Other Mathematical Entertainments10. Elevators
1973MarThe calculating rods of John Napier, the eccentric father of the logarithm11. Knotted Doughnuts and Other Mathematical Entertainments7. Napier's Bones
1973AprHow to turn a chessboard into a computer and to calculate with negabinary numbers11. Knotted Doughnuts and Other Mathematical Entertainments8. Napier’s Abacus
1973MayA new miscellany of problems11. Knotted Doughnuts and Other Mathematical Entertainments6. The Tour of the Arrows and Other Problems
1973JunPlotting the crossing number of graphs11. Knotted Doughnuts and Other Mathematical Entertainments11. Crossing Numbers
1973JulFree will revisited, with a mind-bending prediction paradox by William Newcomb11. Knotted Doughnuts and Other Mathematical Entertainments13. Newcomb’s Paradox
1973AugAn astounding self-test of clairvoyance by Dr. Matrix4. The Magic Numbers of Dr. Matrix16. Clairvoyance Test
1973SepProblems on the surface of a sphere offer an entertaining introduction to point sets11. Knotted Doughnuts and Other Mathematical Entertainments12. Point Sets on the Sphere
1973Oct"Look-see" diagrams that offer visual proof of complex algebraic formulas11. Knotted Doughnuts and Other Mathematical Entertainments16. Look-See Proofs
1973NovFantastic patterns traced by programmed "worms"11. Knotted Doughnuts and Other Mathematical Entertainments17. Worm Paths
1973DecOn expressing integers as the sum of cubes and other unsolved number-theory problems11. Knotted Doughnuts and Other Mathematical Entertainments18. Waring’s Problems
1974JanThe combinatorial basis of the "I Ching," the Chinese book of divination and wisdom [cover]11. Knotted Doughnuts and Other Mathematical Entertainments20. The I Ching
1974FebCram, crosscram and quadraphage: new games having elusive winning strategies11. Knotted Doughnuts and Other Mathematical Entertainments19. Cram, Bynum and Quadraphage
1974MarReflections on Newcomb's problem: a prediction and free-will dilemma11. Knotted Doughnuts and Other Mathematical Entertainments14. Reflections on Newcomb’s Paradox
1974AprNine challenging problems, some rational and some not11. Knotted Doughnuts and Other Mathematical Entertainments15. Reverse the Fish and Other Problems
1974MayOn the contradictions of time travel12. Time Travel and Other Mathematical Bewilderments1. Time Travel
1974JunDr. Matrix brings his numerological Science to bear on the occult powers of the pyramid4. The Magic Numbers of Dr. Matrix17. Pyramid Lake
1974JulOn the patterns and the unusual properties of figurate numbers12. Time Travel and Other Mathematical Bewilderments2. Hexes and Stars
1974AugOn the fanciful history and the creative challenges of the puzzle game of tangrams12. Time Travel and Other Mathematical Bewilderments3. Tangrams, Part 1
1974SepMore on tangrams: Combinatorial problems and the game possibilities of snug tangrams12. Time Travel and Other Mathematical Bewilderments4. Tangrams, Part 2
1974OctOn the paradoxical situations that arise from nontransitive relations12. Time Travel and Other Mathematical Bewilderments5. Nontransitive Paradoxes
1974NovSome new and dramatic demonstrations of number theorems with playing cards12. Time Travel and Other Mathematical Bewilderments6. Combinatorial Card Problems
1974DecThe arts as combinatorial mathematics, or how to compose like Mozart with dice12. Time Travel and Other Mathematical Bewilderments7. Melody-Making Machines
1975JanThe curious magic of anamorphic art [cover]12. Time Travel and Other Mathematical Bewilderments8. Anamorphic Art
1975FebHow the absence of anything leads to thoughts of nothing8. Mathematical Magic Show1. Nothing
1975MarFrom rubber ropes to rolling cubes, a miscellany of refreshing problems12. Time Travel and Other Mathematical Bewilderments9. The Rubber Rope and Other Problems
1975AprSix sensational discoveries that somehow or another have escaped public attention12. Time Travel and Other Mathematical Bewilderments10. Six Sensational Discoveries
1975MayOn the remarkable Császár polyhedron and its applications in problem solving12. Time Travel and Other Mathematical Bewilderments11. The Császár Polyhedron
1975JunGames of strategy for two players: star nim, meander, dodgem and rex12. Time Travel and Other Mathematical Bewilderments12. Dodgem and Other Simple Games
1975JulOn tessellating the plane with convex polygon tiles12. Time Travel and Other Mathematical Bewilderments13. Tiling with Convex Polygons
1975AugMore about tiling the plane: the possibilities of polyominoes, polyiamonds, and polyhexes12. Time Travel and Other Mathematical Bewilderments14. Tiling with Polyominoes, Polyiamonds, and Polyhexes
1975SepDr. Matrix finds numerological wonders in the King James Bible4. The Magic Numbers of Dr. Matrix18. The King James Bible
1975NovOn map projections (with special reference to some inspired ones) [cover]12. Time Travel and Other Mathematical Bewilderments15. Curious Maps
1975DecA random assortment of puzzles, together with reader responses to earlier problems12. Time Travel and Other Mathematical Bewilderments16. The Sixth Symbol and Other Problems
1976JanA breakthrough in magic squares, and the first perfect magic cube12. Time Travel and Other Mathematical Bewilderments17. Magic Squares and Cubes
1976FebSome elegant brick-packing problems, and a new order-7 perfect magic cube12. Time Travel and Other Mathematical Bewilderments18. Block Packing
1976MarOn the fabric of inductive logic, and some probability paradoxes12. Time Travel and Other Mathematical Bewilderments19. Induction and Probability
1976AprSnarks, Boojums and other conjectures related to the four-color-map theorem15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications23. Trivalent Graphs, Snarks, and Boojums
1976MayA few words about everything there was, is and ever will be8. Mathematical Magic Show19. Everything
1976JunCatalan numbers: an integer sequence that materializes in unexpected places12. Time Travel and Other Mathematical Bewilderments20. Catalan Numbers
1976JulFun and serious business with the small electronic calculator12. Time Travel and Other Mathematical Bewilderments21. Fun with a Pocket Calculator
1976AugThe symmetrical arrangement of the stars on the American flag and related matters12. Time Travel and Other Mathematical Bewilderments22. Tree-Plant Problems
1976SepJohn Horton Conway's book covers an infinity of games13. Penrose Tiles to Trapdoor Ciphers4. Conway's Surreal Numbers
1976OctCombinatorial problems, some old, some new and all newly attacked by computer13. Penrose Tiles to Trapdoor Ciphers5. Back from the Klondike and Other Problems
1976NovIn which DM (Dr. Matrix) is revealed as the guru of PM (Pentagonal Meditation)4. The Magic Numbers of Dr. Matrix19. Calcutta
1976DecIn which "monster" curves force redefinition of the word "curve"13. Penrose Tiles to Trapdoor Ciphers3. Mandelbrot’s Fractals
1977JanExtraordinary nonperiodic tiling that enriches the theory of tiles [cover]13. Penrose Tiles to Trapdoor Ciphers1. Penrose Tiling
1977FebThe flip-strip sonnet, the lipogram and other mad modes of wordplay13. Penrose Tiles to Trapdoor Ciphers6. The Oulipo
1977MarCornering a queen leads unexpectedly into corners of the theory of numbers13. Penrose Tiles to Trapdoor Ciphers8. Wythoff's Nim
1977AprThe pool-table triangle, a limerick paradox and divers other challenges13. Penrose Tiles to Trapdoor Ciphers9. Pool-Ball Triangles and Other Problems
1977MayThe "jump proof" and its similarity to the toppling of a row of dominoes13. Penrose Tiles to Trapdoor Ciphers10. Mathematical Induction and Colored Hats
1977JunThe concept of negative numbers and the difficulty of grasping it13. Penrose Tiles to Trapdoor Ciphers11. Negative Numbers
1977JulCutting things into equal parts leads into significant areas of mathematics13. Penrose Tiles to Trapdoor Ciphers12. Cutting Shapes into N Congruent Parts
1977AugA new kind of cipher that would take millions of years to break13. Penrose Tiles to Trapdoor Ciphers13. Trapdoor Ciphers
1977SepOn conic sections, ruled surfaces and other manifestations of the hyperbola13. Penrose Tiles to Trapdoor Ciphers15. Hyperbolas
1977OctOn playing New Eleusis, the game that simulates the search for truth13. Penrose Tiles to Trapdoor Ciphers16. The New Eleusis
1977NovIn which joining sets of points by lines leads into diverse (and diverting) paths13. Penrose Tiles to Trapdoor Ciphers17. Ramsey Theory
1977DecDr. Matrix goes to California to apply punk to rock study4. The Magic Numbers of Dr. Matrix20. Stanford
1978JanThe sculpture of Miguel Berrocal can be taken apart like an interlocking mechanical puzzle13. Penrose Tiles to Trapdoor Ciphers18. From Burrs to Berrocal
1978FebOn checker jumping, the Amazon game, weird dice, card tricks and other playful pastimes13. Penrose Tiles to Trapdoor Ciphers19. Sicherman Dice, the Kruskal Count and Other Curiosities
1978MarCount Dracula, Alice, Portia and many others consider various twists of logic13. Penrose Tiles to Trapdoor Ciphers20. Ramond Smullyan's Logic Puzzles
1978AprWhite and brown music, fractal curves and one-over-f fluctuations [cover]14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine1. White, Brown, and Fractal Music
1978MayThe Bells: versatile numbers that can count partitions of a set, primes and even rhymes14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine2. The Tinkly Temple Bells
1978JunA mathematical zoo of astounding critters, imaginary and otherwise14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine3. The Mathematical Zoo
1978JulOn Charles Sanders Peirce: philosopher and gamesman14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine4. Charles Sanders Peirce
1978AugA Möbius band has a finite thickness, and so it is actually a twisted prism14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine5. Twisted Prismatic Rings
1978SepPuzzling over a problem-solving matrix, cubes of many colors and three-dimensional dominoes14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine6. The Thirty Color Cubes
1978OctPuzzles and number-theory problems arising from the curious fractions of ancient Egypt14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine7. Egyptian Fractions
1978NovIn which a mathematical aesthetic is applied to modern minimal art14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine8. Minimal Sculpture
1978DecIs it a superintelligent robot or does Dr. Matrix ride again?4. The Magic Numbers of Dr. Matrix21. Chautauqua
1979JanThe diverse pleasures of circles that are tangent to one another14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine10. Tangent Circles
1979FebAbout rectangling rectangles, parodying Poe and many another pleasing problem14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine11. The Rotating Table and Other Problems
1979MarOn altering the past, delaying the future and other ways of tampering with time14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine12. Does Time Ever Stop? Can the Past Be Altered?
1979AprIn which players of ticktacktoe are taught to hunt bigger game14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine13. Generalized Ticktacktoe
1979MayHow to be a psychic, even if you are a horse or some other animal14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine14. Psychic Wonders and Probability
1979JunChess problems on a higher plane, including mirror images, rotations and the superqueen14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine15. Mathematical Chess Problems
1979JulDouglas R. Hofstadter's "Gödel, Escher, Bach"14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine16. Douglas Hofstadter's Gödel, Escher, Bach
1979AugThe imaginableness of the imaginary numbers14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine17. Imaginary Numbers
1979SepIn some patterns of numbers or words there may be less than meets the eye14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine18. Pi and Poetry: Some Accidental Patterns
1979OctSome packing problems that cannot be solved by sitting on the suitcase14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine20. Packing Squares
1979NovThe random number omega bids fair to hold the mysteries of the universe14. Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine21. Chaitin's Omega
1979DecA pride of problems, including one that is virtually impossible15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications21. A Toroidal Paradox and Other Problems
1980JanCheckers, a game that can be more interesting than one might think15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications13. Checker Recreations, Part I
1980FebThe coloring of unusual maps leads into uncharted territory15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications6. M-Pire Maps
1980MarGraphs that can help cannibals, missionaries, wolves, goats and cabbages get there from here15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications7. Directed Graphs and Cannibals
1980AprFun with eggs: uncooked, cooked and mathematical15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications3. Fun with Eggs, Part I
1980MayWhat unifies dinner guests, strolling schoolgirls and handcuffed prisoners?15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications8. Dinner Guests, Schoolgirls, and Handcuffed Prisoners
1980JunThe capture of the monster: a mathematical group with a ridiculous number of elements15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications9. The Monster and Other Sporadic Groups
1980JulThe pleasures of doing Science and technology in the planiverse15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications1. The Wonders of a Planiverse
1980AugOn the fine art of putting players, pills and points into their proper pigeonholes15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications11. The Power of the Pigeonhole
1980SepDr. Matrix, like Mr. Holmes, comes to an untimely and mysterious end4. The Magic Numbers of Dr. Matrix22. Istanbul
1980OctFrom counting votes to making votes count: the mathematics of elections15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications20. Voting Mathematics
1980NovTaxicab geometry offers a free ride to a non-Euclidean locale15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications10. Taxicab Geometry
1980DecPatterns in primes are a clue to the strong law of small numbers15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications12. Strong Laws of Small Primes
1981FebGauss's congruence theory was mod as early as 180115. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications15. Modulo Arithmetic and Hummer’s Wicked Witch
1981AprHow Lavinia finds a room on University Avenue, and other geometric problems15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications16. Lavinia Seeks a Room and Other Problems
1981JunThe inspired geometrical symmetries of Scott Kim15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications17. The Symmetry Creations of Scott Kim
1981AugThe abstract parabola fits the concrete world15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications18. Parabolas
1981OctEuclid's parallel postulate and its modern offspring15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications19. Non-Euclidean Geometry
1981DecThe Laffer curve and other laughs in current economics11. Knotted Doughnuts and Other Mathematical Entertainments21. The Laffer Curve
1983AugTasks you cannot help finishing no matter how hard you try to block finishing them15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications2. Bulgarian Solitaire and Other Seemingly Endless Tasks
1983SepThe topology of knots15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications5. The Topology of Knots
1986JunCasting a net on a checkerboard and other puzzles of the forest 15. The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications22. Minimal Steiner Trees

Other articles

There are five article in Scientific American written by Martin Gardner which are not collected into one of these books, one of which was a Mathematical Games column.

YearMonthArticle title
1952MarLogic Machines
1975OctConcerning an effort to demonstrate extrasensory perception by machine [Mathematical Games]
1998AugA Quarter-Century of Recreational Mathematics
2007AprIs Beauty Truth and Truth Beauty? [book review]
2967JanCan Time go Backward?