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Selected Papers on Fun and Games

Donald E. Knuth
CSLI Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
, on

Don Knuth is a serious mathematician and computer scientist, but he has always known that having fun is important. Accepting the Frontiers of Knowledge Award from the BBVA Foundation in Spain, Knuth argued that three elements came together when he did his best work: theory, practice, and fun. He noted that the best theories come from thinking about practice and that good practice needs to be informed by solid theoretical underpinnings. Nevertheless, he said, the strongest motivation to do the work, the thing that brought theory and practice together and made it all sing, was the joy of it all:

In fact my theoretical work has been driven by intellectual curiosity, by a compulsion to answer intriguing questions that seem to have begged for answers. And I’ve also experienced a thrill whenever I’ve been able to train a computer to produce beautiful patterns of numbers or images. It’s enormously exciting to imagine how electrons dance inside a machine when it is performing computations. So it seems to me that the joy of such so-called “aha moments” is what really lies behind all scientific discoveries and advances in technology.

(You can find the acceptance speech in the Companion to the Papers of Donald Knuth.)

Selected Papers on Fun and Games is mostly just joy, without any ulterior purpose. It is about Knuth having fun and bringing the reader along. Knuth says he saved this, the last of eight volumes of collected papers, as a kind of “dessert course” at the end of a rich and satisfying meal. In the other volumes, Knuth’s sense of fun was visible, but was mostly serving more serious ends. Here, it’s all just for fun.

Of course, there is always an underlying seriousness. As Martin Gardner said, “no sharp line separates entertaining math from serious math” (in A Gardner’s Workout, quoted by Knuth in the preface). Knuth agrees: “I’ve never been able to see any boundary between scientific research and game-playing.” That doesn’t mean, of course, that there is no distinction; rather, the two things sometimes approach each other quite closely and even seem to blend together. So in this book one finds a range of things, from pure zaniness and parodies to seriously entertaining mathematics.

The book opens with Knuth’s first publication, in MAD magazine, 1957. It actually appears in three versions: first as it appeared in MAD with illustrations by Wally Wood, then in the form it was originally submitted, and finally in a version published in a college magazine. (Have any other mathematicians managed to publish in MAD? And oh, to have Wood illustrate one’s work!)

Next comes Knuth’s first rejected paper, “submitted to MAD magazine on 28 April 1960 and promptly returned by their Ideas Editor.” A crossword puzzle didn’t quite fit MAD’s goals, it seems. It is helpfully presented here with a solution.

Most of the volume is devoted to “recreational mathematics,” a fuzzy category that includes everything from interesting problems to serious mathematics done for fun: billiards, probability, recursive sequences, magic squares, combinatorial games, even an algorithm that generates many different harmonizations for any given melody. There are many chapters on games, from basketball (!) to combinatorial games. Several chapters deal with word play, which mathematicians notoriously enjoy. There are chapters on puzzles and even one on “geek art.” The book closes with “An Earth-Shattering Announcement,” describing a successor to TeX.

It’s all delightful. I own and cherish copies of some of the earlier collections of Knuth’s papers, but I already know that this one is going to be my favorite.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College. He has never published any papers with illustrations.

  • 1 The Potrzebie System of Weights and Measures
  • 2 Official Tables of the Potrzebie System
  • 3 The Revolutionary Potrzebie
  • 4 A MAD Crossword
  • 5 Counterexample to a Statement of Peano
  • 6 The Complexity of Songs
  • 8 Math Ace: The Plot Thickens
  • 9 Billiard Balls in an Equilateral Triangle
  • 10 Representing Numbers Using Only One 4
  • 11 Very Magic Squares
  • 12 The Gamow-Stern Elevator Problem
  • 13 Fibonacci Multiplication
  • 14 A Fibonacci-like Sequence of Composite Numbers
  • 15 Transcendental Numbers Based on the Fibonacci Sequence
  • 16 Supernatural Numbers
  • 17 Mathematical Vanity Plates
  • 18 Diamond Signs
  • 19 The Orchestra Song
  • 20 Gnebbishland
  • 21 A Carol for Advent
  • 22 Randomness in Music
  • 23 Basketball's Electronic Coach
  • 24 The Triel: A New Solution
  • 25 The Computer as Master Mind
  • 26 Move It Or Lose It
  • 27 Adventure
  • 28 Ziegler's Giant Bar
  • 29 Th5 E CH3 EmIC2 Al2 Ca3 P4Er
  • 30 N-ciphered texts
  • 31 Disappearances
  • 32 Lewis Carroll's word-ward-ware-dare-dame-game
  • 33 Blood, Sweat, and Tears
  • 34 Biblical Ladders
  • 35 ETAOIN SHRDLU Non-Crashing Sets
  • 36 Quadrata Obscura (Hidden Latin Squares)
  • 37 5 x 5 x 5 Word Cubes by Computer
  • 38 Dancing Links
  • 39 Nikoli Puzzle Favors
  • 40 Uncrossed Knight's Tours
  • 41 Celtic Knight's Tours
  • 42 Long and Skinny Knight's Tours
  • 43 Leaper Graphs
  • 44 Number Representations and Dragon Curves
  • 45 Mathematics and Art: The Dragon Curve in Ceramic Tile
  • 46 Christmas Cards
  • 47 Geek Art
  • 48 Remembering Martin Gardner
  • 49 An Earthshaking Announcement