99 Variations on a Proof
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99 Variations on a Proof

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eBook - PDF

99 Variations on a Proof

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About This Book

An exploration of mathematical style through 99 different proofs of the same theorem This book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem. Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.Inspired by the experiments of the Paris-based writing group known as the Oulipo—whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp—Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor.Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

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Information

Publisher
Princeton University Press
Year
2019
ISBN
9780691185422
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. 0 Omitted
  8. 1 One-Line
  9. 2 Two-Column
  10. 3 lllustrated
  11. 4 Elementary
  12. 5 Puzzle
  13. 6 Axiomatic
  14. 7 Found
  15. 8 Prerequisite
  16. 9 Monosyllabic
  17. 10 Wordless
  18. 11 Exam
  19. 12 Ruler and Compass
  20. 13 Reductio ad Absurdum
  21. 14 Contrapositive
  22. 15 Matrices
  23. 16 Ancient
  24. 17 Interpreted
  25. 18 Indented
  26. 19 Jargon
  27. 20 Definitional
  28. 21 Blackboard
  29. 22 Substitution
  30. 23 Symmetry
  31. 24 Another Symmetry
  32. 25 Open Collaborative
  33. 26 Auditory
  34. 27 Algorithmic
  35. 28 Flow Chart
  36. 29 Model
  37. 30 Formulaic
  38. 31 Counterexample
  39. 32 Another Counterexample
  40. 33 Calculus
  41. 34 Medieval
  42. 35 Typeset
  43. 36 Social Media
  44. 37 Preprint
  45. 38 Parataxis
  46. 39 Origami
  47. 40 Induction
  48. 41 Newsprint
  49. 42 Analytic
  50. 43 Screenplay
  51. 44 Omitted with Condescension
  52. 45 Verbal
  53. 46 Cute
  54. 47 Clever
  55. 48 Computer Assisted
  56. 49 Outsider
  57. 50 Chromatic
  58. 51 Topological
  59. 52 Antiquity
  60. 53 Marginalia
  61. 54 Arborescent
  62. 55 Prefix
  63. 56 Prefix
  64. 57 Calculator
  65. 58 Inventor’s Paradox
  66. 59 Patented
  67. 60 Geometric
  68. 61 Modern
  69. 62 Axonometric
  70. 63 Back of the Envelope
  71. 64 Research Seminar
  72. 65 Tea
  73. 66 Hand Waving
  74. 67 Approximate
  75. 68 Word Problem
  76. 69 Statistical
  77. 70 Another Medieval
  78. 71 Blog
  79. 72 Translated
  80. 73 Another Translated
  81. 74 Yet Another Translated
  82. 75 Slide Rule
  83. 76 Experimental
  84. 77 Monte Carlo
  85. 78 Probabilistic
  86. 79 Intuitionist
  87. 80 Paranoid
  88. 81 Doggerel
  89. 82 Inconsistency
  90. 83 Correspondence
  91. 84 Tabular
  92. 85 Exhaustion
  93. 86 Another Substitution
  94. 87 Mechanical
  95. 88 Dialogue
  96. 89 Interior Monologue
  97. 90 Retrograde
  98. 91 Mystical
  99. 92 Refereed
  100. 93 Neologism
  101. 94 Authority
  102. 95 First Person
  103. 96 Electrostatic
  104. 97 Psychedelic
  105. 98 Mondegreen
  106. 99 Prescribed
  107. Postscript
  108. Acknowledgments
  109. Notes
  110. Sources
  111. Index