# Five-Minute Mathematics

### About this Title

**Ehrhard Behrends**, *Freie Universität Berlin, Berlin, Germany*. Translated by **David Kramer**

Publication: Miscellaneous Books

Publication Year:
2008; Volume 53

ISBNs: 978-0-8218-4348-2 (print); 978-1-4704-2484-8 (online)

DOI: https://doi.org/10.1090/mbk/053

MathSciNet review: MR2402654

MSC: Primary 00A05; Secondary 00A08

### Table of Contents

**Front/Back Matter**

**Chapters**

- Chapter 1. You can’t beat the odds
- Chapter 2. Magical mathematics: The integers
- Chapter 3. How old is the captain?
- Chapter 4. Vertiginously large prime numbers
- Chapter 5. Loss plus loss equals win
- Chapter 6. When it comes to large numbers, intuition fails
- Chapter 7. The key for encryption is the telephone book
- Chapter 8. The village barber who shaves himself
- Chapter 9. Quit while you’re ahead?
- Chapter 10. Can a monkey create great literature?
- Chapter 11. The birthday paradox
- Chapter 12. Horror vacui
- Chapter 13. Sufficient difficulties with the logic of mathematics are in fact a necessity
- Chapter 14. To change or not to change? The Monty Hall problem
- Chapter 15. In Hilbert’s Hotel there is always a vacancy
- Chapter 16. That fascinating number pi
- Chapter 17. How random events become calculable quantities
- Chapter 18. A one-million-dollar prize: How are the prime numbers distributed?
- Chapter 19. The five-dimensional cake
- Chapter 20. One night stand
- Chapter 21. Fly me to the Moon
- Chapter 22. Using residues
- Chapter 23. Top secret!
- Chapter 24. Magical mathematics: Order amidst chaos
- Chapter 25. How does one approach genius?
- Chapter 26. On semitones and twelfth roots
- Chapter 27. Why am I always standing in the wrong line?
- Chapter 28. Zero: An undeservedly underrated number
- Chapter 29. I love to count!
- Chapter 30. Genius autodidact: The Indian mathematician Ramanujan
- Chapter 31. I hate mathematics because...
- Chapter 32. The traveling salesman: A modern odyssey
- Chapter 33. Squaring the circle
- Chapter 34. A step into the infinite
- Chapter 35. Mathematics in your CD player
- Chapter 36. The logarithm: A dying breed
- Chapter 37. Prizeworthy mathematics
- Chapter 38. Why axioms of all things?
- Chapter 39. Proof by computer?
- Chapter 40. The lottery: The small prizes
- Chapter 41. Formulas = concentrated thought
- Chapter 42. Endless growth
- Chapter 43. How do quanta compute?
- Chapter 44. Extremes!
- Chapter 45. Infinitely small?
- Chapter 46. Mathematical observations at the fire department
- Chapter 47. The first mathematical proof is 2,500 years old
- Chapter 48. There is transcendence in mathematics, though it has nothing to do with mysticism
- Chapter 49. Is every even number the sum of two primes?
- Chapter 50. Why we invert conditional probabilities incorrectly
- Chapter 51. Millionaire or billionaire?
- Chapter 52. Mathematics and chess
- Chapter 53. “The book of nature is written in the language of mathematics”
- Chapter 54. The search for Mersenne primes
- Chapter 55. Berlin, eighteenth century: A beatuful formula is discovered
- Chapter 56. The first really complicated number
- Chapter 57. P = NP: In mathematics, is luck sometimes unnecessary?
- Chapter 58. Happy 32nd birthday!
- Chapter 59. Buffon’s needle
- Chapter 60. Running hot and cold: Controlled cooling solves optimization problems
- Chapter 61. Who didn’t pay?
- Chapter 62. What can statistics tell us?
- Chapter 63. Arbitrage
- Chapter 64. Farewell to risk: Options
- Chapter 65. Is mathematics a reflection of the world?
- Chapter 66. Mathematics that you can hear
- Chapter 67. Chance as composer
- Chapter 68. Do dice have a guilty conscience?
- Chapter 69. Strawberry ice cream can kill you!
- Chapter 70. Prosperity for all
- Chapter 71. No risk, thank you!
- Chapter 72. A Nobel Prize in mathematics?
- Chapter 73. Chance as reckoner: Monte Carlo methods
- Chapter 74. Fuzzy logic
- Chapter 75. Secret messages in the Bible?
- Chapter 76. How knotted can a knot be?
- Chapter 77. How much mathematics does a person need?
- Chapter 78. Big, bigger, biggest
- Chapter 79. It is probably correct
- Chapter 80. Is the world a crooked place?
- Chapter 81. Is there a mathematical bureau of standards?
- Chapter 82. The butterfly that fluttered by
- Chapter 83. Guaranteed to make you rich
- Chapter 84. Don’t trust anyone over thirty
- Chapter 85. Equality in mathematics
- Chapter 86. Magical invariants
- Chapter 87. Mathematics goes to the movies
- Chapter 88. The lazy eight: Infinity
- Chapter 89. Books need bigger margins!
- Chapter 90. Visualizing internal organs with mathematics
- Chapter 91. A brain in the computer
- Chapter 92. Cogito, ergo sum
- Chapter 93. Does the world have a hole?
- Chapter 94. Complex numbers are not so complex as their name suggests
- Chapter 95. M. C. Escher and infinity
- Chapter 96. A one at the beginning is much more likely than a two
- Chapter 97. The Leipzig town hall and the sunflower
- Chapter 98. Information optimally packaged
- Chapter 99. Four colors suffice!
- Chapter 100. Mathematics makes billionaires