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The cover of Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

John Derbyshire

How many primes lie below a given number, and why has one guess about the answer puzzled mathematicians for more than a century?

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At a glance

Author
John Derbyshire

Why read it

  • You will understand what a long unsolved guess about prime numbers actually claims
  • You will see how counting primes connects to deeper mathematics and even physics
  • You will learn how a casual remark in a short paper can occupy mathematicians for generations

Who it is for

  • A reader with school maths who wants an honest explanation
  • A puzzle lover who enjoys an open problem
  • Someone who likes seeing how mathematicians think and argue

Contents

  1. PROLOGUE
  2. THE PRIME NUMBER THEOREM
  3. CARD TRICK
  4. THE SOIL, THE CROP
  5. THE PRIME NUMBER THEOREM
  6. ON THE SHOULDERS OF GIANTS
  7. RIEMANN'S ZETA FUNCTION
  8. THE GREAT FUSION
  9. THE GOLDEN KEY, AND AN IMPROVED PRIME NUMBER THEOREM
  10. NOT ALTOGETHER UNWORTHY
  11. DOMAIN STRETCHING
  12. A PROOF AND A TURNING POINT
  13. II
  14. THE RIEMANN HYPOTHESIS
  15. NINE ZULU QUEENS RULED CHINA
  16. HILBERT'S EIGHTH PROBLEM
  17. THE ARGUMENT ANT AND THE VALUE ANT
  18. IN THE GRIP OF AN OBSESSION
  19. BIG OH AND MÖBIUS MU
  20. CLIMBING THE CRITICAL LINE
  21. A LITTLE ALGEBRA
  22. NUMBER THEORY MEETS QUANTUM MECHANICS
  23. TURNING THE GOLDEN KEY
  24. THE RIEMANN OPERATOR AND OTHER APPROACHES
  25. THE ERROR TERM
  26. EITHER IT'S TRUE, OR ELSE IT ISN'T
  27. EPILOGUE
  28. CHAPTER 2
  29. CHAPTER 3
  30. CHAPTER 4
  31. CHAPTER 5
  32. CHAPTER 6
  33. CHAPTER 7
  34. CHAPTER 8
  35. CHAPTER 9
  36. CHAPTER 10
  37. CHAPTER 11
  38. CHAPTER 12
  39. CHAPTER 13
  40. CHAPTER 14
  41. CHAPTER 15
  42. CHAPTER 16
  43. CHAPTER 17
  44. CHAPTER 18
  45. CHAPTER 20
  46. CHAPTER 21
  47. CHAPTER 22
  48. EPILOGUE
  49. Appendix
  50. THE RIEMANN HYPOTHESIS IN SONG

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