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

by Derbyshire, John

• ISBN13: 9780452285255
• ISBN10: 0452285259
• Edition: Reprint
• Format: Paperback
• Copyright: 2004-05-25
• Publisher: Plume

Summary

In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled On the Number of Prime Numbers Less Than a Given Quantity.” Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first person to conquer it.Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsessionis a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.

Author Biography

John Derbyshire is a mathematician and linguist by education, a systems analyst by profession, and a celebrated writer in his spare time. His work appears frequently in National Review and The New Criterion. Born and raised in England, he has made his home in the United States for the past fifteen years.

Table of Contents

Prologue	ix
Part I The Prime Number Theorem
1 Card Trick	3	(16)
2 The Soil, the Crop	19	(13)
3 The Prime Number Theorem	32	(16)
4 On the Shoulders of Giants	48	(15)
5 Riemann's Zeta Function	63	(19)
6 The Great Fusion	82	(17)
7 The Golden Key, and an Improved Prime Number Theorem	99	(19)
8 Not Altogether Unworthy	118	(19)
9 Domain Stretching	137	(14)
10 A Proof and a Turning Point	151	(18)
Part II The Riemann Hypothesis
11 Nine Zulu Queens Ruled China	169	(15)
12 Hilbert's Eighth Problem	184	(17)
13 The Argument Ant and the Value Ant	201	(22)
14 In the Grip of an Obsession	223	(15)
15 Big Oh and Mobius Mu	238	(14)
16 Climbing the Critical Line	252	(13)
17 A Little Algebra	265	(15)
18 Number Theory Meets Quantum Mechanics	280	(16)
19 Turning the Golden Key	296	(16)
20 The Riemann Operator and Other Approaches	312	(15)
21 The Error Term	327	(23)
22 Either It's True, or Else It Isn't	350	(12)
Epilogue	362	(3)
Notes	365	(28)
Appendix: The Riemann Hypothesis in Song	393	(12)
Picture Credits	405	(2)
Index	407