Stalking the Riemann hypothesis : the quest to find the hidden law of prime numbers

When Albert Einstein sought the mathematics to bring his general theory of relativity to life, he found his solution in the works of none other than Bernard Reimann. And although Reimann died young (at 39) apparently the special math necessary for relativity was not Reimann's only masterstroke. He also developed a theta function or formula for predicting the placement of prime numbers in the number line. As you may recall from elementary mathematics, prime numbers are those numbers only divisible by themselves and one. Though casual thought on the matter may initially lead one to conclude that prime numbers would eventually be exhausted (indeed the higher you go the more rare they do become) mathematical proofs dating back to Euclid show that like the integer line they accompany they go on forever. But again figuring out how they can be located algorithmically within that forever was long a mathematics holy grail until 1859 when Bernard Reimann posited a hypothesis for locating them. His hypothesis or zeta function involves incredibly complicated mathematics certainly beyond the scope of this book so if you want to understand it you may do better to read Reimann's Zeta Function. However if you want the outlines of search that goes from ancient Greece all the way to modern times, this book makes quick accessible reading. Acknowledgements / ix 1 / Prologue: It All Begins with Zero /3 2 / The God-Given Natural Numbers / 7 3 / The Shape of the Primes / 21 4 / Primal Cartographers / 30 5 / Shoulders to Stand Upon / 46 6 / Riemann and His "Very Likely" Hypothesis / 63 7 / A Dutch Red Herring / 95 8 / A Prime Number Theorem , After All.... and More /105 9 / Good, but Not Good Enough / 118 10 / First Steps / 128 11 / A Chance Meeting of Two Minds / 154 12 / God Created the Natural Numbers ... but in a Billiard Hall? /186 13 / Making Order Out of (Quantum) Chaos / 213 14 / God May Not Play Dice, but What about Cards? / 232 15 / The Millennium Meeting / 261 Glossary / 267 Further Reading and Sources / 277 Index /279 Stalking The Riemann Hyothesis Takes You On A Guided Tour Of The Deepest Mystery In Mathematics. Prologue -- It All Begins With Zero -- The God-given Natural Numbers -- The Shape Of The Primes -- Primal Cartographers -- Shoulders To Stand Upon -- Riemann And His Very Likely Hypothesis -- A Dutch Red Herring -- A Prime Number Theorem, After All--and More -- Good, But Not Good Enough -- First Steps -- A Chance Meeting Of Two Minds -- God Created The Natural Numbers-- But, In A Billiard Hall? -- Making Order Out Of (quantum) Chaos -- God May Not Play Dice, But What About Cards? -- The Millennium Meeting. Dan Rockmore. Includes Bibliographical References (p. [277]-278) And Index. Presents a study of one of the great unsolved mysteries of mathematics, the mid-nineteenth-century Riemann hypothesis, which describes the occurrence of prime numbers, and of the quest to prove or disprove the theory.