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Index
COVER PAGE
TITLE PAGE
TABLE OF CONTENTS
DEDICATION
ACKNOWLEDGMENTS
CHAPTER 1
CHAPTER 2
BEGINNING “THE WORK”
PRIMES: THE FUNDAMENTAL PATTERN WITHIN THE PATTERN
PRIMES: THE INTEGRAL ATOMS
IN SEARCH OF PRIMES
SPEAKING IN PRIMES
EUCLID’S PROOF OF THE INFINITUDE OF PRIMES
CHAPTER 3
CARDINALITY: HOW MANY PRIMES ARE THERE?
ASYMPTOTICS: HOW DO THE PRIMES GROW?
SEEING THE FOREST FOR THE TREES
CHAPTER 4
LEGENDRE
GAUSS: PRINCE AMONG MEN
CHAPTER 5
EULER: A BRIDGE-BUILDER
DIRICHLET: FIRST ONE OVER THE BRIDGE . . .
POSTSCRIPT
CHAPTER 6
THE ROAD TO THE RIEMANN HYPOTHESIS
A COMPLEX DISSERTATION
COMPLEXIFYING EULER: THE CREATION OF THE RIEMANN ZETA FUNCTION, A NUMBER THEORIST’S PDA
RIEMANN’S EXPLICIT FORMULA AND THE ZEROS OF THE ZETA FUNCTION
THE RIEMANN HYPOTHESIS
A QUIET ENDING
CHAPTER 7
AN INVERTED APPROACH TO THE RIEMANN HYPOTHESIS
A CHANCE THAT STIELTJES IS RIGHT
CHAPTER 8
WE HAVE A WINNER!
EDGING TOWARD THE RIEMANN HYPOTHESIS
PERIODIC TABLES OF THE PRIMES
FIRST WE ORGANIZE, THEN WE EXAMINE: GAUSSIAN INTEGERS AND GAUSSIAN PRIMES
THE RISING OF THE RIEMANN HYPOTHESIS
CHAPTER 9
TO ERR IS RIEMANN
THE COMING CENTURY
A CALL TO ARMS
AND IN THE EIGHTH POSITION, PLAYING CENTRAL PROBLEM . . .
AN ERROR TERM WORTH THE EFFORT
CHAPTER 10
PLAYING THE PERCENTAGES
TWO CAUTIONARY TALES
A GOOD CHANCE THAT THE RIEMANN HYPOTHESIS IS TRUE
EVIDENCE ACCUMULATES
WORLD WAR II AND A RIEMANN HYPOTHESIS THAT IS TRUE
A “ZOO” OF ZETA FUNCTIONS
ANDRÉ WEIL
CLOSE, BUT NO CIGAR
PUSHING FORWARD
GLIMMERS OF THE NEXT GREAT IDEA
CHAPTER 11
“THE INSTITUTE”
MONTGOMERY AND THE PAIR CORRELATION
A RANDOM COLLISION WITH FREEMAN DYSON
MATRICES: THE MATHEMATICIAN’S SPREADSHEETS
THE RANDOM CONNECTION
THE DYSON-ODLYZKO-MONTGOMERY LAW
CHAPTER 12
LIFE AT THE SEMICLASSICAL LIMIT
A KNIGHT OF THE BILLIARD TABLE
QUANTUM CHAOS
BILLIARD TABLES FOR PHYSICISTS
THE BASIC CONJECTURE OF QUANTUM CHAOS
BILLIARDS IN THE POINCARÉ DISK
SELBERG’S TRACE FORMULA
A NEAR HYPERBOLIC HUSTLE
BACK TO THE GAME ROOM
CHAPTER 13
A GRAND MASTER OF THE RIEMANN HYPOTHESIS
IS IT ALL A COINCIDENCE?
IN SEARCH OF A HAMILTONIAN TO SETTLE THE HYPOTHESIS
IF YOU BUILD IT, THEY WILL COME: THE VISION OF A CONNES MAN
AN ENDGAME STRATEGY FOR THE RIEMANN HYPOTHESIS?
CHAPTER 14
A CALIFORNIA COLLABORATION
FROM A GRAND UNIFICATION TO A GRAND UNIVERSALITY
EIGENVALUES ON THE EDGE
A NEW UNIVERSALITY IN TOWN: TRACY-WIDOM DISTRIBUTIONS
EDUCATION OF A MATHEMATICAL MINER
A MYSTICAL CONNECTION
COMING FULL CIRCLE
CHAPTER 15
EPILOGUE
GLOSSARY
FURTHER READING AND SOURCES
ABOUT THE AUTHOR
COPYRIGHT PAGE
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