Book:Keith Devlin/The Millennium Problems

Subject Matter

 * The Millennium Problems

Contents

 * Preface


 * ZERO The Gauntlet is Thrown


 * ONE The Music of the Primes:
 * The Riemann Hypothesis
 * APPENDIX 1. EUCLID'S PROOF THAT THERE ARE INFINITELY MANY PRIMES
 * APPENDIX 2. HOW DO MATHEMATICIANS WORK OUT INFINITE SUMS?
 * APPENDIX 3. HOW EULER DISCOVERED THE ZETA FUNCTION


 * TWO The Fields We Are Made Of:
 * Yang-Mills Theory and the Mass Gap Hypothesis
 * APPENDIX. GROUP THEORY: THE MATHEMATICS OF SYMMETRY


 * THREE When Computers Fail:
 * The P vs. NP Problem


 * FOUR Making Waves:
 * The Navier-Stokes Equations


 * FIVE The Mathematics of Smooth Behavior:
 * The Poincaré Conjecture


 * SIX Knowing When the Equation Can't Be Solved:
 * The Birch and Swinnerton-Dyer Conjecture


 * APPENDIX: NOTATION FOR INFINITE SUMS AND PRODUCTS


 * SEVEN Geometry Without Pictures:
 * The Hodge Conjecture


 * Further Reading


 * Index