Book:Keith Devlin/The Millennium Problems

Keith Devlin: The Millennium Problems: the Seven Greatest Unsolved Mathematical Puzzles of Our Time

Published $\text {2002}$, Granta

ISBN 1-86207-735-5

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