The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta

330 Pages·2018·5.227 MB·English

by  Thomas Lin (Editor)

THE PRIME NUMBER CONSPIRACY

THE PRIME NUMBER CONSPIRACY
The Biggest Ideas in Math from Quanta
edited by Thomas Lin
The MIT Press
© 2018 The Simons Foundation, Inc.
All rights reserved. No part of this book may be reproduced in any form by any
electronic or mechanical means (including photocopying, recording, or information
storage and retrieval) without permission in writing from the publisher.
This book was set in Stone Serif Medium by Westchester Publishing Services. Printed
and bound in the United States of America.
Library of Congress Cataloging-in-Publication Data
Names: Lin, Thomas (Journalist), editor.
Title: The prime number conspiracy : the biggest ideas in math from
Quanta / edited by Thomas Lin ; foreword by James Gleick.
Other titles: Quanta math stories
Description: Cambridge, MA : The MIT Press, [2018] | Includes bibliographical
references and index.
Identifiers: LCCN 2018013314 | ISBN 9780262536356 (pbk. : alk. paper)
Subjects: LCSH: Mathematics--Popular works.
Classification: LCC QA93 .P75 2018 | DDC 510--dc23 LC record available
at https://lccn.loc.gov/2018013314
10 9 8 7 6 5 4 3 2 1
Men fear thought as they fear nothing else on earth—more than ruin, more even
than death. Thought is subversive and revolutionary, destructive and terrible;
thought is merciless to privilege, established institutions, and comfortable habits;
thought is anarchic and lawless, indifferent to authority, careless of the well-tried
wisdom of the ages. Thought looks into the pit of hell and is not afraid. It sees
man, a feeble speck, surrounded by unfathomable depths of silence; yet it bears
itself proudly, as unmoved as if it were lord of the universe. Thought is great and
swift and free, the light of the world, and the chief glory of man.
—Bertrand Russell, Why Men Fight

CONTENTS
FOREWORD xi
James Gleick
INTRODUCTION xvii
Thomas Lin
I WHAT’S SO SPECIAL ABOUT PRIME NUMBERS?
UNHERALDED MATHEMATICIAN BRIDGES THE PRIME GAP 3
Erica Klarreich
TOGETHER AND ALONE, CLOSING THE PRIME GAP 9
Erica Klarreich
KAISA MATOMÄKI DREAMS OF PRIMES 17
Kevin Hartnett
MATHEMATICIANS DISCOVER PRIME CONSPIRACY 23
Erica Klarreich
II IS MATH THE UNIVERSAL LANGUAGE OF NATURE?
MATHEMATICIANS CHASE MOONSHINE’S SHADOW 29
Erica Klarreich
IN MYSTERIOUS PATTERN, MATH AND NATURE CONVERGE 37
Natalie Wolchover
AT THE FAR ENDS OF A NEW UNIVERSAL LAW 43
Natalie Wolchover
A BIRD’S-EYE VIEW OF NATURE’S HIDDEN ORDER 51
Natalie Wolchover
viii Contents
A UNIFIED THEORY OF RANDOMNESS 59
Kevin Hartnett
STRANGE NUMBERS FOUND IN PARTICLE COLLISIONS 73
Kevin Hartnett
QUANTUM QUESTIONS INSPIRE NEW MATH 81
Robbert Dijkgraaf
III HOW ARE SURPRISING PROOFS DISCOVERED?
A PATH LESS TAKEN TO THE PEAK OF THE MATH WORLD 89
Kevin Hartnett
A LONG-SOUGHT PROOF, FOUND AND ALMOST LOST 103
Natalie Wolchover
“OUTSIDERS” CRACK 50-YEAR-OLD MATH PROBLEM 109
Erica Klarreich
MATHEMATICIANS TAME ROGUE WAVES, LIGHTING UP
FUTURE OF LEDS 117
Kevin Hartnett
PENTAGON TILING PROOF SOLVES CENTURY-OLD MATH
PROBLEM 123
Natalie Wolchover
SIMPLE SET GAME PROOF STUNS MATHEMATICIANS 129
Erica Klarreich
A MAGICAL ANSWER TO AN 80-YEAR-OLD PUZZLE 135
Erica Klarreich
SPHERE PACKING SOLVED IN HIGHER DIMENSIONS 139
Erica Klarreich
IV HOW DO THE BEST MATHEMATICAL MINDS WORK?
A TENACIOUS EXPLORER OF ABSTRACT SURFACES 147
Erica Klarreich
A “REBEL” WITHOUT A PH.D. 155
Thomas Lin
Contents ix
A BRAZILIAN WUNDERKIND WHO CALMS CHAOS 163
Thomas Lin and Erica Klarreich
THE MUSICAL, MAGICAL NUMBER THEORIST 173
Erica Klarreich
THE ORACLE OF ARITHMETIC 181
Erica Klarreich
AFTER PRIME PROOF, AN UNLIKELY STAR RISES 187
Thomas Lin
IN NOISY EQUATIONS, ONE WHO HEARD MUSIC 193
Natalie Wolchover
MICHAEL ATIYAH’S IMAGINATIVE STATE OF MIND 201
Siobhan Roberts
V WHAT CAN OR CAN’T COMPUTERS DO?
HACKER-PROOF CODE CONFIRMED 211
Kevin Hartnett
WILL COMPUTERS REDEFINE THE ROOTS OF MATH? 219
Kevin Hartnett
LANDMARK ALGORITHM BREAKS 30-YEAR IMPASSE 229
Erica Klarreich
A GRAND VISION FOR THE IMPOSSIBLE 235
Thomas Lin and Erica Klarreich
VI WHAT IS INFINITY?
TO SETTLE INFINITY DISPUTE, A NEW LAW OF LOGIC 245
Natalie Wolchover
MATHEMATICIANS BRIDGE FINITE--INFINITE DIVIDE 253
Natalie Wolchover
MATHEMATICIANS MEASURE INFINITIES AND FIND THEY’RE
EQUAL 261
Kevin Hartnett