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

CONTENTS......Page 8
FOREWORD......Page 12
INTRODUCTION......Page 18
I. WHAT’S SO SPECIAL ABOUT PRIME NUMBERS?......Page 22
UNHERALDED MATHEMATICIAN BRIDGES THE PRIME GAP......Page 24
THE PROBLEM OF PAIRS......Page 25
A PRIME SIEVE......Page 26
CLOSING THE GAP......Page 27
TOGETHER AND ALONE, CLOSING THE PRIME GAP......Page 30
COMBING THE NUMBER LINE......Page 31
PRIME FISHING GROUNDS......Page 32
A SECRET WEAPON......Page 34
KAISA MATOMÄKI DREAMS OF PRIMES......Page 38
MATHEMATICIANS DISCOVER PRIME CONSPIRACY......Page 44
PRIME PREFERENCES......Page 45
RANDOM PRIMES......Page 46
II. IS MATH THE UNIVERSAL LANGUAGE OF NATURE?......Page 48
MATHEMATICIANS CHASE MOONSHINE’S SHADOW......Page 50
MONSTROUS MOONSHINE......Page 52
NEW MOONSHINE......Page 54
MOONSHINE’S SHADOWS......Page 55
FINDING THE BEAST......Page 56
IN MYSTERIOUS PATTERN, MATH AND NATURE CONVERGE......Page 58
AT THE FAR ENDS OF A NEW UNIVERSAL LAW......Page 64
LOPSIDED CURVE......Page 65
GOING THROUGH A PHASE......Page 67
WEAK TO STRONG......Page 69
A BIRD’S-EYE VIEW OF NATURE’S HIDDEN ORDER......Page 72
A SECRET ORDER......Page 74
MATERIAL MENAGERIE......Page 75
A UNIFIED THEORY OF RANDOMNESS......Page 80
A RANDOM WALK ON A QUANTUM STRING......Page 81
THE PROBLEM WITH RANDOM GROWTH......Page 85
RANDOM EXPLORATION......Page 89
TURNING RANDOMNESS INTO A TOOL......Page 92
STRANGE NUMBERS FOUND IN PARTICLE COLLISIONS......Page 94
A RECURRING THEME......Page 95
FEYNMAN’S ARDUOUS PATH......Page 97
A SURPRISING CONNECTION......Page 99
NATURE’S GROUPS......Page 100
QUANTUM QUESTIONS INSPIRE NEW MATH......Page 102
QUANTUM CALCULATORS......Page 103
DUALITY OF EQUALS......Page 105
III. HOW ARE SURPRISING PROOFS DISCOVERED?......Page 108
A PATH LESS TAKEN TO THE PEAK OF THE MATH WORLD......Page 110
THE ACCIDENTAL APPRENTICE......Page 111
A CRACK IN A GRAPH......Page 113
A SEARCH FOR HIDDEN STRUCTURE......Page 117
CROSSING BOUNDARIES......Page 119
A PARTNERSHIP GROWS......Page 120
THE STUDENT SETS OFF ON HIS OWN......Page 122
A LONG-SOUGHT PROOF, FOUND AND ALMOST LOST......Page 124
“OUTSIDERS” CRACK 50-YEAR-OLD MATH PROBLEM......Page 130
A COMMON PROBLEM......Page 131
ELECTRICAL PROPERTIES......Page 133
MATHEMATICIANS TAME ROGUE WAVES, LIGHTING UP FUTURE OF LEDS......Page 138
ROGUE WAVES......Page 139
THE LAY OF THE LANDSCAPE......Page 140
ORDER AND LIGHT......Page 142
PENTAGON TILING PROOF SOLVES CENTURY-OLD MATH PROBLEM......Page 144
GOOD SETS......Page 146
SEEKING EINSTEIN......Page 147
SIMPLE SET GAME PROOF STUNS MATHEMATICIANS......Page 150
GAME, SET, MATCH......Page 151
A MAGICAL ANSWER TO AN 80-YEAR-OLD PUZZLE......Page 156
HANDLES ON THE WRECKING BALL......Page 157
HOISTING THE WRECKING BALL......Page 158
SPHERE PACKING SOLVED IN HIGHER DIMENSIONS......Page 160
FILLING THE GAPS......Page 161
MINING FOR GOLD......Page 163
IV. HOW DO THE BEST MATHEMATICAL MINDS WORK?......Page 166
A TENACIOUS EXPLORER OF ABSTRACT SURFACES......Page 168
TEHRAN......Page 169
HARVARD......Page 170
“A TITANIC WORK”......Page 172
A HISTORIC FIRST......Page 175
A “REBEL” WITHOUT A PH.D.......Page 176
A BRAZILIAN WUNDERKIND WHO CALMS CHAOS......Page 184
MATH ON THE BEACH......Page 185
DYNAMICAL SYSTEMS......Page 187
HAMMER AND NAILS......Page 189
BRAZILIAN SUPERSTAR......Page 191
THE MUSICAL, MAGICAL NUMBER THEORIST......Page 194
MUSICIAN......Page 195
MATHEMATICIAN......Page 196
MAGICIAN......Page 199
THE ORACLE OF ARITHMETIC......Page 202
LEARNING ARITHMETIC......Page 203
FAST FORWARD......Page 206
AFTER PRIME PROOF, AN UNLIKELY STAR RISES......Page 208
IN NOISY EQUATIONS, ONE WHO HEARD MUSIC......Page 214
A LOGICAL MIND......Page 216
REGULARITY IN RANDOMNESS......Page 218
STOCHASTIC FUTURE......Page 220
MICHAEL ATIYAH’S IMAGINATIVE STATE OF MIND......Page 222
V. WHAT CAN OR CAN’T COMPUTERS DO?......Page 230
HACKER-PROOF CODE CONFIRMED......Page 232
THE DREAM OF PERFECT PROGRAMS......Page 233
BLOCK-BASED SECURITY......Page 235
VERIFYING THE INTERNET......Page 237
WILL COMPUTERS REDEFINE THE ROOTS OF MATH?......Page 240
SET THEORY AND A PARADOX......Page 241
TOWARD A NEW FOUNDATIONAL SYSTEM......Page 245
FROM IDEA TO ACTION......Page 246
LANDMARK ALGORITHM BREAKS 30-YEAR IMPASSE......Page 250
A BLIND TASTE TEST......Page 251
PAINT BY NUMBERS......Page 253
A GRAND VISION FOR THE IMPOSSIBLE......Page 256
THREE COOKIES......Page 257
PROVING THE IMPOSSIBLE......Page 259
TRUE OR FALSE......Page 262
VI. WHAT IS INFINITY?......Page 264
TO SETTLE INFINITY DISPUTE, A NEW LAW OF LOGIC......Page 266
INFINITE PARADOXES......Page 268
UNIVERSE OF SETS......Page 270
EXPANDING THE UNIVERSE......Page 272
MATHEMATICIANS BRIDGE FINITE-INFINITE DIVIDE......Page 274
THE RISE OF INFINITY......Page 276
AN EXCEPTIONAL CASE......Page 278
MANY INFINITIES......Page 282
FORCED OUT......Page 284
AN ORDER OF COMPLEXITY......Page 285
VII. IS MATHEMATICS GOOD FOR YOU?......Page 288
A LIFE INSPIRED BY AN UNEXPECTED GENIUS......Page 290
TO LIVE YOUR BEST LIFE, DO MATHEMATICS......Page 296
WHY MATH IS THE BEST WAY TO MAKE SENSE OF THE WORLD......Page 302
ACKNOWLEDGMENTS......Page 308
CONTRIBUTORS......Page 310
NOTES......Page 312
INDEX......Page 326