The Prime Number Conspiracy: The Biggest Ideas in Math from Quanta (The MIT Press)

**__Quanta Magazine__'s stories of mathematical explorations show that "inspiration strikes willy-nilly," revealing surprising solutions and exciting discoveries.**These stories from__Quanta Magazine__map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, "inspiration strikes willy-nilly." One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a "bathroom sink epiphany" and discovers the key to solving the Gaussian correlation inequality. Readers of__The Prime Number Conspiracy__, says__Quanta__editor-in-chief Thomas Lin, are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge."__Quanta__is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the "conspiracy" of the title); consider whether math is the universal language of nature (allowing for "a unified theory of randomness"); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question "Is mathematics good for you?"**Contributors**Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie WolchoverCopublished with__Quanta Magazine__ 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 Quanta Magazine 's stories of mathematical explorations show that "inspiration strikes willy-nilly," revealing surprising solutions and exciting discoveries. These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, "inspiration strikes willy-nilly." One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a "bathroom sink epiphany" and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy , says Quanta editor-in-chief Thomas Lin, are headed on "breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge." Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the "conspiracy" of the title); consider whether math is the universal language of nature (allowing for "a unified theory of randomness"); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question "Is mathematics good for you?" Contributors Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie Wolchover Copublished with Quanta Magazine Quanta Magazine's stories of mathematical explorations show that “inspiration strikes willy-nilly,” revealing surprising solutions & exciting discoveries. If you're a science & data nerd like me, you may be interested in "Alice and Bob Meet the Wall of Fire" and "The Prime Number Conspiracy" from Quanta Magazine and Thomas Lin. - Bill Gates These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” & discovers the key to solving the Gaussian correlation inequality. Quanta editor-in-chief Thomas Lin says, readers are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.” Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good f