Table of Contents
Foreword James Gleick xi
Introduction Thomas Lin xvii
I What's So Special About Prime Numbers?
Unheralded Mathematician Bridges The Prime Gap Erica Klarreich 3
Together And Alone, Closing The Prime Gap Erica Klarreich 9
Kaisa Matomäki Dreams Of Primes Kevin Hartnett 17
Mathematicians Discover Prime Conspiracy Erica Klarreich 23
II Is Math The Universal Language Of Nature?
Mathematicians Chase Moonshine's Shadow Erica Klarreich 29
In Mysterious Pattern, Math And Nature Converge Natalie Wolchover 37
At The Far Ends Of A New Universal Law Natalie Wolchover 43
A Bird's-Eye View Of Nature's Hidden Order Natalie Wolchover 51
A Unified Theory Of Randomness Kevin Hartnett 59
Strange Numbers Found In Particle Collisions Kevin Hartnett 73
Quantum Questions Inspire New Math Robbert Dijkgraaf 81
III How Are Surprising Proofs Discovered?
A Path Less Taken To The Peak Of The Math World Kevin Hartnett 89
A Long-Sought Proof, Found And Almost Lost Natalie Wolchover 103
"Outsiders" Crack 50-Year-Old Math Problem Erica Klarreich 109
Mathematicians Tame Rogue Waves, Lighting Up Future Of Leds Kevin Hartnett 117
Pentagon Tiling Proof Solves Century-Old Math Problem Natalie Wolchover 123
Simple Set Game Proof Stuns Mathematicians Erica Klarreich 129
A Magical Answer To An 80-Year-Old Puzzle Erica Klarreich 135
Sphere Packing Solved In Higher Dimensions Erica Klarreich 139
IV How Do The Best Mathematical Minds Work?
A Tenacious Explorer Of Abstract Surfaces Erica Klarreich 147
A "Rebel" Without A Ph.D. Thomas Lin 155
A Brazilian Wunderkind Who Clams Chaos Thomas Lin Erica Klarreich 163
The Musical, Magical Number Theorist Erica Klarreich 173
The Oracle Of Arithmetic Erica Klarreich 181
After Prime Proof, An Unlikely Star Rises Thomas Lin 187
In Noisy Equations, One Who Heard Music Natalie Wolchover 193
Michael Atiyah's Imaginative State Of Mind Siobhan Roberts 201
V What Can Or Can't Computers Do?
Hacker-Proof Code Confirmed Kevin Hartnett 211
Will Computers Redefine The Roots Of Math? Kevin Hartnett 219
Landmark Algorithm Breaks 30-Year Impasse Erica Klarreich 229
A Grand Vision For The Impossible Thomas Lin Erica Klarreich 235
VI What Is Infinity?
To Settle Infinity Dispute, A New Law Of Logic Natalie Wolchover 245
Mathematicians Bridge Finite-Infinite Divide Natalie Wolchover 253
Mathematicians Measure Infinities And Find They're Equal Kevin Hartnett 261
VII Is Mathematics Good For You?
A Life Inspired By An Unexpected Genius John Pavlus 269
To Live Your Best Life, Do Mathematics Kevin Hartnett 275
Why Math Is The Best Way To Make Sense Of The World Ariel Bleicher 281
Acknowledgments 287
Contributors 289
Notes 291
Index 305