Table of Contents
Foreword Paul Hoffman x
Introduction Gina Kolata xiii
Chapter 1 What Is Mathematics?
Useful Invention or Absolute Truth: What Is Math? George Johnson 3
But Aren't Truth and Beauty Supposed to be Enough? James Gleick 9
Mathematicians Meet Computerized Ideas Gina Kolata 13
Mathematicians Finally Log On James Gleick 16
With Major Math Proof, Brute Computers Show Flash of Reasoning Power Gina Kolata 19
Computers Still Can't Do Beautiful Mathematics Gina Kolata 24
100 Quadrillion Calculations Later, Eureka! Gina Kolata 27
Theorist Applies Computer Power to Uncertainty in Statistics Gina Kolata 29
Chapter 2 Statistics, Coincidences and Surprising Facts
1-in-a-Trillion Coincidence, You Say? Not Really, Experts Find Gina Kolata 35
Sometimes Heavier Objects Go to the Top: Here's Why James Gleick 40
Behind Monty Hall's Doors: Puzzle, Debate and Answer? John Tierney 43
What If They Closed 42d Street and Nobody Noticed? Gina Kolata 48
Down for the Count; Why Some Numbers Are Only Very Good Guesses Gina Kolata 51
Could It Be? Weather Has Nothing to Do with Your Arthritis Pain? Gina Kolata 54
Electronics to Aid Weather Figuring Sidney Shalett 58
Insurance as a Study; Something of the Men Who Figure Business by Algebra 62
Leontief's Contribution Leonard Silk 64
Many Small Events May Add Up to One Mass Extinction Malcolm W. Browne 67
Metric Mania John Allen Paulos 70
In Shuffling Cards, 7 Is a Winning Number Gina Kolata 73
Can Game Theory Predict When Iran Will Get the Bomb? Clive Thompson 77
In Modeling Risk, the Human Factor Was Left Out Steve Lohr 88
Playing the Odds George Johnson 92
Monday Puzzle: Solution to Birthday Problem Pradeep Mutalik 95
Just What Are Your Odds in Genetic Roulette? Go Figure Gina Kolata 102
The 2000 Election: The Science of Counting Gina Kolata 106
Prospectus; Can a Computer Program Figure Out the Market? A Former Analyst and a Mathematician Are Betting That Theirs Can Janet Stites 107
New Tools for the I.R.S. to Sniff Out Tax Cheats David Cay Johnston 110
Chapter 3 Famous Problems, Solved and As Yet Unsolved
New Mathematics Links Two Worlds William L. Laurence 115
An Elusive Proof and Its Elusive Prover Dennis Overbye 119
Ask Science: Poincare's Conjecture Dennis Overbye 125
Grigori Perelman's Beautiful Mind Jascha Hoffman 131
A Math Problem Solver Declines a $1 Million Prize Dennis Overbye 133
"Four-Color Problem" Attacked William L. Laurence 135
Four-Color Proof 136
Goldbach's Conjecture; This One May Be Provable, but We May Never Know George Johnson 137
Mathematics Expert May Soon Resolve A 350-Year Problem James Gleick 139
Fermat's Theorem Solved? Not This Time James Gleick 141
Fermat's Last Theorem Still Has 0 Solutions James Gleick 142
At Last, Shout of "Eureka!" in Age-Old Math Mystery Gina Kolata 145
Fermat's Theorem James Gleick 150
Flaw Is Found in Math Proof, but Repairs Are Under Way Gina Kolata 155
A Year Later Fermat's Puzzle Is Still Not Quite Q.E.D. Gina Kolata 157
How a Gap in the Fermat Proof Was Bridged Gina Kolata 158
Two Key Mathematics Questions Answered after Quarter Century John A. Osmundsen 164
Mathematical Theory of Poker Is Applied to Business Problems Will Lissner 169
Soap Bubbles Get a New Role in Old Mathematics Problem Joseph Williams 173
Math Advance Penetrates Secrets of Knots James Gleick 175
Packing Tetrahedrons, and Closing in on a Perfect Fit Kenneth Chang 181
Finding Order in the Apparent Chaos of Currents Bina Venkataraman 184
In Bubbles and Metal, the Art of Shape-Shifting Kenneth Chang 188
The Scientific Promise of Perfect Symmetry Kenneth Chang 190
143-Year-Old Problem Still Has Mathematicians Guessing Bruce Schechter 192
What Is the Most Important Problem in Math Today? Gina Kolata 196
Solution to Old Puzzle: How Short a Shortcut? Gina Kolata 198
Chapter 4 Chaos, Catastrophe and Randomness
Chaos Is Defined by New Calculus 202
Experts Debate the Prediction of Disasters Malcolm W. Browne 204
Solving the Mathematical Riddle of Chaos James Gleick 208
The Man Who Reshaped Geometry James Gleick 223
Snowflake's Riddle Yields to Probing of Science James Gleick 235
Tales of Chaos: Tumbling Moons and Unstable Asteroids James Gleick 239
Fluid Math Made Simple-Sort Of James Gleick 243
When Chaos Rules the Market James Gleick 246
New Appreciation of the Complexity in a Flock of Birds James Gleick 256
Indestructible Wave May Hold Key to Superconductors James Gleick 261
The Quest for True Randomness Finally Appears Successful James Gleick 265
Coin-Tossing Computers Found to Show Subtle Bias Malcolm W. Browne 270
Science Squints at a Future Fogged by Chaotic Uncertainty Malcolm W. Browne 274
Probing Disease Clusters: Easier to Spot Than Prove Gina Kolata 278
The Odds of That Lisa Belkin 281
Fractal Vision James Gleick 298
Chapter 5 Cryptography and the Emergence of Truly Unbreakable Codes
Harassment Alleged over Code Research Malcolm W. Browne 303
Researchers to Permit Pre-Publication Review by U.S. Richard Severo 306
Tighter Security Rules for Advances in Cryptology Walter Sullivan 308
A New Approach to Protecting Secrets Is Discovered James Gleick 312
Brief U.S. Suppression of Proof Stirs Anger 316
A Most Ferocious Math Problem Tamed Malcolm W. Browne 319
Biggest Division a Giant Leap in Math Gina Kolata 324
Scientists Devise Math Tool to Break a Protective Code John Markoff 328
Tied Up in Knots, Cryptographers Test Their Limits Gina Kolata 331
A Public Battle over Secret Codes John Markoff 334
U.S. Code Agency Is Jostling for Civilian Turf John Markoff 338
Researchers Demonstrate Computer Code Can Be Broken Sara Robinson 343
Nick Patterson; A Cold War Cryptologist Takes a Crack at Deciphering DNA's Deep Secrets Ingfei Chen 345
Adding Math to List of Security Threats John Markoff 349
Prizes Aside, the P-NP Puzzler Has Consequences John Markoff 351
Chapter 6 Computers Enter the World of Mathematics
"Thinking Machine" Does Higher Mathematics; Solves Equations That Take Humans Months 355
New Giant "Brain" Does Wizard Work 356
"Brain" Speeded Up for War Problems Will Lissner 358
The Electronic Digital Computer: How It Started, How It Works and What It Does Henry L. Lieberman Dr. Louis Robinson 360
New Shortcut Found for Long Math Proofs Gina Kolata 381
New Technique Stores Images More Efficiently Gina Kolata 385
Giant Computer Virtually Conquers Space and Time George Johnson 390
Rear Adm. Grace M. Hopper Dies; Innovator in Computers Was 85 John Markoff 395
Frances E. Holberton, 84, Early Computer Programmer Steve Lohr 398
Squeezing Data like an Accordion Peter Wayner 400
A Digital Brain Makes Connections Anne Eisenberg 403
A Soviet Discovery Rocks World of Mathematics Malcolm W. Browne 406
The Health Care Debate: Finding What Works Gina Kolata 410
Step 1: Post Elusive Proof. Step 2: Watch Fireworks John Markoff 415
Chapter 7 Mathematicians and Their World
Paul Erdos, 83, a Wayfarer in Math's Vanguard, Is Dead Gina Kolata 420
Journeys to the Distant Fields of Prime Kenneth Chang 423
Highest Honor in Mathematics Is Refused Kenneth Chang 428
Scientist at Work: John H- Conway; At Home in the Elusive World of Mathematics Gina Kolata 430
Claude Shannon, B. 1916-Bit Player James Gleick 436
An Isolated Genius Is Given His Due James Gleick 438
Scientist at Work: Andrew Wiles; Math Whiz Who Battled 350-Year-Old Problem Gina Kolata 444
Scientist at Work: Leonard Adleman; Hitting the High Spots of Computer Theory Gina Kolata 449
Dr. Kurt Gödel, 71, Mathematician Peter B. Flint 456
Genius or Gibberish? The Strange World of the Math Crank George Johnson 458
Contributors' Biographies 463
Photography and Illustration Credits 467
Ackowledgments 468
Index 469
