| |
| |
| Foreword | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| |
| What Is Mathematics? | |
| |
| |
| Useful Invention or Absolute Truth: What Is Math? | |
| |
| |
| |
| But Aren't Truth and Beauty Supposed to be Enough? | |
| |
| |
| |
| Mathematicians Meet Computerized Ideas | |
| |
| |
| |
| Mathematicians Finally Log On | |
| |
| |
| |
| With Major Math Proof, Brute Computers Show Flash of Reasoning Power | |
| |
| |
| |
| Computers Still Can't Do Beautiful Mathematics | |
| |
| |
| |
| 100 Quadrillion Calculations Later, Eureka! | |
| |
| |
| |
| Theorist Applies Computer Power to Uncertainty in Statistics | |
| |
| |
| |
| |
| Statistics, Coincidences and Surprising Facts | |
| |
| |
| 1-in-a-Trillion Coincidence, You Say? Not Really, Experts Find | |
| |
| |
| |
| Sometimes Heavier Objects Go to the Top: Here's Why | |
| |
| |
| |
| Behind Monty Hall's Doors: Puzzle, Debate and Answer? | |
| |
| |
| |
| What If They Closed 42d Street and Nobody Noticed? | |
| |
| |
| |
| Down for the Count; Why Some Numbers Are Only Very Good Guesses | |
| |
| |
| |
| Could It Be? Weather Has Nothing to Do with Your Arthritis Pain? | |
| |
| |
| |
| Electronics to Aid Weather Figuring | |
| |
| |
| |
| Insurance as a Study; Something of the Men Who Figure Business by Algebra | |
| |
| |
| Leontief's Contribution | |
| |
| |
| |
| Many Small Events May Add Up to One Mass Extinction | |
| |
| |
| |
| Metric Mania | |
| |
| |
| |
| In Shuffling Cards, 7 Is a Winning Number | |
| |
| |
| |
| Can Game Theory Predict When Iran Will Get the Bomb? | |
| |
| |
| |
| In Modeling Risk, the Human Factor Was Left Out | |
| |
| |
| |
| Playing the Odds | |
| |
| |
| |
| Monday Puzzle: Solution to Birthday Problem | |
| |
| |
| |
| Just What Are Your Odds in Genetic Roulette? Go Figure | |
| |
| |
| |
| The 2000 Election: The Science of Counting | |
| |
| |
| |
| Prospectus; Can a Computer Program Figure Out the Market? A Former Analyst and a Mathematician Are Betting That Theirs Can | |
| |
| |
| |
| New Tools for the I.R.S. to Sniff Out Tax Cheats | |
| |
| |
| |
| |
| Famous Problems, Solved and As Yet Unsolved | |
| |
| |
| New Mathematics Links Two Worlds | |
| |
| |
| |
| An Elusive Proof and Its Elusive Prover | |
| |
| |
| |
| Ask Science: Poincare's Conjecture | |
| |
| |
| |
| Grigori Perelman's Beautiful Mind | |
| |
| |
| |
| A Math Problem Solver Declines a $1 Million Prize | |
| |
| |
| |
| "Four-Color Problem" Attacked | |
| |
| |
| |
| Four-Color Proof | |
| |
| |
| Goldbach's Conjecture; This One May Be Provable, but We May Never Know | |
| |
| |
| |
| Mathematics Expert May Soon Resolve A 350-Year Problem | |
| |
| |
| |
| Fermat's Theorem Solved? Not This Time | |
| |
| |
| |
| Fermat's Last Theorem Still Has 0 Solutions | |
| |
| |
| |
| At Last, Shout of "Eureka!" in Age-Old Math Mystery | |
| |
| |
| |
| Fermat's Theorem | |
| |
| |
| |
| Flaw Is Found in Math Proof, but Repairs Are Under Way | |
| |
| |
| |
| A Year Later Fermat's Puzzle Is Still Not Quite Q.E.D. | |
| |
| |
| |
| How a Gap in the Fermat Proof Was Bridged | |
| |
| |
| |
| Two Key Mathematics Questions Answered after Quarter Century | |
| |
| |
| |
| Mathematical Theory of Poker Is Applied to Business Problems | |
| |
| |
| |
| Soap Bubbles Get a New Role in Old Mathematics Problem | |
| |
| |
| |
| Math Advance Penetrates Secrets of Knots | |
| |
| |
| |
| Packing Tetrahedrons, and Closing in on a Perfect Fit | |
| |
| |
| |
| Finding Order in the Apparent Chaos of Currents | |
| |
| |
| |
| In Bubbles and Metal, the Art of Shape-Shifting | |
| |
| |
| |
| The Scientific Promise of Perfect Symmetry | |
| |
| |
| |
| 143-Year-Old Problem Still Has Mathematicians Guessing | |
| |
| |
| |
| What Is the Most Important Problem in Math Today? | |
| |
| |
| |
| Solution to Old Puzzle: How Short a Shortcut? | |
| |
| |
| |
| |
| Chaos, Catastrophe and Randomness | |
| |
| |
| Chaos Is Defined by New Calculus | |
| |
| |
| Experts Debate the Prediction of Disasters | |
| |
| |
| |
| Solving the Mathematical Riddle of Chaos | |
| |
| |
| |
| The Man Who Reshaped Geometry | |
| |
| |
| |
| Snowflake's Riddle Yields to Probing of Science | |
| |
| |
| |
| Tales of Chaos: Tumbling Moons and Unstable Asteroids | |
| |
| |
| |
| Fluid Math Made Simple-Sort Of | |
| |
| |
| |
| When Chaos Rules the Market | |
| |
| |
| |
| New Appreciation of the Complexity in a Flock of Birds | |
| |
| |
| |
| Indestructible Wave May Hold Key to Superconductors | |
| |
| |
| |
| The Quest for True Randomness Finally Appears Successful | |
| |
| |
| |
| Coin-Tossing Computers Found to Show Subtle Bias | |
| |
| |
| |
| Science Squints at a Future Fogged by Chaotic Uncertainty | |
| |
| |
| |
| Probing Disease Clusters: Easier to Spot Than Prove | |
| |
| |
| |
| The Odds of That | |
| |
| |
| |
| Fractal Vision | |
| |
| |
| |
| |
| Cryptography and the Emergence of Truly Unbreakable Codes | |
| |
| |
| Harassment Alleged over Code Research | |
| |
| |
| |
| Researchers to Permit Pre-Publication Review by U.S. | |
| |
| |
| |
| Tighter Security Rules for Advances in Cryptology | |
| |
| |
| |
| A New Approach to Protecting Secrets Is Discovered | |
| |
| |
| |
| Brief U.S. Suppression of Proof Stirs Anger | |
| |
| |
| A Most Ferocious Math Problem Tamed | |
| |
| |
| |
| Biggest Division a Giant Leap in Math | |
| |
| |
| |
| Scientists Devise Math Tool to Break a Protective Code | |
| |
| |
| |
| Tied Up in Knots, Cryptographers Test Their Limits | |
| |
| |
| |
| A Public Battle over Secret Codes | |
| |
| |
| |
| U.S. Code Agency Is Jostling for Civilian Turf | |
| |
| |
| |
| Researchers Demonstrate Computer Code Can Be Broken | |
| |
| |
| |
| Nick Patterson; A Cold War Cryptologist Takes a Crack at Deciphering DNA's Deep Secrets | |
| |
| |
| |
| Adding Math to List of Security Threats | |
| |
| |
| |
| Prizes Aside, the P-NP Puzzler Has Consequences | |
| |
| |
| |
| |
| Computers Enter the World of Mathematics | |
| |
| |
| "Thinking Machine" Does Higher Mathematics; Solves Equations That Take Humans Months | |
| |
| |
| New Giant "Brain" Does Wizard Work | |
| |
| |
| "Brain" Speeded Up for War Problems | |
| |
| |
| |
| The Electronic Digital Computer: How It Started, How It Works and What It Does | |
| |
| |
| |
| New Shortcut Found for Long Math Proofs | |
| |
| |
| |
| New Technique Stores Images More Efficiently | |
| |
| |
| |
| Giant Computer Virtually Conquers Space and Time | |
| |
| |
| |
| Rear Adm. Grace M. Hopper Dies; Innovator in Computers Was 85 | |
| |
| |
| |
| Frances E. Holberton, 84, Early Computer Programmer | |
| |
| |
| |
| Squeezing Data like an Accordion | |
| |
| |
| |
| A Digital Brain Makes Connections | |
| |
| |
| |
| A Soviet Discovery Rocks World of Mathematics | |
| |
| |
| |
| The Health Care Debate: Finding What Works | |
| |
| |
| |
| Step 1: Post Elusive Proof. Step 2: Watch Fireworks | |
| |
| |
| |
| |
| Mathematicians and Their World | |
| |
| |
| Paul Erdos, 83, a Wayfarer in Math's Vanguard, Is Dead | |
| |
| |
| |
| Journeys to the Distant Fields of Prime | |
| |
| |
| |
| Highest Honor in Mathematics Is Refused | |
| |
| |
| |
| Scientist at Work: John H- Conway; At Home in the Elusive World of Mathematics | |
| |
| |
| |
| Claude Shannon, B. 1916-Bit Player | |
| |
| |
| |
| An Isolated Genius Is Given His Due | |
| |
| |
| |
| Scientist at Work: Andrew Wiles; Math Whiz Who Battled 350-Year-Old Problem | |
| |
| |
| |
| Scientist at Work: Leonard Adleman; Hitting the High Spots of Computer Theory | |
| |
| |
| |
| Dr. Kurt G�del, 71, Mathematician | |
| |
| |
| |
| Genius or Gibberish? The Strange World of the Math Crank | |
| |
| |
| |
| Contributors' Biographies | |
| |
| |
| Photography and Illustration Credits | |
| |
| |
| Ackowledgments | |
| |
| |
| Index | |