9781402793226

1402793227

What is mathematics?

Statistics, coincidences, and surprising facts

Famous problems, solved and as yet unsolved

Chaos, catastrophe, and randomness

Cryptography and the emergence of truly unbreakable codes

Computers enter the world of mathematics

Mathematicians and their world.

Foreword / Paul Hoffman

Introduction / Gina Kolata.

Chapter 1. What is mathematics?: Useful invention or absolute truth : what is math? / George Johnson ; But aren't truth and beauty supposed to be enough? / James Gleick ; Mathematicians meet computerized ideas / Gina Kolata ; Mathematicians finally log on / James Gleick ; With major math proof, brute computers show flash of reasoning power / Gina Kolata ; Computers still can't do beautiful mathematics / Gina Kolata ; 100 quadrillion calculations later, eureka! / Gina Kolata ; Theorist applies computer power to uncertainty in statistics / Gina Kolata.

Chapter 2. Statistics, coincidences, and surprising facts: 1-in-a-trillion coincidence, you say? Not really, experts find / Gina Kolata ; Sometimes heavier objects go to the top : here's why / James Gleick ; Behind Monty Hall's doors : puzzle, debate and answer? / John Tierney ; What if they closed 42nd Street and nobody noticed? / Gina Kolata ; Down for the count : why some numbers are only very good guesses / Gina Kolata ; Could it be? Weather has nothing to do with your arthritis pain? / Gina Kolata ; Electronics to aid weather figuring / Sidney Shalett ; Insurance as a study : something of the men who figure business by algebra ; Leontief's contribution / Leonard Silk ; Many small events may add up to one mass extinction / Malcolm W. Browne ; Metric mania / John Allen Paulos ; In shuffling cards, 7 is a winning number / Gina Kolata ; Can game theory predict when Iran will get the bomb? / Clive Thompson ; In modeling risk, the human factor was left out / Steve Lohr ; Playing the odds / George Johnson ; Monday puzzle : solution to birthday problem / Pradeep Mutalik ; Just what are your odds in genetic roulette? Go figure / Gina Kolata ; The 2000 election : the science of counting / Gina Kolata ; Prospectus : can a computer program figure out the market? A former analyst and a mathematician are betting that theirs can / Janet Stites ; New tools for the I.R.S. to sniff out tax cheats / David Cay Johnston.

Chapter 3. Famous problems, solved and as yet unsolved: New mathematics links two worlds / William L. Laurence ; An elusive proof and its elusive prover / Dennis Overbye ; Ask science : Poincaré's conjecture / Dennis Overbye ; Grigori Perelman's beautiful mind / Jascha Hoffman ; A math problem solver declines a $1 million prize / Dennis Overbye ; "Four-color problem" attacked / William L. Laurence ; Four-color proof ; Goldbach's conjecture : this one may be provable, but we may never know / George Johnson ; Mathematics expert may soon resolve a 350-year problem / James Gleick ; Fermat's theorem solved? Not this time / James Gleick ; Fermat's last theorem still has 0 solutions / James Gleick ; At last, shout of "Eureka!" in age-old math mystery / Gina Kolata ; Fermat's theorem / James Gleick ; Flaw is found in math proof, but repairs are under way / Gina Kolata ; A year later Fermat's puzzle is still not quite Q.E.D. / Gina Kolata ; How a gap in the Fermat proof was bridged / Gina Kolata ; Two key mathematics questions answered after quarter century / John A. Osmundsen ; Mathematical theory of poker is applied to business problems / Will Lissner ; Soap bubbles get a new role in old mathematics problem / Joseph Williams ; Math advance penetrates secrets of knots / James Gleick ; Packing tetrahedrons, and closing in on a perfect fit / Kenneth Chang ; Finding order in the apparent chaos of currents / Bina Venkataraman ; In bubbles and metal, the art of shape-shifting / Kenneth Chang ; The scientific promise of perfect symmetry / Kenneth Chang ; 143-year-old problem still has mathematicians guessing / Bruce Schechter ; What is the most important problem in math today? / Gina Kolata ; Solution to old puzzle : how short a shortcut? / Gina Kolata.

Chapter 4. Chaos, catastrophe, and randomness: Chaos is defined by new calculus ; Experts debate the prediction of disasters / Malcolm W. Browne ; Solving the mathematical riddle of chaos / James Gleick ; The man who reshaped geometry / James Gleick ; Snowflake's riddle yields to probing of science / James Gleick ; Tales of chaos : tumbling moons and unstable asteroids / James Gleick ; Fluid math made simple

sort of / James Gleick ; When chaos rules the market / James Gleick ; New appreciation of the complexity in a flock of birds / James Gleick ; Indestructible wave may hold key to superconductors / James Gleick ; The quest for true randomness finally appears successful / James Gleick ; Coin-tossing computers found to show subtle bias / Malcolm W. Browne ; Science squints at a future fogged by chaotic uncertainty / Malcolm W. Browne ; Probing disease clusters : easier to spot than prove / Gina Kolata ; The odds of that / Lisa Belkin ; Fractal vision / James Gleick.

Chapter 5. Cryptography and the emergence of truly unbreakable codes: Harassment alleged over code research / Malcolm W. Browne ; Researchers to permit pre-publication review by U.S. / Richard Severo ; Tighter security rules for advances in cryptology / Walter Sullivan ; A new approach to protecting secrets is discovered / James Gleick ; Brief U.S. suppression of proof stirs anger ; A most ferocious math problem tamed / Malcolm W. Browne ; Biggest division a giant leap in math / Gina Kolata ; Scientists devise math tool to break a protective code / John Markoff ; Tied up in knots, cryptographers test their limits / Gina Kolata ; A public battle over secret codes / John Markoff ; U.S. code agency is jostling for civilian turf / John Markoff ; Researchers demonstrate computer code can be broken / Sara Robinson ; Nick Patterson, a cold war cryptologist takes a crack at deciphering DNA's deep secrets / Ingfei Chen ; Adding math to list of security threats / John Markoff ; Prizes aside, the P-NP puzzler has consequences / John Markoff.

Chapter 6. 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 / Will Lissner ; The electronic digital computer : how it started, how it works and what it does / Henry L. Lieberman and Dr. Louis Robinson ; New shortcut found for long math proofs / Gina Kolata ; New technique stores images more efficiently / Gina Kolata ; Giant computer virtually conquers space and time / George Johnson ; Rear Adm. Grace M. Hopper dies, innovator in computers was 85 / John Markoff ; Frances E. Holberton, 84, early computer programmer / Steve Lohr ; Squeezing data like an accordion / Peter Wayner ; A digital brain makes connections / Anne Eisenberg ; A Soviet discovery rocks world of mathematics / Malcolm W. Browne ; The health care debate : finding what works / Gina Kolata ; Step 1 : post elusive proof. Step 2 : watch fireworks / John Markoff.

Chapter 7. Mathematicians and their world: Paul Erdos, 83, a wayfarer in math's vanguard, is dead / Gina Kolata ; Journeys to the distant fields of prime / Kenneth Chang ; Highest honor in mathematics is refused / Kenneth Chang ; Scientist at work : John H. Conway, at home in the elusive world of mathematics / Gina Kolata ; Claude Shannon, B. 1916

bit player / James Gleick ; An isolated genius is given his due / James Gleick ; Scientist at work : Andrew Wiles, math whiz who battled 350-year-old problem / Gina Kolata ; Scientist at work : Leonard Adleman, hitting the high spots of computer theory / Gina Kolata ; Dr. Kurt Gödel, 71, mathematician / Peter B. Flint ; Genius or gibberish? The strange world of the math crank / George Johnson.