Synopses & Reviews
In August 1859 Bernhard Riemann, a 32-year old mathematician, posed a deceptively simple question to the Berlin Academy: Is there a general rule for figuring out how many prime numbers there are? More than 150 years later, the solution to this critical problem eludes our grasp.
Riemann initially believed that he was tackling a straightforward matter of arithmetic. He started with something very simple. How many prime numbers numbers that cannot be evenly divided except by themselves and 1 are there less than twenty? The (easy) answer: there are eight: 2, 3, 5, 7, 11, 13, 17, and 19. He went on to contemplate how many there are less than 100...which led him to wonder how many there were less than a million...or even a trillion.
As the questions progressed and grew in scope and magnitude, the answers became increasingly elusive. But might there be some logical formula for calculating the answers? As long ago as the third century B.C., Euclid proved that no one could ever find the "largest" prime number that they are infinite in number. What Riemann wanted to know was whether there was a pattern to the primes. He devoted his life to the search for this subtle but presumably precise pattern. Ultimately, it would become not only his obsession, but that of generations of mathematicians up to the present day.
Alternating chapters of extraordinarily lucid mathematical exposition with chapters of biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited over a century ago, Riemann's hypothesis is an enduring intellectual feast for the cognoscenti and the curious alike even today, the solution is still eagerly sought since prime numbers are an essential key to both code making and code breaking. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof and those who have been consumed by it.
Review
"The most detailed, and consequently the most rewarding account of the Riemann Hypothesis....This remarkable constellation of interests results in a math book that reads like a mystery novel. When, some 300 pages into the book, Derbyshire finally presents Riemann's conclusion, it is with literally breathtaking impact." The Christian Science Monitor
Review
"Derbyshire is a talented expositor determined to make the reader understand some serious mathematics. A general reader with some memory of high school algebra who is willing to concentrate will come away with a grasp of what the problem is and why insiders are excited. Mathematicians in other fields will deepen any superficial understanding they may have, as well as picking up some new ideas on how to explain mathematical ideas." The New Criterion
Review
"A remarkable book." John F. Nash, Jr., 1994 Nobel Prize Winner in Economics
Review
"The Riemann Hypothesis is one of the deepest of all unsolved problems in mathematics. Unfortunately it is difficult to state exactly what the hypothesis is. It is high time that someone would write a book explaining the hypothesis in ways understandable by ordinary mathematicians and even by laymen. Three cheers to John Derbyshire for having finally done it." Martin Gardner, "Mathematical Games" columnist for Scientific American and author of Did Adam and Eve Have Navels?
Review
"John Derbyshire's tour de force Prime Obsession guides one through a 200-year-long story of the world's best-known, unsolved mathematical mystery. The formulation, study, and significance of the Riemann hypothesis each represent immense areas of mathematical thought; this book expertly tackles them all. The chapters filled with anecdotes alternate with chapters that lead the novice gently by hand into the exploration of fundamental ideas captivating the reader and creating a lasting impression." Arthur Jaffe, Harvard University
Review
"An informative, comprehensive, well written account of the unsolved problem that most mathematicians regard as the most important open problem in the field. Derbyshire not only tells the historical story behind the problem the people stuff he also includes all the mathematics needed to understand what the problem is about and how people are trying to solve it." Keith Devlin, Stanford University, author of The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
Synopsis
Alternating chapters of extraordinarily lucid mathematical exposition with chapters of biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world.
Synopsis
In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: "On the Number of Prime Numbers Less Than a Given Quantity." In the middle of that paper, Riemann made an incidental remark a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?
Riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark the Riemann Hypothesis that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.
It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many the veritable "great white whale" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.
Alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof and those who have been consumed by it.
About the Author
John Derbyshire is a mathematician and linguist by education, a systems analyst by profession, and a celebrated writer in his spare time. He is best known as the author of Seeing Calvin Coolidge in a Dream, the highly acclaimed 1996 novel that was extravagantly praised by Jonathan Yardley in the Washington Post Book World and uniformly well reviewed in the New York Times Book Review, the New Yorker, and the Boston Globe, among others. His work appears frequently in National Review and The New Criterion. Born and raised in England, he has made his home in the U.S. for the past 15 years. He currently lives in Huntington, New York, with his wife and two children.