Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

jhpress

jhpressJohn Derbyshire

448 pages, 5.5 x.8.5, 2003.

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.

“A remarkable book.”
— John F. Nash, Jr., 1994 Nobel Prize Winner in Economics

“…[this book] will reward the effort paid to [it]… the most demanding, and for that reason most rewarding, is probably Derbyshire’s.”
— Washington Post, May 4, 2003

“The most detailed, and consequently the most rewarding account of the Riemann Hypothesis is John Derbyshire’s Prime Obsession. The author, a trained mathematician with a day job as an investment banker, moonlights as a novelist. 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, April 10, 2003

“…Riemann and his colleagues come to life as real characters and not just adjectives for conjectures and theorems. … Parts of Prime Obsession read almost like a novel, others like a mathematical text. Its author, Derbyshire, segmented the book so that most of the math falls into odd chapters and the history and biographical material in even ones, but the math is as interesting as the rest.”
— Scientific American, May 2003

“The Riemann hypothesis, as Derbyshire shows through approachable examples and colorful quotes from leading mathematicians, has now acquired a life of its own. It is hardly easy to explain, but Derbyshire does his very best. He also takes his time to do so. … [a] difficult but rewarding book…”
— Popular Science, May 2003

“…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. …Late in his book, Derbyshire ambitiously but successfully unpacks [Riemann’s] short and difficult [1859] paper… Explaining from a standing start what the Riemann zeta function and its zeros are in only half a book is not easy, and Derbyshire proves himself a leading mathematical communicator in being able to do it.”
— The New Criterion, April 2003

“Derbyshire, a National Review columnist, has written the most mathematically detailed of the trio [of new books on the Riemann Hypothesis].”
— Village Voice, April 22, 2003

“[Derbyshire] first takes readers through well-organized mathematical fundamentals in order to give them a good understanding of Riemann’s discovery and its consequences. …an excellent introduction for nonspecialists.”
— Library Journal

“…presents more technical details about the hypothesis and will probably attract math recreationists… It requires, however, only a college-prep level of knowledge because of its crystalline explanations.”
— Booklist, April 15, 2003

“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?

“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

“…a good introduction — and an infuriating challenge.”
— FOCUS, June 1, 2003

“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

“Every so often I read something mathematical and I fall in love with math all over again. Oh, I’m not that bright, mathematically speaking. … In any event, I recently bought John Derbyshire’s Prime Obsession and I’ve been eating up its chapters like cupcakes.”
— Be Here Mondays, May 18, 2003.