Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae. In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

From Booklist
Bernhard Riemann would make any list of the greatest mathematicians ever. In 1859, he proposed a formula to count prime numbers that has defied all attempts to prove it true. This new book tackles the Riemann hypothesis. Partly a biography of Riemann, Derbyshire's work 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. Derbyshire treats the hypothesis historically, tracking increments of progress with sketches of well-known people, such as David Hilbert and Alan Turing, who have been stymied by it. Carrying a million-dollar bounty, the hypothesis is the most famous unsolved problem in math today, and interest in it will be both sated and stoked by these able authors. Gilbert Taylor
Copyright © American Library Association. All rights reserved

From Book News, Inc.
Riemann's hypothesis for a general rule to determine how many prime numbers exist in a given quantity was first posed offhandedly to the Berlin Academy in 1859. Today, having been neither proved or disproved, it remains the "great white whale" of mathematics and a missing key to advances in code theory and atomic physics. Derbyshire introduces this captivating mathematical problem in alternating chapters of mathematical exposition (some college calculus required) and biography and history (for general readers interested in mathematics). Derbyshire, a mathematician and linguist by education, is the author of Seeing Calvin Coolidge in a Dream (1996).Copyright © 2004 Book News, Inc., Portland, OR

Unresolved References, September 12, 2004
"Derbyshire makes complex mathematical functions understandable even to someone who hasn't looked at calculus in more than twenty years."

Physics Today, June 2004
"...accessible to anyone comfortable with simple mathematical formulas. ...Derbyshire’s remarkable book is, in my view, a gem."

The Mathematical Intelligencer, Winter 2004
"...a wonderful book. ...interestingly and skillfully written... it approaches many aspects of the subject in imaginative and thought-provoking ways."

Washington Post, May 4, 2003
"...[this book] will reward the effort paid to [it]"

Los Angeles Times, June 15, 2003
"...rewarding for those up to the challenge. Energetic and conversational, it puts one at ease."

Mark Haddon in The Daily Telegraph, BOOKS OF THE YEAR column, November 22, 2003
"...mind-expanding..."

The New York Sun, June 18, 2003
"...warm and witty ... a genuinely enjoyable and enlightening experience."

Science, October 3, 2003
"...a remarkably accessible and deeply researched description of this fascinating problem. ... eminently successful at bringing this story to life."

Mathematical Reviews, 2004
"...a nice history..."

Mathematics Teacher, April 2004
"...a wonderfully lucid and captivating explanation and history of the hypothesis and of the life and times of Riemann."

Book Description
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, Riemann’s 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.

From the Inside Flap
"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 "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? "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

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 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.

FROM THE PUBLISHER

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.

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.

FROM THE CRITICS

Martin Gardner

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.—"Mathematical Games" columnist for Scientific American and author of Did Adam and Eve Have Navels?

Keith Devlin

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.—Stanford University, author of The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time

Arthur Jaffe

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.—Harvard University

The New Criterion

...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. ... 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 Christian Science Monitor