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.
This is a paperbound reprint of a 2003 book (Joseph Henry Press), about which Book News wrote: 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

The Christian Science Monitor
A math book that reads like a mystery novel.

Los Angeles Times
Derbyshire’s attempt to take nonmathematicians into this subject had me on the edge of my seat.

Scientific American
Riemann and his colleagues come to life as real characters and not just adjectives for conjectures and theorems.

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