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.
Listed on the Christian Science Monitor's 2003 Noteworthy Nonfiction List
Named to Library Journal's Best Sci-Tech Books 2003 List
Named to Science Books & Films' 2003 Best Books List
"A remarkable book."
-- John F. Nash, Jr., 1994 Nobel Prize Winner in Economics
-- Mark Haddon in The Daily Telegraph, BOOKS OF THE YEAR column, November 22, 2003
"There have been a lot of books and plays about eccentric mathematicians, but Bernhard Riemann blows the stereotype away. He had a quiet family life, was shy, and didn�t go crazy like John Nash. It's nice to read about someone ordinary who was perhaps as bright a mathematician as has ever been. Derbyshire goes into great depth, and the math is quite difficult. If you're interested in it, there it is -- the real equations. But if you're not, you can skip it. This is one of the best mathematical biographies I've read -- and I've read a lot."
-- Jef Raskin in Wired Magazine, June 2004
"...[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
"John Derbyshire's Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics is a more difficult book [than the other two Riemann books] but is even more rewarding for those up to the challenge. Energetic and conversational, it puts one at ease. ... Derbyshire's attempt to take nonmathematicians into this subject had me on the edge of my seat. Was he really going to introduce Moebius inversions in polite company? He did, and I found his treatment, and his chutzpah, consistently interesting. His account of what has happened in the last 30 years is sure-footed and perceptive."
-- Los Angeles Times, June 15, 2003
"Mr. Derbyshire's tone is warm and witty, and reading his book, I felt as though he was sitting next to me, guiding my ascent into one of math's more rarefied fields. ... Many people have terror on sight when it comes to the arcane symbols of mathematics, and they might not consider picking up a book about a problem the greatest minds in the world haven't solved. That would be a shame; like any great teacher, John Derbyshire's passion for his subject transforms unfamiliar and difficult material into a genuinely enjoyable and enlightening experience."
-- The New York Sun, June 18, 2003
"In Prime Obsession, John Derbyshire has produced a remarkably accessible and deeply researched description of this fascinating problem. ... Derbyshire interweaves a fascinating history -- embedded in the political turmoil of western Europe -- of how the Riemann hypothesis came to be posed and how it has influenced the work of 20th-century mathematicians. Moreover, he gives us a detailed account of exactly what the hypothesis says mathematically. ... Derbyshire is eminently successful at bringing this story to life."
-- Science, October 3, 2003
"For those interested in the mathematics of the Riemann Hypothesis, a background in algebra, geometry, and introductory calculus should be sufficient. But surely most everyone can enjoy Mr. Derbyshire's lucid and informatively anecdotal description of the thinkers who contributed to our understanding of prime numbers. ... John Derbyshire's Prime Obsession is an intellectual tour de force and an excellent read."
-- The Washington Times, August 17, 2003
"Alternating between telling Riemann's life story and presenting a mathematical primer on the elements of his hypothesis, Derbyshire elegantly explores a vexing topic."
-- Science News, August 2, 2003
"In common with almost all books of this kind, there are parts that you will skim, and which these are will depend on your mathematical background--but the bits you do read will be extremely well explained. A major and most unusual strength of the book, which even experts will enjoy, is a sort of intimacy between the author and the zeta function itself. ... The chapters of Derbyshire's book alternate between mathematical ones and more historical ones, a device that works well."
-- Nature, October 9, 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's book includes significantly more mathematics than the other [two books on the Riemann Hypothesis], but it is still accessible to anyone comfortable with simple mathematical formulas. The author's goal is to explain Riemann's connection between the primes and the zeros of the zeta function, as well as other important 20th-century mathematical developments. For Derbyshire to have pulled his objective off so successfully is a remarkable achievement. ...for readers who seek a deeper level of understanding of the hypothesis and more biographical details about Riemann, Derbyshire's remarkable book is, in my view, a gem."
-- Physics Today, June 2004
"Derbyshire begins with a riveting account of Riemann's times... I like the historical account, which is well woven and accurate as far as I could check. A fair picture of the problem is presented... Altogether the author has succeeded in writing a very readable and interesting book. The appendix provides a funny song describing the Riemann hypothesis, written by Tom Apostol in 1955. It makes a fitting finish, showing that mathematicians also have a light side."
-- American Scientist, July-August 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  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's] layout is unusual; he uses the odd-numbered chapters for the mathematical story and the even-numbered chapters for the history. This approach works very well -- the difficult technical pieces are interlaced with an entertaining and well-told historical narrative. A less technically inclined reader might concentrate on the history and lightly skim the odd-numbered chapters. On the other hand, the mathematically inclined should not skip the even-numbered chapters -- they tell a good story that should not be missed."
-- MAA (Mathematical Association of America) Online, 2003
"Derbyshire attempts to walk the reader slowly up the mathematical slope... the reader willing to work through Derbyshire's presentation will understand something of Riemann's insights."
-- The New York Times Book Review, July 6, 2003
"[Derbyshire] has written a wonderful book. He does not fudge the mathematics ...for the most important audience of non-mathematicians--those young ones who might consider becoming mathematicians--it will be a great resource and inspiration. And for mathematicians and readers with a fair amount of mathematical sophistication, it is a book that will inspire, inform, and entertain. ... It is interestingly and skillfully written, and it approaches many aspects of the subject in imaginative and thought-provoking ways."
-- The Mathematical Intelligencer, Winter 2004
"This is a striking and brilliant book, in many ways the most ambitious science-for-the-public attempt I have ever read. John Derbyshire undertakes a task which is (we are more or less convinced by the end) impossible, and yet the book succeeds, and at its best it is beautiful. ...the book is compelling ... Derbyshire writes with a novelist's eye and ear, and a novelist's feel for the concrete image, the telling detail, the come-hither sentence."
-- National Review, July 28, 2003
"...a historical adventure. Chapters alternate between broad-scale historical accounts and detailed mathematical presentation. ... His historical chapters link mathematical developments to the lives and personalities of the mathematicians involved and are full of interesting stories."
-- The Economist, July 12, 2003
"Prime Obsession, a highly nontechnical introduction to the [Riemann Hypothesis] and its history, is for the mathematically curious and adventurous. The mathematics is leavened with biography, history, and anecdote. Derbyshire, a mathematician and linguist, has made a serious attempt to explain a deep mathematical problem in a way that can be skimmed by mathematicians and lingered over by nonmathematicians. ... Summing up: Highly recommended."
-- CHOICE, November 2003
"Three things help to make this math book accessible. The first is the breezy conversational style. ... The second element that makes this book accessible is its alternating chapters on technical and historical matters. ... Finally, the third factor that makes this book accessible is its numerical examples."
-- Science Books & Films, July 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
-- Math League News, November 2003
"Prime Obsession teaches the literate and intelligent lay reader the basic mathematical knowledge necessary to understand Riemann's hypothesis, and then allows one to wonder and ponder the possibilities. Prime Obsession is an intrinsically fascinating work which is very highly recommended for anyone curious about this great unsolved mathematical mystery."
-- Midwest Book Review and Small Press Bookwatch, 2003
"...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
"...a wonderfully lucid and captivating explanation and history of the hypothesis and of the life and times of Bernhard Riemann. ...Derbyshire's lively account helps the reader get a 'feel' for the Riemann hypothesis, as well as a good overview of the mathematics."
-- Mathematics Teacher, April 2004
"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
"John Derbyshire's book has fascinating historical vignettes that link mathematical problem to persons and events."
-- The Manila Times, July 29, 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
"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
"Writing a book about something as obscure as the zeta function for the non-mathematician is a daunting proposition but John Derbyshire is up to the challenge. ... By starting off slowly and holding our hands as he moves through the math, Derbyshire makes complex mathematical functions understandable even to someone who hasn't looked at calculus in more than twenty years. So even if non-trivial zeros, natural logs, and prime number distribution theories sound over your head, Derbyshire will explain it in a way that will make it clear and interesting. Derbyshire breaks the book up so that the odd-numbered chapters cover mathematical details and the even-numbered chapters cover historical background of the story. So even if you do get lost in the math, you still can still follow the story which is fascinating in itself."
-- Unresolved References, September 12, 2004
"In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem... Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. ... 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."
"Riemann's life and work form the subject of John Derbyshire's touching biography Prime Obsession."
-- L.A. Weekly, August 22, 2003
"...a nice history..."
-- Mathematical Reviews, 2004