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

~ John Derbyshire (Author) "In August 1859, Bernhard Riemann was made a corresponding member of the Berlin Academy, a great honor for a young mathematician (he was 32)..." (more)
Key Phrases: argument ant, total overhang, prime counting function, Golden Key, Power Rule, Bernhard Riemann (more...)

Editorial Reviews

Amazon.com Review

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

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Product Details

• Hardcover: 448 pages
• Publisher: Joseph Henry Press (April 23, 2003)
• Language: English
• ISBN-10: 0309085497
• ISBN-13: 979-0309085495
• Product Dimensions: 8.6 x 5.6 x 1.4 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (88 customer reviews)
• Amazon.com Sales Rank: #445,455 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

175 of 180 people found the following review helpful:

5.0 out of 5 stars Reads Like a Gripping Mystery, June 8, 2003

By	S. Greene (Sarasota, FL United States) - See all my reviews (REAL NAME)

Prime Obsession is a delight: a book about a hypothesis on the distribution of prime numbers that reads like a gripping mystery. Most fiction isn't this vivid, moving, and well written, and this is no fiction. It is history, biography, philosophy, and, yes, mathematics brought to life with wit and wonder. You have to read this extraordinary book.

This is the story of the Reimann Hypothesis, the greatest unsolved problem in mathematics today. Here it is in all its glory: "All non-trivial zeros of the zeta function have real part one-half."

What on earth does it mean? Mr. Derbyshire, a gifted storyteller, takes the reader on an exhilarating journey of discovery as he painstakingly illuminates the meaning, mystery, and power of those eleven short words.

I have never taken a course in calculus and am intimidated by even moderately complex math notation. There's lots of that in this book, and I had my doubts I could get through it. But Mr. Derbyshire knows that some of his readers will have fear of flying, or only be able to fly for short distances, so he patiently breaks scary-looking formulae into bite-size pieces and gives you the general rules you need to know to digest them. He knows how to explain things with crystal clarity and easy wit. And the man knows how to turn a phrase.

Still, he does not coddle his readers, so you need to be prepared to roll up your sleeves and fasten your seat belt. This is a challenging book, no bones about it. I needed to read it twice just to get a passing feel for chunks of it. Why, you may ask, would I twice read a book I had difficulty comprehending? Because with Mr. Derbyshire's gentle urging I could glimpse the beauty and feel the deep wonder of Bernhard Riemann's hypothesis, even if it remained just beyond grasp. And this was enough, more than enough, to rivet my attention for days and give me hours of entertaining, informative reading.

This is a gem of book. It left me gasping for air and wanting more. I cannot more strongly recommend it.

58 of 62 people found the following review helpful:

5.0 out of 5 stars A Beautiful Read. Well Done, May 14, 2003

By	Walter Fekula (New York, NY USA) - See all my reviews (REAL NAME)

John Derbyshire has done a great job with Prime Obsession. I am not a mathematician and I'd never even heard of the Riemann Hypothesis, but Derbyshire feeds it to you a bite at a time, and I think I now at least understand what all the excitement is about. Derbyshire doesn't pretend it's easy and doesn't spare you any of the necessary math, but he makes it as palatable as it can be made, I think, and gives just as much as you need.
I agree with the statement in his prologue: "If you don't understand the Hypothesis after finishing my book, you can be pretty sure you will never understand it."
When you get overloaded with math, there is plenty of historical and biographical detail to keep your attention--some physics, too. The writing is fluent and occasionally beautiful. The book's epilogue, where we say goodbye to Bernhard Riemann, is actually very moving.
And the footnotes are wonderful! This is a nonfiction book, but Derbyshire is a natural novelist, and it shows--he has made a really good story out of the Riemann Hypothesis.
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43 of 45 people found the following review helpful:

5.0 out of 5 stars It's got that certain "can't put it down" feel, December 18, 2003

By	MagicSkip "magicskip" (Marriottsville, MD) - See all my reviews (VINE VOICE)

This is a fascinating and very well-written book about a singular problem in mathematics history. Derbyshire presents a look at the history of the Riemann hypothesis (or is it "conjecture"? Derbyshire asks, as an aside, what the real difference is between the two, in mathematical terminology) -- the people and their political context as well as the equation and efforts to prove it.

As a blessing to those of us who are not hard-core mathematicians, Derbyshire takes the approach of alternating chapters between (even numbered chapters) math and (odd chapters) people and context. This gives the effect of telling two intimately linked stories simultaneously, and keeping the reader in just a bit of suspense in each while telling the other. I found myself enjoying each of the two tales, yet impatient to see where the other was going next.

Derbyshire's style of writing is thoroughly entertaining, as well. His personality comes through as someone who is a "fan" of math. In "Peanuts", the late, great Charles Shultz has Lucy commenting to Schroeder that Beethoven couldn't have been so great, because he never had his picture on bubble-gum cards. It is apparent that if there was ever a set of mathematical gurus bubble-gum cards, Derbyshire would have been a collector. His admiration for genius only added to my enjoyment of the book.

Derbyshire directly lets you know which people he holds in high esteem. He clearly honors those with a work ethic, those with dedication to their craft, family, and faith. He almost apologetically admits his appreciation for these sympathetic characters with a style reminiscent of a sports broadcaster who is also quietly rooting for "the good guys" -- not the home team, but the high-character-quality players. Thomas Boswell and George Will both use a similar "aw shucks, I just LIKE the guy" style when writing about Cal Ripken.

In any case, Derbyshire reveals his own character by telling which mathematicians he likes best and why. Similarly, his humility in how he presents the mathematical concepts is also telling. Derbyshire has obviously had to cut some strong math chops to be able to understand and present all that he does, as clearly as he does, and he repeatedly comments on keeping the level down to where most readers can comprehend -- yet he does all this in a self-deprecating fashion that made me comfortable to keep reading and learning. Even when the math was more than I wanted to plow through, I just read those parts lightly and kept going, and Derbyshire's style kept the story together through that.

As an engineer and semi-pop-science geek wannabe, I found this book to be a bit heavy on math theory and a bit light on applications for my tastes. Derbyshire admits this tendency, to the effect that once the theoretical knowledge is gained, people will find applications for it. That's Derbyshire's point of view, and another glimpse of his character. It makes me want to meet him -- he seems to be the type of person who would be a good friend.

I wouldn't classify this as a "must read", but it is a very good read. It is both entertaining and educational. I'm not quite sure why I picked it up, but once I did I couldn't put it down.