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Prime Obsession: Berhhard Riemann and the Greatest Unsolved Problem in Mathematics (Paperback) (平装)
by John Derbyshire
| Category:
Mathematics, Science |
| Market price: ¥ 178.00
MSL price:
¥ 168.00
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| Stock:
Pre-order item, lead time 3-7 weeks upon payment [ COD term does not apply to pre-order items ] |
MSL rating:
 Good for Gifts |
| MSL Pointer Review:
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. |
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AllReviews |
1 Total 1 pages 10 items |
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Scientific American (MSL quote), USA
<2007-01-30 00:00>
Riemann and his colleagues come to life as real characters and not just adjectives for conjectures and theorems.
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Science (MSL quote), USA
<2007-01-30 00:00>
...a remarkably accessible and deeply researched description of this fascinating problem. ... eminently successful at bringing this story to life. |
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Keith Carr (MSL quote), USA
<2007-01-30 00:00>
John Derbyshire does a wonderful job making the math behind Riemann's Hypothesis available to the layman. Most of us have some familiarity with high school-level alegebra, and Derbyshire capitalizes on this familarity, boiling down complex topics (e.g. number theory, complex numbers, calculus) into their elementary functions. While a background (or a least an acquaintance) with calculus is of some help, it is by no means required to understand Derbyshire's work and walk away with at least an understanding of Riemann's Hypothesis.
While the math section of the book (odd-numbered chapters) is well-planned and masterfully executed, the book's hidden gems are the even-numbered chapters-Derbyshire really demonstrates an understanding of historical nuance; his injection of wit, coupled with a cogent historical analysis is refreshing.
Prime Obsession is much better than Karl Sabbagh's work "The Riemann Hypothesis," in my opinion. In Derbyshire's work, the math is much better explained and the historical commentary is more developed and clear. That said, Keith Devlin's book, "The Millennium Problems" also offers a very clear insight into the Hypothesis. I would say that Devlin's work is even more clear than Derbyshire's, but the Riemann Hypothesis takes up only a short chapter of his book (which is devoted to the 7 gretest unsolved problems in mathematics, of which Riemann's Hypothesis is only one).
I give Prime Obsession 4 well-earned stars. Highly recommended.
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Stewart W. Smith (MSL quote), USA
<2007-01-30 00:00>
What an extraordinary book. It's beautifully written, with wit and style, and is a joy to read. Derbyshire provides some wonderful new insight into both mathematics and mathematicians. The mathematically inclined will enjoy the personal stories and historical context he attaches to the famous figures with whom they are only mathematically acquainted.
The proofs and clear and elegantly presented, and lead one down a path toward understanding the beauty and importance of the Riemann Hypothesis.
The highlight of the book for me was the connection he was ultimately able to make with modern physics. If you've ever wondered what pure number theory is really good for, this is the book to read!
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A. Badus (MSL quote), USA
<2007-01-30 00:00>
As a math graduate student, I find a lot of "popular" math books rather boring, incorrect or both. "Prime Obsession", however, is not in any of those categories.
The mix of history chapters and math chapters makes it easy for the mathematically inclined to skip some of the easy explanations, and for the math phobic to skip them completely. They are, however, well written and quite enjoyable to read; it can be difficult to grasp the entirety of the Riemann Hypothesis by reading scientific papers, and Derbyshire does a superb job explaining the hypothesis and its importance in mathematics.
The historical and biographical chapters are detailed and very enjoyable to read. The author touches on the greatest figures of modern mathematics, and his respect for all of them, even the most eccentric, is admirable.
This is one of the best non-technical math books I've ever read, and a must (I believe) for anyone contemplating a career in mathematics. It might be best read in high school or early college, but if you missed it then - it's never too late. I believe it can be enjoyed even after you've seen a lot of stuff.
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Bryan Jacobs (MSL quote), USA
<2007-01-30 00:00>
I was first skeptical that this book was going to be too elementary, with too much history and not enough math. This is not the case as Derbyshire has put together an excellent book covering such topics as Hermitian matrices, the logarithmic integral, and the p-adic numbers among others. It is odd though, since at times Derbyshire will stop to remind the reader of something as simple as "-3 times -3 is 9, not -9." Luckily he will only pause for a sentence and then continue straight on to the more interesting math.
This book builds up to explaining what Riemann showed in his landmark paper where he proposed the hypothesis. This involves deriving the prime counting function in terms of the zeta function zeros. At that point the reader will understand the relevance of the zeros, but not necessarily the importance of the hypothesis which states where to find those zeros. While the hypothesis does put a stronger bound on the prime couting function as Derbyshire explains, the main reason to solve it is because it's there. This may be disappointing for some, but the jounrey is well worth it.
I recommend this book for readers who want to learn about the zeta function and have a basic knowledge of number theory and calculus. The combination of math and history was better than I expected, and the book is enlightening in both areas.
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Thomas Paul (MSL quote), USA
<2007-01-30 00:00>
In 1859, Bernhard Riemann, one of the greatest mathematicians of his day, wrote a paper about the distribution of prime numbers. In that paper as an incidental remark he wrote, "All non-trivial zeros of the zeta function have real part one-half." Riemann had no proof that this was true but he suspected that it was true based on his intuition and his understanding of prime numbers. For nearly 150 years, mathematicians have been trying to either prove or disprove Riemann's hypothesis.
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. In a book on a topic like this, you expect the author to not be afraid to discuss complicated mathematics. 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.
At the time of writing this review, a possible solution proving the Riemann hypothesis to be true has been produced by Louis de Branges of Purdue University. That makes "Prime Obsession" both fascinating and timely.
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A reader (MSL quote), USA
<2007-01-30 00:00>
From those reviewers who didn't rate this well (there were only a few), two reasons are clear: not enough math, or too much math. This is not a math book, it is a book about a math problem and the people who've tried to solve it. If you want the deep mathematics, pick up a college-level text on the subject. For those who thought there was too much math (or that the math was too difficult), give up your dream as a recreational mathematician because if you couldn't grasp what Derbyshire included in the math chapters you won't ever understand higher mathematics. That's just the way it is, mathematics is not for everyone.
I think the book was written well, and the history of the key players made the story much more interesting. I admit, I too wanted more of the deeper mathematics, but Derbyshire set out to make the story interesting to the lay-person and I think he did a fine job. As a non-mathematician with a passion for math, I think he covered the subject well as an introduction to the RH. Sure there were lots of holes that could have been covered, but that would have led to a voluminous work on the level of graduate study. If Derbyshire's book inspires one young person who isn't sure of the path to take in the future, then I think it is worthy of some of the finest publications. Isn't that what its all about, anyway?
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A reader (MSL quote), USA
<2007-01-30 00:00>
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.
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Nobi (MSL quote), USA
<2007-01-30 00:00>
The Riemann Hypothesis, as explained in this book, spans a century of research - some targeted at tackling the Hypothesis itself, and some that arose suddenly from a seemingly unconnected research. The twists and turns that have become a part of the search for a proof of the Riemann Hypothesis is well-recorded and narrated by John Derbyshire. The small biographical passages on the various mathematicians are interesting, and even serve to explain how the personalities and interests of the mathematicians can influence the way their contributions to the Riemann Hypothesis.
That said, this book was still a pain to read. It seemed as though it never found its target audience (which Derbyshire claims is the layman, as he guarantees that a minimal level of calculus is required). For example, he brings up highly abstract ideas such as field theory and abstract algebra, then tries to explain how complex functions work by developing confusing analogies such as an ant walking on a plane. It may have worked in Brian Greene's "The Elegant Universe," but it doesn't work here.
His prose is also lacking and sometimes arrogant, as he claims that readers will never understand the Riemann Hypothesis if they don't understand it after reading his book. I couldn't go a page or two without seeing something along the lines of, "...which we will come back to after sixteen chapters." By the tenth time, it's quite obvious that Derbyshire prefers teasing the reader endlessly (which disrupts the entire narrative) than let the reader figure it out for him/herself that not every concept will be utilized immediately. His overuse of cliches like, "You'll have to trust me on this," and his constant claim that some topic is too advanced for the book is particularly annoying. The reader is supposed to be reading from the point of view of a layman - why does he/she need to be reminded constantly that the Riemann Hypothesis is being oversimplified?
It's evident by the reviews here that by simplifying the Riemann Hypothesis to a jumbled combination of basic calculus and abstract ideas like operator theory, the layman gained an appreciation for mathematical research. Some of the reviewers comment that negative reviews show that the reviewer wanted less math or more math. But I believe the simplification actually hurts the true appreciation of the beauty of the Hypothesis. After reading the book, does the reader gain a solid understanding of why the Hypothesis is so significant, besides "It's a basis for other proofs and it's a difficult problem?" I think that the significance is gained more through Derbyshire's historical narrative than from his mathematical exposition.
Expositions on the Riemann Hypothesis have been popping up quite frequently; I would try the others for mathematical details while using Derbyshire's text for historical context.
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1 Total 1 pages 10 items |
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