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Karl Sabbagh

Dr. Riemann's Zeros

The Riemann Hypothesis seems so far removed from everyday life that those who aren't specialists in number theory might have difficulty in understanding why a million dollars is being offered for its proof. In Dr. Riemann's Zeros Karl Sabbagh gives a well presented account of this area of mathematics in a way that can be followed by non-mathematicians. Sabbagh packs plenty of information into this short book - the meaning of the mathematics, the origins and history of the hypothesis, some of the current work on it, and how similar sorts of mathematics, such as Fermat's last theorem, were finally proved.

In particular the book has quite a bit on the work of Louis de Branges who proved the Bieberbach, and claims to have a proof of the Riemann Hypothesis - but other mathematicians aren't so sure. Sabbagh explains the problems which arise in the checking of such a proof.

The book has a bit of mathematics, but is aimed at those with very little mathematical experience - I think that those with a good grasp of school mathematics who want to get a glimpse into the work done on the hypothesis might do better with a different book. But if you want an easy to read overview of the different ways mathematicians have approached such problems then you should take a look at this book.

Note: in the USA this book is entitled The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics

Amazon.com info

Paperback 342 pages
ISBN: 0374529353
Salesrank: 532171
Weight:0.69 lbs

Published: 2004 Farrar, Straus and Giroux

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Amazon.co.uk info

Paperback 304 pages
ISBN: 1843541017
Salesrank: 23865
Weight:0.66 lbs

Published: 2003 Atlantic Books

Amazon price £6.74

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Amazon.ca info

Paperback 304 pages
ISBN: 1843541017
Salesrank: 1750443
Weight:0.66 lbs

Published: 2003 Atlantic Books

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Product Description
Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematical minds for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann hypothesis. They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995. In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities. Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.

Product Description

Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematical minds for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann hypothesis. They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995.

In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities.

Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.

Others deserve learning about complexity too *****
Karl Sabbagh has done his job well. He never pretended to be a master at this topic. He pretended to give the layman as myself access to the intricate and complex mind of a genius. This is what divulgation is about. I do not understand those hard ratings or much less comments like "which I could probably do here ultra-briefly if I had a charge number for a couple of hours". It is as if I buy a children's book on physics and complain about the depth of its concepts. Some wise pedagogue would say I was completely confused on what divulgation is about. If you think you can enlighten our small minds on this matter dedicating a couple hours, I suggest you send a manuscript to the press. I shall be happy to buy it and rate it afterwards. In scientific literature there ought to be room for books that can be understood by more than one hundred people. Sometimes complexity is an added feature that does not add value... The fact that I am not an expert at math does not make me a conceptual handicapped. I think this book is a good entrance to the topic. In my case it has triggered the purchase of other deeper approaches. Well done Karl!!!

Others deserve learning about complexity too *****

Karl Sabbagh has done his job well. He never pretended to be a master at this topic. He pretended to give the layman as myself access to the intricate and complex mind of a genius. This is what divulgation is about.

I do not understand those hard ratings or much less comments like "which I could probably do here ultra-briefly if I had a charge number for a couple of hours". It is as if I buy a children's book on physics and complain about the depth of its concepts. Some wise pedagogue would say I was completely confused on what divulgation is about.

If you think you can enlighten our small minds on this matter dedicating a couple hours, I suggest you send a manuscript to the press. I shall be happy to buy it and rate it afterwards.

In scientific literature there ought to be room for books that can be understood by more than one hundred people. Sometimes complexity is an added feature that does not add value...

The fact that I am not an expert at math does not make me a conceptual handicapped. I think this book is a good entrance to the topic. In my case it has triggered the purchase of other deeper approaches.

Well done Karl!!!

Eh ***
There are a few mistakes: 1) p. 133 In the smallest n-digit primes sequence, there are incorrect 8th and 11th members. 2) p. 190 The values of the Mobius function are listed from one to ten, the 7th is incorrect (should be -1) 3) p. 206 The inline formula for the gamma function is incorrect. It reads "Gamma(n) = n * Gamma(n-1)" but should read "Gamma(n) = (n-1) * Gamma(n-1)". There is also a fuzzy explanation which contradicts another explanation of T. H. White's "everything not forbidden is compulsory" (p. 185). Sabbagh claims that Gell-Mann says this is how the laws of physics work--that if something is predicted to exist by a theory, then it exists somewhere. Kip Thorne clearly explains in 'Black Holes & Time Warps' that this is not how the laws of physics work. From the book, "Many of the things permitted by the laws of physics are so highly improbable that in practice they will never happen." (p 137) It may be that I misunderstood Sabbagh's writing or that Sabbagh misunderstood Gell-Mann. Nevertheless there is something going on here that doesn't match up. Other than that, the book was pretty good. It didn't quite give me the dose of mathematics I was looking for, but then again I always ask for more than I can handle. It was very readable.

Eh ***

There are a few mistakes:
1) p. 133 In the smallest n-digit primes sequence, there are incorrect 8th and 11th members.
2) p. 190 The values of the Mobius function are listed from one to ten, the 7th is incorrect (should be -1)
3) p. 206 The inline formula for the gamma function is incorrect. It reads "Gamma(n) = n * Gamma(n-1)" but should read "Gamma(n) = (n-1) * Gamma(n-1)".

There is also a fuzzy explanation which contradicts another explanation of T. H. White's "everything not forbidden is compulsory" (p. 185). Sabbagh claims that Gell-Mann says this is how the laws of physics work--that if something is predicted to exist by a theory, then it exists somewhere. Kip Thorne clearly explains in 'Black Holes & Time Warps' that this is not how the laws of physics work. From the book, "Many of the things permitted by the laws of physics are so highly improbable that in practice they will never happen." (p 137) It may be that I misunderstood Sabbagh's writing or that Sabbagh misunderstood Gell-Mann. Nevertheless there is something going on here that doesn't match up.

Other than that, the book was pretty good. It didn't quite give me the dose of mathematics I was looking for, but then again I always ask for more than I can handle. It was very readable.

Where's the Beef? **
Nice to have a book to read on the mathematical history and personalities hooked on the search. Way too soft on what the search is for and actual progress in any direction. Has an appendix with some current effort at a proof but without any surrounding discussion it's hardly worth the effort.

Where's the Beef? **

Nice to have a book to read on the mathematical history and personalities hooked on the search. Way too soft on what the search is for and actual progress in any direction. Has an appendix with some current effort at a proof but without any surrounding discussion it's hardly worth the effort.

The Riemann Hypothesis for non-mathematicians ***
The book is really about the search for solutions to the Riemann Hypothesis, and contains lots of stories about mathematicians, and mathematical topics. It also includes a wide variety of tangential topics, such as the resolution of previously unsolved problems: the Bierbach Conjecture and Fremat's Last Theorem. While intended as an accessible account of the Riemann Zeta Function and the Riemann Hypothesis for the non-mathematician, it uses overly trite and simplistic descriptions of basic mathematical concepts such as prime numbers, complex numbers, and zeros of functions, while glossing over more advanced concepts, such as L-functions, Hilbert Spaces, and Random Matrices. Clearly, this was written by a mathematical novice.

The Riemann Hypothesis for non-mathematicians ***

The book is really about the search for solutions to the Riemann Hypothesis, and contains lots of stories about mathematicians, and mathematical topics. It also includes a wide variety of tangential topics, such as the resolution of previously unsolved problems: the Bierbach Conjecture and Fremat's Last Theorem.

While intended as an accessible account of the Riemann Zeta Function and the Riemann Hypothesis for the non-mathematician, it uses overly trite and simplistic descriptions of basic mathematical concepts such as prime numbers, complex numbers, and zeros of functions, while glossing over more advanced concepts, such as L-functions, Hilbert Spaces, and Random Matrices. Clearly, this was written by a mathematical novice.

YOU can understand the Riemann Hypothesis....after this commercial break. ***
I'm halfway through this book and am getting very frusturated. The beginning chapters did a very good job laying out the foundations of the RH. You begin to think you may, finally, be able to understand what the RH is about. However, I am realizing that less and less of the book is actually about the RH or the RZF the farther I progress. An entire chapter will waste space describing a mathematician (physical appearance, quirky behavorial traits), his unrelated contributions to math, and either a vague description of the work he is doing to prove the RH or some opinion on whether it will be solved or not. The book has devolved into irritating tangents unrelated to my understanding of the RH/RZF...clever math poems, crap about Fermats theorem, etc. I would even be forgiving if he was describing the life and times of Riemann himself. There are plenty of cute little math stories here, but I didnt waste $14.00 on a book about the RH to NOT read about the RH. I want every single chapter to build on the previous, start slow, explain the concepts, and raise the bar. If you get stuck, too bad...research the web and pick the book up later. Thats what I wanted here, and this book is turning out to be a letdown. There is very good information for someone completely new to the concept of the RH or RZF, but this book is 4 chapters of useful material spread out into an entire book filled with math-related lore. I appreciate what Sabbagh is trying to do here, but lets be realistic. This is a very advanced mathematical concept; you can't hand-hold someone through this from start to finish. At some point he should challenge the reader and escalate the difficulty of the book, but this does not appear to happen. Instead we get a smoke-screen...a cliffhanger. Would I recommend this book? Only to those who have absolutely no understanding of what the RH/RZF is and want a springboard to something else.

YOU can understand the Riemann Hypothesis....after this commercial break. ***

I'm halfway through this book and am getting very frusturated. The beginning chapters did a very good job laying out the foundations of the RH. You begin to think you may, finally, be able to understand what the RH is about. However, I am realizing that less and less of the book is actually about the RH or the RZF the farther I progress. An entire chapter will waste space describing a mathematician (physical appearance, quirky behavorial traits), his unrelated contributions to math, and either a vague description of the work he is doing to prove the RH or some opinion on whether it will be solved or not. The book has devolved into irritating tangents unrelated to my understanding of the RH/RZF...clever math poems, crap about Fermats theorem, etc. I would even be forgiving if he was describing the life and times of Riemann himself. There are plenty of cute little math stories here, but I didnt waste $14.00 on a book about the RH to NOT read about the RH. I want every single chapter to build on the previous, start slow, explain the concepts, and raise the bar. If you get stuck, too bad...research the web and pick the book up later. Thats what I wanted here, and this book is turning out to be a letdown.
There is very good information for someone completely new to the concept of the RH or RZF, but this book is 4 chapters of useful material spread out into an entire book filled with math-related lore. I appreciate what Sabbagh is trying to do here, but lets be realistic. This is a very advanced mathematical concept; you can't hand-hold someone through this from start to finish. At some point he should challenge the reader and escalate the difficulty of the book, but this does not appear to happen. Instead we get a smoke-screen...a cliffhanger. Would I recommend this book? Only to those who have absolutely no understanding of what the RH/RZF is and want a springboard to something else.

Fun to read, but disappointing ***
Popular science writing is not easy even when the subject matter is as accessible as cuddly beasties or space travel, and popular writing about mathematics is very much harder. So hard that you wonder if it should be attempted by anyone but the exceptionally gifted. Karl Sabbagh is a very fine writer indeed, but I don't think he's the man to write a popular account of the Riemann Hypothesis and recent attempts to prove it. For a start, he seems to have a shaky grasp of who he is writing for. Anybody who picks up this book in the first place is likely to be a bit of a geek, and such a person will not be satisfed with the way Sabbagh frequently refuses to explain things on the grounds that he thinks that the reader will not be interested, or won't be able to follow them; so for example, when he talks about an attempt to prove "something called the parallel postulate", he neglects to explain what the parallel postulate is. It's not even a very difficult subject to explain, but people who read popular books about maths do so partly in order to pick up a bit of math, and Sabbagh's careful focus on the personalities of the people he's talking about and his lack of interest in handing over chunks of carefully digested and clearly explained theory means that this book is extremely light in weight. So in the end, as with so many books of popular science, the interested reader is forced to throw the book away and go straight back to the bookshop in search of stuff in the Further Reading list. I am now very interested in the Riemann Hypothesis, not so much in the stories Sabbagh had to tell about it.

Fun to read, but disappointing ***

Popular science writing is not easy even when the subject matter is as accessible as cuddly beasties or space travel, and popular writing about mathematics is very much harder. So hard that you wonder if it should be attempted by anyone but the exceptionally gifted. Karl Sabbagh is a very fine writer indeed, but I don't think he's the man to write a popular account of the Riemann Hypothesis and recent attempts to prove it.

For a start, he seems to have a shaky grasp of who he is writing for. Anybody who picks up this book in the first place is likely to be a bit of a geek, and such a person will not be satisfed with the way Sabbagh frequently refuses to explain things on the grounds that he thinks that the reader will not be interested, or won't be able to follow them; so for example, when he talks about an attempt to prove "something called the parallel postulate", he neglects to explain what the parallel postulate is. It's not even a very difficult subject to explain, but people who read popular books about maths do so partly in order to pick up a bit of math, and Sabbagh's careful focus on the personalities of the people he's talking about and his lack of interest in handing over chunks of carefully digested and clearly explained theory means that this book is extremely light in weight.

So in the end, as with so many books of popular science, the interested reader is forced to throw the book away and go straight back to the bookshop in search of stuff in the Further Reading list. I am now very interested in the Riemann Hypothesis, not so much in the stories Sabbagh had to tell about it.

A neat balance ****
It appears that Sabbagh was not intending to write a comprehensive history of the Riemann conjecture, but merely to give a personal account of the state of play at the moment, with some welcome mathematical background. (Many authors seem to believe that including actual raw equations in their works will alienate their readers, to which one is tempted to say: Bah, humbug.) I found this an interesting balance between hard maths and soft chat, and as such is somewhat superior to some of the other works in the field. If you're after learning about where we're at with this problem, then this is an interesting, if not essential, addition to your reading list.

A neat balance ****

It appears that Sabbagh was not intending to write a comprehensive history of the Riemann conjecture, but merely to give a personal account of the state of play at the moment, with some welcome mathematical background. (Many authors seem to believe that including actual raw equations in their works will alienate their readers, to which one is tempted to say: Bah, humbug.)

I found this an interesting balance between hard maths and soft chat, and as such is somewhat superior to some of the other works in the field.

If you're after learning about where we're at with this problem, then this is an interesting, if not essential, addition to your reading list.

The Riemann Hypothesis ****
I really enjoyed this book. It skips between explanations of some of the mathematical concepts associated with the subject and the stories and experiences of the mathematicians who are working, and have worked, on the topic. It is evident that a lot of research and interviewing of top mathematicians has gone into the book. It's an interesting insight into the world of mathematicians and does well to get the gist of the Hypothesis across, without going into the mathematical detail that would make it incomprehensible to most of us. Though some explanations were very good, I'm not sure whether all the mathematical discussion would be followed by someone not familiar with maths, but I guess they're unlikely to read the book anyway. I'm am currently doing a maths degree, and thought it was a great read!

The Riemann Hypothesis ****

I really enjoyed this book. It skips between explanations of some of the mathematical concepts associated with the subject and the stories and experiences of the mathematicians who are working, and have worked, on the topic. It is evident that a lot of research and interviewing of top mathematicians has gone into the book. It's an interesting insight into the world of mathematicians and does well to get the gist of the Hypothesis across, without going into the mathematical detail that would make it incomprehensible to most of us. Though some explanations were very good, I'm not sure whether all the mathematical discussion would be followed by someone not familiar with maths, but I guess they're unlikely to read the book anyway. I'm am currently doing a maths degree, and thought it was a great read!

Riemann Hypothesis.... *
This book covers a fascinating subject matter, however ultimately I was disappointed in this book. I thought the initial introduction to the “Riemann Hypothesis” was well constructed. The book then seems to almost randomly jump from one mathematician to the next as the author interviews them or describes past mathematicians. The writings are definitely humorous but they lack any depth in making a connection to the Hypothesis and there is too much irrelevant material presented about the peculiarities of the mathematics in question, which although sometimes funny is for the most part tiresome and boring. Lastly there is absolutely no historic information about Riemann himself which I thougth very shallow given that at least 50 other mathematicians are mentioned in the book. Also the scientific implications of the hypothesis (which would have made fascinating reading) are barely touched on. There are some much better books on the subject available....

Riemann Hypothesis.... *

This book covers a fascinating subject matter, however ultimately I was disappointed in this book.
I thought the initial introduction to the “Riemann Hypothesis” was well constructed. The book then seems to almost randomly jump from one mathematician to the next as the author interviews them or describes past mathematicians. The writings are definitely humorous but they lack any depth in making a connection to the Hypothesis and there is too much irrelevant material presented about the peculiarities of the mathematics in question, which although sometimes funny is for the most part tiresome and boring. Lastly there is absolutely no historic information about Riemann himself which I thougth very shallow given that at least 50 other mathematicians are mentioned in the book. Also the scientific implications of the hypothesis (which would have made fascinating reading) are barely touched on. There are some much better books on the subject available....

Reimann Hypothesis **
A a fascinating subject matter, however ultimately I was disappointed by this book. I thought the initial introduction to the “Riemann Hypothesis” is well constructed. The book then seems to almost randomly jump from one mathematician to the next as the author interviews them. The writings are definitely humerous but they lack any depth in making a connection to the original hypothesis and there is too much irrelevant material presented about the peculiarities of the mathematics in question. For examples jokes, songs and witty quotations. Although sometimes funny, for the most part they are tiresome and boring. Lastly there is absolutely no historic information about Riemann himself (yes the book is about him I check the cover!). I thought it strange that the author described in great detail over 10 mathematicians but excluded Riemann. How did Reimann start off? why did he get interested in Prime Numbers? What did the hypothesis mean to him? The scientific implications of the hypothesis (which would have made fascinating reading) are barely touched upon, e.g the connection with Quantum Mechanics, the implications to encryption codes etc. There is a book covering the same material, called “Prime Obsession” by John Derbyshire which is far superior to this book, sorry....

Reimann Hypothesis **

A a fascinating subject matter, however ultimately I was disappointed by this book. I thought the initial introduction to the “Riemann Hypothesis” is well constructed. The book then seems to almost randomly jump from one mathematician to the next as the author interviews them. The writings are definitely humerous but they lack any depth in making a connection to the original hypothesis and there is too much irrelevant material presented about the peculiarities of the mathematics in question. For examples jokes, songs and witty quotations. Although sometimes funny, for the most part they are tiresome and boring. Lastly there is absolutely no historic information about Riemann himself (yes the book is about him I check the cover!). I thought it strange that the author described in great detail over 10 mathematicians but excluded Riemann. How did Reimann start off? why did he get interested in Prime Numbers? What did the hypothesis mean to him?

The scientific implications of the hypothesis (which would have made fascinating reading) are barely touched upon, e.g the connection with Quantum Mechanics, the implications to encryption codes etc.

There is a book covering the same material, called “Prime Obsession” by John Derbyshire which is far superior to this book, sorry....

BE ADVISED ****
This an excellent book for an introduction to the Riemann Hypothesis and the individuals working to solve it. BUT BE ADVISED: This is the same book as the authors recently released: The Riemann Hypothesis. If you already have a copy of The Riemann Hypthsis by Karl Sabbagh, don't buy this book!!!!

BE ADVISED ****

This an excellent book for an introduction to the Riemann Hypothesis and the individuals working to solve it.
BUT BE ADVISED: This is the same book as the authors recently released: The Riemann Hypothesis. If you already have a copy of The Riemann Hypthsis by Karl Sabbagh, don't buy this book!!!!