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on 19 May 2003
Prime Obsession, is a wonderful book based on the history and insight of the brilliant mathematician, Bernhard Riemann. As the title suggests, the main aim of the book is to give the reader a clear and understandable definition of what the Riemann Hypothesis actually is. To do this, Derbyshire has structured the book so the reader is given a chapter of mathematical tools, followed by a chapter of the history of Riemann and other great mathematicians, such as Gauss, Euler, Hardy, followed by a math chapter etc... However, don't let the math sections put you off this book, as Derbyshire explains, he uses minimal calculus to get the reader through the book. He takes the reader though basic analysis, then onto prime numbers, domain streching, followed by what he calls the Golden Key which uses the Euler product. Then he introduces basic complex number theory, and finally he pulls them all together to start to explain the RH (Riemann Hypothesis). Riemanns ideas and visualizations of complex functions are difficult to comprehend for even the most accomplished mathematician, but Derbyshire employs a method that any lay person can understand perfectly, using his "Argument Ant". Any person interested in mathematics, should read this book, as it serves as a wonderful insight into one of the greatest mathematicians, and problems that has ever existed. And for those who are just interested in the RH but were never quite sure where the zeros come from, then the chapter on domain streching and subsequent chapters will make it all clear. This is the best popular science book I have read since Feynmans "QED: The strange theory of light and matter".
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on 13 April 2007
I have read this book and two of the other three popularisations about the Riemann hypothesis. Instead of interviewing mathematicians who may be near to solving it or writing around the subject, this book actually works through the mathematics of Riemann's 1859 paper.

"Prime obsession" emphasises the centrality of the other parts of Riemann's paper apart from the famous Hypothesis. By doing this it helps to explain why some 30 years later that mathematicians were able to prove the Prime Number Theorem, independently of the truth or otherwise of the famous Hypothesis. The Prime Number Theorem states, roughly that: as numbers get larger the number of primes less than that number tends to about the number divided by its logarithm (base e). The reason the Prime Number Theorem could be proved, irrespective of Riemann's Hypothesis' truth, is because of the techniques that Riemann invented in his 1859 paper.

Riemann's starting point was to generalise Euler's formula which relates the sum of the reciprocals of natural numbers:


to the product of the inverses of the prime numbers


Derbyshire's explanation is far clearer and much easier to follow than those in the other popularisations.

This book is precise and clear: one really feels that one has some insight into an astonishing piece of creative mathematical work by the time one has read the book. That alone in my opinion should qualify it as one of the greatest pieces of popular science writing of this or any other decade.

This book needs to be more actively marketed: whatever its faults, the author has made a genuine attempt to really explain a great piece of science technically to a non -technical audience, rather than just waffling around the subject and making us all feel these things are so far above our heads we will never understand them in any way. This courage on the author's part needs to be more widely feted.

I cannot do more than endorse the other reviewers' praise for this classic-to-be. for those interested in pursuing this fascinating subject further, I found Gamma: Exploring Euler's Constant (Princeton Science Library) by Havil to be a wonderful book.
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on 18 December 2008
I am a bit of a junkie for books on maths, revisiting my degree of 15-20 years ago. The quality varies a lot though and I am very often disappointed. This I supose is not surprising: I want not to be patronised but I also want accessibility, context (historical, personal), and some insight into the underlying beauty of the mathematics in question. But this book pushes all the right buttons.

The Riemann Hypothesis is really quite advanced - you wouldn't find much in-depth study of it in any compulsory modules of undergraduate courses. But Derbyshire brings it to life. The book is challenging but accessible, and ultimately a very fulfilling read.

I think the key to his success is the interleaving of chapters on the lives of the protagonists with those on the maths leading up to and surrounding the Hypothesis. Because an understanding of the relevant mathematics helps understand the importance of a given mathematician's life, and an understanding of historical context helps bring the maths to life, these chapters are mutually reinforcing. As such the whole is greater than the sum of the parts (I think I might just have found that 1+1>2). And because so many of the great mathematicians contributed to the foundations of number theory and analysis, and many subsequently worked on the Riemann Hypothesis itself, this book kind of doubles as a selective history of modern (from Newton) mathematics.

I can't recommend this book enough. Even for those with no background in maths, but with an enquiring spirit, there is enough here (crucially, without turgidity) to dimly comprehend the profound beauty and true mystery of maths. It makes you believe somehow in the Platonic Ideals and that those blessed with true insight get closer to them than the rest of us. I have always felt that advanced pure mathematics is as worthy an art as painting or sculpture, and the great mathematicians as worthy artists as Van Gogh etc. But because of the inaccessibility of the subject matter to the layman this great art couldn't be widely-enough shared. With more books like Prime Obsession this wrong will be righted.
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on 19 January 2005
Having read Marcus de Sautoy's book on prime numbers my appetite was sufficiently wetted to go out and by Edwards book on the Zeta function. Unfirtunately one look at this told me I wasn't going to be able to get through it. I picked this book up by accident and it was fascinating in that the author goes through the whole of Riemanns 1859 paper and explains the whole theorem, which is quite breathtaking in its brilliance. He loses it a bit at the end, but he can be forgiven for that as it does become very complicated. That combined with the way he weaves the history of prime numbers in alternative chapters makes this a thoroughly enjoyable book. If you like maths go and buy it!
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on 4 December 2004
This book by John Derbyshire is absolutely fantastic. Giving a thorough insight into the history of Riemann, and mathematics for that matter, provides the reader with a fuller knowledge before the author tries to smash through the hypothesis bit by bit. Breaking down the ideas mathematicians have developed over the past 140 years in trying to solve this greatest 'unsolved' problem in mathematics, Derbyshire gives the reader the feeling that Riemann truly was a fantastic mathematician and his innovative ideas are truly unique. The proof in which is that this hypothesis is still today unsolved. If you want a book about this complex hypothesis, I reccomend this. Easily illustrated and not too difficult to understand, Derbyshire makes this hypothesis seem so trivial in complexity and worthiness to the lay mathematician, yet to those with a keener knowledge this book relays the hidden answers beautifully.
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TOP 1000 REVIEWERon 31 March 2013
" it was with Riemann. Outwardly he was pitiable; inwardly, he burned brighter than the sun."

So says the author of this work on Bernhard Riemann and his famous hypothesis.

This is an excellent book on the subject. But the lay reader will find it difficult. Knowledge of Maths is required to navigate it.

Riemann was an incredible genius. Another area of Maths that his name has been lent to is Riemannian Geometry. Einstein later availed of Riemann's creation to build the mathematical formalism of General Relativity. On the shoulders of giants.

The Riemann Hypothesis is currently unsolved. We don't know if the hypothesis is true or false. (It has nothing to do with Riemannian geometry.)

Why is the Riemann Hypothesis so important? One reason is there is a connection between it and the distribution of the prime numbers. Is there a pattern hidden in the primes? Nobody knows.

Tantalising hints of some hidden order remain. See Chapter 18 - "Number Theory Meets Quantum Mechanics." (Hugh Montgomery meets Freeman Dyson ).

Then there is the strange story recounted in Chapter 22, the last chapter of the book. Two mathematicians go to Gottingen to see Riemann's notes from 1859. One wants to look at some pure number theory stuff. The other, the applied mathematician with no interest in all that, wants to look at some work Riemann had done on perturbation theory. Both put in their separate requests to the librarian.

She comes back with just one set of notes. It turned out that Riemann had been working on both of these problems at the SAME TIME.
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on 22 January 2012
If you are interested in maths (and number theory in particular) this is one of the better "popular" books. Whereas other books in the genre often dumb things down a tad too much and leave you wanting for more (what does that formula look like? what does a graph of that function look like? how was that theorem proved? etc.) this book is not afraid to show formulas and graphs and at least the gist of complex issues. It also breathes life into the people who did the work (as well as their historical, political and mathematical context) and whom we otherwise mostly know because they have a theorem named after them.

Minor gripes: does the Lindelöf hypothesis really not deserve more than a footnote to an appendix? Why weren't the often informative footnotes put at the bottom of the page they refer to?
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VINE VOICEon 12 June 2016
* Physical

The book i have has 422 pages of text, is printed on a fair size of font for those who require specs, and the paper is of reasonable quality too.

* Target audience, A level / H.N.D, Undergraduate,Graduate, Post Graduate?

This book is accessible when considering its quality of writing, but (i.m.h.o) this is better introductory read by second year mathematics students and above.

* What's the best topics then?

With some books it is a historical journey with what they have done added. This book gives a fair explanation of the maths and his life.The more accessible bits of the Riemann contribution to mathematical knowledge is very well explained. The critical theory of arithmetic that all numbers greater than one are a compound of prime numbers is very well explored too. Zeta function, the one of the many function forms, the prime number generating function and its simpler proofs is as well explained as i have seen in other small number of samples. The way the calculation of the number of primes up to any integer is engaging to read. The many forms of the Zeta function, sums and products equivalence, 'golden key' the supporting fundamental math in this topic is really nicely completed. The writer knows his limits as this is a popular science, math book. And this needs to be limited to not overwhelm the general reader. But the math student in particular will find this book supportive of their topics and when, importantly, you access videos from a very well known video sharing website, (you know the one) you may find this knowledge comprehension greatly accelerated. By using both this book and the videos at whichever level of academic difficulty you're at the moment, you may have a clearer time on this introductory level of the important math topic. Its encouraging me to have another look at further books too.

* Summary

With reading this book, ands watching and rewatching the videos on the very well known website that cover these same areas, you may find this a real interest and enjoyable way to gather knowledge in this area. This limited math level dexterity is fair, comprehensible, and really clearly written. You need the online videos, (and a reasonable bb connection), and (this) book together then you're more likely to make progress. (i.m.h.o)
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on 13 September 2004
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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on 12 March 2004
This is by far the best introductory book on the Riemann Hypothesis, so look no further. I was impressed by how the author has managed to convey both the historic background of the hypothesis, as well as a very well constructed mathematical explanation of the meaning and implications of the result. The mathematics is pitched a very reasonable level. The history and mathematics are divided cleverly into two different strands in the book, leaving the reader with the choice of how they cover the material. A stroke of genius !.
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