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

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Summary: elegant formular...
Review: The Euler formular relating the integers and the prime numbers is so beautifully derived. How could some people be so genius? Then Reimann used his intuition to postulate and extend it to cover the complex variables. Since the pre-Euclidean era until the present time, the distribution of prime numbers always fascinates the researchers. The application of prime numbers is still very important in secured commmunication. The proof of Reimann Hypothesis (or dis-proof it) will reveal the secret of prime number distribution. So important is this hypothesis that 1 million-dollar reward has been offered for it.
Author's (first and) interesting analogy of the calculation of the over-hang of the playing cards and the harmonic series (which is divergent) trigged me to buy the book. I could not understand (only 5% so far) all his explanations, but the stories and discoveries associated with the RH are so beautiful. To understand the book requires lots of thinkings, however to enjoy the stories only requires a cup of warm tea, a sofa and a pillow (a blanket if you're in a cold weather.)
If you read this far, you must have loved math as much as I do... ;-)

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Summary: So much stuff, packed in so small a book: I loved it!
Review: There is lots of stuff in that book. It took me a long time to read it. It was relaxing, which is not to say that it did not require energy and concentration.


Obviously, John Derbyshire talks about maths. The required level of math includes notions about real and complex number functions, infinite series, a little calculus, etc. Having a degree in engineering, it did not make me break a sweat. Still, it was enough to embrak me on a wonderfull trip about the inner beauty of math.

John Derbyshire will tell you about Bernard Riemann, his life, his character, the world he lived in , about history , about the life of many famous mathematicians. Derbyshire's style is easy and convivial, contains amusing and interesting anecdotes and reflexions. I felt like I was chatting with a friend in my living room.

It was also fascinating to see how the historical figures are interconnected, and their life intertwined , to an unexpected level.
Ultimately, I was fascinated to see how intuitive an insight one can get about such an abstruse concept as number theory and prime numbers.

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Summary: Fascinating book
Review: Prime Obsession is a great book.

John Derbyshire does a great job of taking a most obscure mathematical topic and makes it not only interesting, but also readable.

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Summary: Enjoyable even for the specialist
Review: 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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Summary: The Work of an Accomplished and Clever Teacher
Review: Not only is the author a gifted prose stylist, this book actually had me engrossed in higher mathematics. Face it, though number theory can be beguiling--my introduction was the fine biography of Erdos by Paul Hoffman--many of the recent popular works on mathematics are difficult and too often leave the reader disappointed. To this reviewer, Prime Obsession is every bit as fun to read as the latest pulp fiction but after the story is over, this work leaves the reader with a gift of understanding.

What made Prime Obsession so fun to read was the excellent balance between exposition of the story and exposition of the underlying ideas. This book was not afraid to go deeper into the mathematics than similar works, such as The Music of the Primes by du Sautoy. Derbyshire alternated between chapters of narrative with chapters purely about the underlying mathematics. Not only did the author produce a compelling story but the science was surpassingly well taught--the understanding of the zeta function engendered in the reader adds punch to the story. It is always nice to have at least a little knowledge of what is going on.

Although the typical non-mathematician who chooses to read this book will already appreciate the intellectual achievements of Berhard Riemann, it is the gift of Derbyshire's work that with a reasonable investment of thought any reader can begin to glimpse the beauty and elegance of higher mathematics.

This book was so good that as soon as I finished I ran out and bought "Seeing Calvin Coolidge in a Dream"; frankly, that says it all. This is a must read.

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Summary: A very readable book
Review: For some reason, the subject of this book has been very popular recently; I've seen at least 4 books on the Riemann Hypothesis and the distribution of prime numbers in the past year or 2, this among them. I think this book is one of the best of the set.

The author attempts to write the book at a level accessible to someone with a very small background in mathematics, even nearly omitting the use of calculus (though he finds that he cannot totally omit calculus). I can't easily put myself in the place of his intended reader, since my mathematical background is rather better than that, but I still think this book is better at putting a highly abstruse mathematical topic within reach of the general public than most authors can manage.

The book melds history with mathematics, I think quite successfully, giving the reader a chance to learn about some of the people involved as well as learning what interests mathematicians so much about the Riemann hypothesis.

If you are not math-phobic, you might like this book. try it!

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Summary: A "Must Read"
Review: This is a fascinating book that blends mathematical ideas and concepts with a compelling narration of the history related to these ideas. This is one of the few books on mathematics that is so interesting that it's difficult to put down.

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Summary: Zeta Function Fun
Review: 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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Summary: Decent history, but the author never gets to the point.
Review: If you were to write a book about a 400 page book on the Riemann Hypothesis, about what page would you describe why that particular problem is important? Page 5, 10? Well, Derbeyshire weaves in and out of tangents and refuses to get to the point until after 320 pages. While it is obvious he knows what he's talking about, the author does not move to a single point.

He alternates between the history and the mathematics of the Riemann hypothesis chapter by chapter. The history is fun and interesting, but it was hard to see what he was talking about because he never seemed to explain the title of the book, "Prime obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics". Why is the greatest unsolved problem in mathematics? Why is it called Prime obsession when on the surface it looks the formula has nothing to do with prime numbers? He only tells you near the end, giving no context to most of the book.

He utterly fails at the mathematics part. For example, he'll start to get somewhere, but will end up with phrase, "let's first look at...". And he'll explain in annoying detail the most basic, ninth grade mathematics instead of finishing his initial thought. For example, he is about to explain the Zeta function and it seems like he is about to tell you about it, but then suddenly bores you with power rules. You know, the stuff you learned eighth grade. a to X times a to the Y equals a to the (X + Y). He'll bore you with this stuff. This would be fine, if he prefaced every chapter with "if you know this, then skip to...", but he doesn't, so you're stuck sifting through the most basic information to get what you need. Truly annoying.

If you do decide to read this (I hope you don't), and have actually completed high school and some college mathematics, then you should skip all odd chapters, with the following exceptions (pages 43-47, 75-81, 100-105, 216-218, 233-237, 302-310, 327-349). There you go, I saved you immense time and effort. Does this mean that nearly half the book is useless? Yes, useless and tedious.