Customer Reviews

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

5 star:		(79)
4 star:		(15)
3 star:		(5)
2 star:		(4)
1 star:		(3)

 

 

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.

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.

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.
---------------------------------------------------------------

There seems to be a plethora of books about the Riemann Hypothesis (RH) lately. This book is very through for the non-mathematician. Every other chapter is mathematical in nature but is tractable with plenty of illustrations to guide the weary reader along the way. For the most part I couldn't see how Mr. Derbyshire could make it any easier.

The other chapters are historical in nature and describe not only Mr. Riemann's life but how RH has touched mathematicians, physicists and the rest of humanity until present day.

Mr. Derbyshire has written an absolutely excellent book on the Riemann hypothesis. The Riemann hypothesis, which relates to prime and complex numbers, has yet to be proved. It is the most famous unproved problem in mathematics. In fact, the first person to prove the Riemann hypothesis will be awarded a large sum of money from the Clay Mathematics Institute.

Mr. Derbyshire's book is perfect for folks like me with a mathematics background and also for those who lack formal training but are interested nonetheless. The mathematics are very well explained, and much of the book requires no understanding of mathematics at all. "Prime Obsession" is easily the most accessible book ever written on the Riemann hypothesis.

Pure mathematics is more of a mysterious art than a science, and this work serves to illuminate one very important mathematical mystery. This book is on my shelf, and it should be on yours too!

The Riemann hypothesis is one of the greatest unsolved problems in mathematics, with a $1,000,000 bounty for its solution. Although the Riemann hypothesis is intimately related with prime numbers, one of the most elementary notions in mathematics, the statement of the Riemann hypothesis is much more difficult to understand. This book attempts to explain the meaning, significance, and history of the Riemann hypothesis, while assuming minimal math background, as one might get from a good high school education. In the introduction the author provocatively writes, "if you don't understand the [Riemann] Hypothesis after finishing my book, you can be pretty sure you will never understand it". I think that what the author means here is that he gives the most elementary possible treatment of the subject. However I think that his treatment is a bit TOO elementary for one to REALLY understand what the Riemann hypothesis says. For example, although the Riemann hypothesis concerns the zeta function of complex numbers, I don't think he ever actually defines the zeta function of a general complex number. Nonetheless, given the level at which he chooses to write, I think he does about as well as one could hope to convey the rough idea of what is going on from various points of view.

I should say here that my perspective is that of a professional mathematician who does not know much about the Riemann hypothesis.

The format of the book is interesting. Roughly speaking, odd numbered chapters explain math, while even numbered chapters present history, although the history chapters have a bit of math in them and vice-versa. I found the history chapters quite enjoyable. The math chapters are a mixed bag. Some parts review basic math; I skipped over those. Other parts introduce the key players in the Riemann hypothesis. There is excellent use of pictures and numerical evidence to motivate various theorems and conjectures. Because every other chapter is devoted to history, and because so much math needs to be introduced, it takes a long time to get to the heart of the matter, which appears near the end of the book. There is also a major speedup near the end, with more and more mathematical details omitted.

If the proof or disproof of the Riemann hypothesis is a mountain summit, and if the statement of the Riemann hypothesis and its connection with prime numbers is base camp, then this book leads us on a walk through the foothills while discussing the history of various people who have explored this mountain, and then makes a mad dash for base camp which ends up requiring a helicopter rescue.

The book overreaches a bit in discussing speculative connections of the Riemann hypothesis with physics. In doing so the book spends some time discussing eigenvalues of random matrices, without giving any clue what an eigenvalue is, so I don't know how much the target audience is going to get out of this. I think it would have been better to just say, "here is the distribution of the first 500 zeroes of the zeta function, here are 500 random numbers, notice that the spacing looks different, a similar spacing appears in physics via eigenvalues of random matrices, no one knows if this is a coincidence or if there is an actual connection, here is a reference where you can read more about this."

It would have been nice to include Riemann's original paper on the subject as an appendix. While only experts can understand this, it is pretty inspiring. (A translation with a few notes can be found for example in "God created the integers".)

Despite my nitpicking above, I heartily approve of this book, because I think that mathematics needs more popularization, and this book has done an admirable job with difficult material.

Also, silly as this is to say, I have become much more of a Riemann fan after reading this book. I use Riemann integrals, Riemann surfaces, Cauchy-Riemann equations, Riemannian geometry, etc. on an everyday basis, but I never paid attention to the fact that they all have the same name in them. His accomplishments are brilliant and spectacular and completely transformed mathematics.

There are now three books on the Riemann Hypothesis readily
available for those interested on the history of this
famous problem. Prime Obsession is the book to choose if you
want to see the mathematics involved. John Derbyshire is
a mathematician with a talent for writing so that both the
history and the mathematics are covered well. By cleverly
alternating the chapters with math and history, Derbyshire
lets you decide how you want to read the book. I read Stewart,
Devlin, Gardner, Peterson, and any other writer who explains
mathematics to the public. Mr. Derbysire's book is as good as
it gets.

The tenor of this book reminded me somewhat of Ulam's Adventures of a Mathematician. Specifically what came to mind was a Ulam quote: "It is still an unending source of surprise for me to see how a few scribbles on a blackboard or on a sheet of paper could change the course of human affairs". Is the RH one of these "scribbles"? We probably won't know until quite some time after it is proven to be true or false.

One has to wonder what contributions to mathematics Bernhard Riemann would have made if he had lived longer and especially if his health had not been so poor during the span of time he was allotted. I vaguely remembered Riemann sums from math courses taken many years ago. Like so many names in technical books one never connects a real person to them except in a very abstract way. Derbyshire provides us with a real person who manages to make a great contribution to his profession despite his personal tragedies, ill health, and short life. As a bonus for those of us who are many years removed from formal mathematics courses, he provides a reasonably lucid explanation of Riemann's seminal work. We might be producing a few more scientists, engineers, and mathematicians in the USA if teachers here took a "page" from Derbyshire's book.

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.

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.