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

4.07  ·  Rating Details ·  2,267 Ratings  ·  115 Reviews
In 1859, Bernhard Riemann, a little-known thirty-two year old mathematician, made a hypothesis while presenting a paper to the Berlin Academy titled  “On the Number of Prime Numbers Less Than a Given Quantity.”  Today, after 150 years of careful research and exhaustive study, the Riemann Hyphothesis remains unsolved, with a one-million-dollar prize earmarked for the first ...more
Paperback, 422 pages
Published by Plume (first published January 1st 2003)
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Alejandro The original pi(n) ~ li(n) is correct: I was using the scipy.integrate.quad function in Python and the results were misleading. (Although I made some…moreThe original pi(n) ~ li(n) is correct: I was using the scipy.integrate.quad function in Python and the results were misleading. (Although I made some proves with Mathematica). Are there perhaps different definitions for the integral log?
I changed to MATLAB's function quad and now the numerical results are as they are supposed to be.(less)
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Jun 23, 2015 Manny rated it it was amazing
Shelves: science
The best popular mathematics book I can recall reading. I had heard about the Riemann Hypothesis a zillion times and never understood what the fuss was about. After going through this book, it all made sense! Requires college-level math, but if you have that, can't recommend too highly.

An anecdote from Lambert's biography of Georges Lemaître which may amuse mathematicians. At one stage, young Lemaître was being supervised by the famous number theorist de Vallée-Pou
Jonathan Chuang
Jun 13, 2014 Jonathan Chuang rated it it was amazing
First of all, this is pretty well-researched, being a 150 year-long history and all. Also, while quite thorough about the math, it wasn't really that involved. Of course, like all attempts to give a popular account of complicated math, it tread too heavily while not penetrating deep enough. So I was a bit disappointed.

I gave it five stars because despite this, it was a real page turner. The prose is light and clear, and the pace is good. Reminds me of James Gleick's Chaos and Genius, at least i
Oct 15, 2009 Jason rated it liked it  ·  review of another edition
You remember the smartest kid in your high school calculus class? Remember the math major in your college dorm, the one doing advanced physics with more Greek symbols than Roman numerals? Both brainiacs at the time, right? Well, the book Prime Obsession deals with mathematical concepts magnitudes of order more complex than those brainiacs could ever wish to comprehend. John Derbyshire describes the Riemann Hypothesis (RH) and the mathematical titans that have tried unsuccessfully to prove the hy ...more
Sanjay Gautam
Dec 29, 2014 Sanjay Gautam rated it really liked it
I read the book somewhere, i don't remember on whose laptop, but I was more than halfway through and the book made me feel really great. Its a very well written book. You need not to know much mathematics to start reading it, he teaches you along the way. And then he takes you from history to rigorous mathematics and that's awesome.
Certainly its one of the books out there in world - to enlighten!
May 02, 2009 trivialchemy rated it liked it
This comparison will probably strike most as directly from left field, but Derbyshire reminds me a lot of Jon Krakauer. Topically, of course, they have nothing in common. But their style both depends heavily on the conspicuousness of the author in the narrative. This isn't necessarily because Krakauer and Derbyshire are narcissistic or self-absorbed, but that their writing is very self-conscious and they feel a continual impetus to advise the reader of where they stand on the issues they are pre ...more
Andrij Zip
Prime Obsession is an engrossing and mind stretching journey to the heart of one of the most enduring and profound mysteries in mathematics - the Riemann Hypothesis:

All non-trivial zeros of the zeta function have real part one-half.

By the time you finish the book, that enigmatic statement along with the math behind it will make sense,you will have a deep understanding of the significance of TRH (namely how it is connected to the distribution of prime numbers) and you will have a feel for the ric
Jul 09, 2007 Elio rated it really liked it
Although I find this author's political views repellent, I really enjoyed this book. He takes an extremely esoteric mathematical puzzle and shows how it emerges organically starting from the simple math we learned in high school. He also provides several excellent character sketches of famous mathematicians who made the key discoveries that allowed the Riemann Hypothesis to come into being in the first place. Most importantly, Derbyshire manages to convey the sense that the field mathematics is ...more
Feb 05, 2016 Dr.J.G. rated it liked it
The book and the style of writing are maddening, especially coming from a professional in the field - as often as not one wishes one could do more than raise eyebrows in a civilised manner and simply bop the fellow one on head, hard. It is bad enough he downplays or speaks degradingly of his professional colleagues in general, although not anyone in particular. He also refuses to provide extremely simple proofs claiming "that way lies madness" thus depriving non professionals of an opportunity ...more
Tara S.
Jun 24, 2016 Tara S. rated it really liked it  ·  review of another edition
3.5 stars.

In terms of mathematics, this book covered some really intriguing ground. The Riemann Hypothesis is fascinating, and its potential applications, particularly with respect to nuclear physics, are definitely fun to think about.

However, the author had an unfortunate tendency to disparage and downplay the actual mathematics, which I found weird and off-putting. This is, after all, a book primarily concerned with MATHEMATICS. Surely the reader won’t be too averse to the subject? Yet here i
Ollie Ford
Aug 16, 2014 Ollie Ford rated it really liked it
Really nice mix of mathematical content and the historical story.

Seemed somewhat as though an editor favouring a lower page count rushed a dump of all remaining explanation in the last couple of chapters - dramatic increase in pace. Toward the end there are some odd mixes of assumed knowledge too.
Oct 24, 2016 Groot rated it it was amazing
Shelves: nonfiction
A delightful book. Exactly what you would expect in a beautifully written story of what the life of a mathematician is like, both intellectually and in an everyday sense. Diving deeply though gently into the math of one of the greatest mathematical conjectures of the last few centuries, the Riemann Hypothesis, one can feel the author's love of the math itself and the admiration he feels for the giants who tackle these problems. Fine for non-mathematicians.
Nov 30, 2016 Vladyslav rated it it was amazing
This book is incredible.

Unfortunately I am simply unable to comprehend the depth of Riemann Hypothesis. Nevertheless it was interesting insight into the world of number theory and pure mathematic.

I believe math teacher from my alma mater will be proud of me reading it.
Artem Huletski
Oct 09, 2016 Artem Huletski rated it really liked it
Честно пытался вникать в математические главы, но на середине признал, что мне это не так интересно. Изложение и увлечённость людей, для которых "радость и очарование заключаются в самой охоте", хороши.
Dan Cohen
May 25, 2014 Dan Cohen rated it really liked it

This is a really good book. It attempts to explain the Riemann Hypothesis ("RH") to anyone with only "high school" mathematical knowledge, or maybe a little bit more. It also contains a lot of historical material on the mathematicians involved and makes many delightful observations and asides on the way.

The book includes a lot of mathematical reasoning. But the author avoids making it a mathematical text-book by simplifying, cheating, and joking his way along. This is a very refreshing and effec
Jun 11, 2010 Andy rated it really liked it
Shelves: nonfiction, math
There are famous math problems that are easy to explain but difficult to solve, such as the four-color map problem or Goldbach's Conjecture; the Riemann Hypothesis is unfortunately not such a problem. Prime Obsession is author John Derbyshire's attempt to explain the RH in simple terms and to illustrate its place and importance in the history of mathematics. It's not an easy task, and I think what Derbyshire has written is suited for a relatively narrow audience of people: those who took some an ...more
Fraser Kinnear
Apr 10, 2011 Fraser Kinnear rated it really liked it
Shelves: math, history
Prime numbers are powerful things. If you multiply one or more primes together, you can create any other positive integer that's bigger than one. And we suspect that every even positive integer greater than 2 is the sum of two primes.

But primes are strange as well - there doesn't appear to be any order to their appearance. The higher you count, the less often you run into them and you'll never stop seeing them. But can we tell when the next one will occur? In other words, is there some sort of p
Dec 22, 2013 Lars rated it liked it
Having had my first impressions of Derbyshire formed by his absurdly offensive "The Talk: Nonblack Version.", and the scandal it evoked, I went into this book with a certain sense of apprehension. Somehow I was not convinced that anyone capable of such crude and disgusting racism would have something appealing to say about, well, anything.

The author's politics are thankfully not on display in Prime Obsession, nor is his trademark crankiness. However, there is a certain sense of stubbornness and
Bryan Higgs
Jul 16, 2011 Bryan Higgs rated it really liked it
This book is one of several books on a mathematical topic, ostensibly for laypersons. The topic in this case is the Riemann Hypothesis, which is one of the -- perhaps THE -- most important unsolved problems in Mathematics. The style and layout of the book follows one that I have seen in other such books, where the chapters alternate between the history and personalities and social and political context for those involved in trying to solve the problem, and an explanation of the mathematical ...more
Thomas Paul
Aug 08, 2013 Thomas Paul rated it it was amazing
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 boo
Apr 03, 2014 Saran rated it liked it
Shelves: sci-phil-math
Prime Obsession has chapters alternating between describing the social, cultural and political history of several mathematicians who've contributed to our understanding of Prime numbers, and a gradual mathematical exposition of concepts building up to the Riemann Hypothesis.

The lazy part in me took this up for light reading as an alternative to working out the maths from Wikipedia, and I wasn't totally disappointed if a little bored. I wasn't familiar with the concept of "domain expansion" of a
Jan 29, 2013 Karl rated it really liked it
Shelves: scients, mathematics
Excellent pop-science work. As a mathematician, it was a little simplistic for me (although as a mathematician who did not specialise in number theory I still got a lot out of this book; mathematics is an evolving and complex discipline with many subfields for specialisation and, as Derbyshire points out in this book, it is no longer possible for a mathematician to be an expert in all fields of mathematics anymore. There's simply not enough time in the day); equally, I can see that a ...more
Nishant Pappireddi
Jun 27, 2014 Nishant Pappireddi rated it it was amazing
Like "Unknown Quantity," this book tries to discuss a mathematical topic with an assumed nonmathematical audience. In this case, Derbyshire talks about the Riemann Hypothesis, as well as parts of the biographies of the people whose work related to it. The odd numbered chapters are the mathematically focused ones, while the even numbered chapters are the biographical ones.

While I'm not sure that I agree with the author's claim that someone who does not understand the RH after reading this book wi
Josh Hamacher
Oct 03, 2010 Josh Hamacher rated it liked it
Reading this reminded me of how much I always enjoyed math back in college. The chapters alternate; odd chapters are a mathematical-oriented exposition of what the Reimann Hypothesis is, what it means, and what it implies. Even chapters give an historical overview of the key players, places, and events in the search.

I can't say I kept up with all of the math. The first third was a review, the second third I felt like I should understand because I had it in college but hadn't used since, and the
Theresa Leone Davidson
If you know of the Riemann Hypothesis and how no one has been able to solve it, or if you have a whole lot of interest in mathematics, particularly calculus, or if you are the type of person who enjoys solving difficult math problems just for fun, then you would probably enjoy this book. I did not learn to love math until college, which I have written about in past reviews, but I do not have an inordinate amount of love for the subject, and this book I found to be tedious and overwhelming. I do ...more
Sep 01, 2015 Jason rated it liked it
This is a hard book to pin down, parts of me liked it, others not so much. It reads like a half proof. There is math and history of those mathematicians featured. He does a decent job of putting some sections in layman's terms, which put me off, I get the need, but I highly doubt many of those without a math interest and background are going to read this. The author's writing style is very informal. I wanted to love this book, it has good books, but I don't feel the author really ever gets to ...more
Dec 08, 2013 Jason rated it it was amazing
Prime Obsession goes deep into the history of the quest to unlock the secrets of prime numbers. Every other chapter (the odd-numbered ones) delve into the mathematics and I learned a lot. The mathematics involved is often remarkable, like peeling back a layer of the universe and seeing what God is doing behind the scenes. We still don't really know what the heck it is but we see clues that it's all interconnected somehow (e^(pi*i)=-1 for example). Anyways you learn the proof to the Prime Number ...more
David Ambrose
Jun 18, 2016 David Ambrose rated it liked it
Shelves: nonfiction
This is probably as good a book as can be written to try to explain difficult mathematics without assuming that the audience knows any mathematics. The author strikes a balance between giving a historical account of the development of, the interest in, and the evidence for the Riemann Hypothesis, and for explaining as much of the mathematics as he can. As a mathematician, I can't say how the effort to explain the mathematics would play to someone who doesn't know much advanced mathematics. For ...more
Angela F
Nov 28, 2016 Angela F rated it really liked it
I was expecting to be underwhelmed given this books status as "pop" --but was pleasantly surprised. A perfect read that manages to be interesting to math/physics professionals but relevant and enjoyable to the average reader. I can't imagine anyone in the physical sciences failing to thoroughly enjoy it.

To those who feel the book may be too narrowly focused to be of interest: rest assured there is a lot more covered than the title eludes to. A very interesting historical context that include fu
Emma Glaisher
Feb 18, 2013 Emma Glaisher rated it it was amazing
This was pitched absolutely right for me. OK, by the end I lost the plot (fields, operators... ) but he handheld beautifully and talked the reader through some actual calculations, and totally explained how you get from the zeta function to the Euler product (a result which Marcus du Sautoy simply states with no explanation, leaving me totally baffled).

Reminded me of matrices and eigenvalues, which we did for maths O level back in the 70s! Need to go back and look more at this.

Perfect complement
Feb 15, 2015 Hollis rated it really liked it
Shelves: history, mathematics
The author came across as a bit of a prick which he is judging from comments he has made in recent newspaper articles including the following:

''Leaving aside the intended malice, I actually think "White Supremacist" is not bad semantically. White supremacy, in the sense of a society in which key decisions are made by white Europeans, is one of the better arrangements History has come up with. There have of course been some blots on the record, but I don't see how it can be denied that net-net, w
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“I tell you, with complex numbers you can do anything.” 9 likes
“It was in 1742 that Christian Goldbach put forward his famous conjecture that every even number greater than 2 can be expressed as the sum of two primes.” 0 likes
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