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By John Derbyshire - Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Hardcover

by unknown author (Author)
4.6 out of 5 stars 522 ratings
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Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
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  1. Language
    English
  2. Publisher
    National Academies Press
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Product details

  • ASIN ‏ : ‎ B008UBCK2W
  • Publisher ‏ : ‎ National Academies Press
  • Language ‏ : ‎ English
  • Item Weight ‏ : ‎ 1 pounds
  • Customer Reviews:
    4.6 out of 5 stars 522 ratings

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John Derbyshire

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4.6 out of 5 stars
522 global ratings

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Customers say

Customers find the book's mathematical content well-explained and accessible to non-experts, while appreciating how it cleverly combines mathematics and history. Moreover, the writing style is highly readable and engaging, with one customer noting it reads like a page-turner. Additionally, the historical context receives positive feedback, with customers praising how the melding of history and biography provides great background information.

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ReadabilityWriting qualityHistorical contextStorytelling
69 customers mention "Readability"69 positive0 negative

Customers find the book engaging and easy to read, with one customer noting it's particularly suitable for high school students.

"...The reviews made the book look interesting, but I was a bit skeptical as most Math/Science books for layman I found to be well... crap!!!..." Read more

"...a good understanding of higher mathematics but it gives a great tour though this ongoing and exciting journey in finding the Holy Grail in..." Read more

"...Can be read over again many times, as there are plenty of stuff for thinking and wondering. A truly amazing book!" Read more

"...Nonetheless the author does a superb job of taking the middle ground and introducing math concepts slowly with steps that one can follow and takes..." Read more

33 customers mention "Writing quality"28 positive5 negative

Customers praise the writing quality of the book, finding it excellently and highly readable, with one customer noting that it reads like a page-turner.

"This is a very well-written account of the most famous unsolved problem in mathematics, the Riemann Hypothesis...." Read more

"...The text is always clear, logical and easy to follow, bringing a lot of surprises and pleasures...." Read more

"...What made Prime Obsession so fun to read was the excellent balance between exposition of the story and exposition of the underlying ideas...." Read more

"...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..." Read more

27 customers mention "Historical context"27 positive0 negative

Customers appreciate the historical context of the book, particularly how it melds history and biography to provide great background information, with one customer noting how it clearly lays out Riemann's life and times.

"...alternating with some history, I learned a lot from both...." Read more

"...The history is interesting enough that the math chapters could be skipped if the reader is so inclined...." Read more

"The 22 chapters are strictly divided, the even-numbered containing biographies and history (no math), the odd-numbered containing the math, and are..." Read more

"...The even-numbered chapters offer historical and biographical background matter."..." Read more

25 customers mention "Storytelling"25 positive0 negative

Customers find the book's storytelling engaging and fascinating, describing it as an exciting journey.

"...All in all it was an enjoyable few years...." Read more

"...mathematics but it gives a great tour though this ongoing and exciting journey in finding the Holy Grail in Mathematics, Physics and perhaps even..." Read more

"...The text is always clear, logical and easy to follow, bringing a lot of surprises and pleasures...." Read more

"...way the author does this as a story of history makes the learning process interesting and consuming...." Read more

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Top reviews from the United States

  • A. Cox
    5.0 out of 5 stars This book changed my life
    Reviewed in the United States on May 3, 2013
    Format: KindleVerified Purchase
    Really, No hyperbole, because of this book I have a Masters in Maths(sic). Well actually I have a Masters in Maths because I studied for it, but yes the inspiration came from this book.

    Having decided to review my (old) Physics knowledge and study The Theory of General Relativity. I chanced across this book whilst browsing Math books on this site, it was of course Riemann's name that caught my eye, since his geometry is (one of) the basis behind Einstein's previously mentioned seminal theory. The reviews made the book look interesting, but I was a bit skeptical as most Math/Science books for layman I found to be well... crap!!! Though I will immediately state an exception for Kip Thorne's excellent Black Holes etc.

    This book captivated me from the get go. I liked the structure, some Math (it's mostly simply Elementary Number Theory and some really basic Analysis) alternating with some history, I learned a lot from both. I'd never studied Number Theory before and learned about a lot of mathematicians I'd never or fleetingly heard of. The tone wasn't too condescending and the Math was just about right for his task, at least until the last chapter or so.

    Anyway, when I hit the proof of the Euler Equation, I read it and read it again and again and got hooked on Number Theory and started my own Prime Obsession. Now by the end of book I never fully understood what the Riemann Hypothesis truly meant or implied; this may be also due to the fact that by the end of the book I was already starting to study more Math and its Queen... Number Theory, as I'd signed up for a Masters in Maths and wanted to be fully prepared for it not having studied for a quite a few years by then. And by the end of the course I got to study Riemann's original paper. All in all it was an enjoyable few years.

    Now to be honest to really understand what Riemann was up to, you do need a wee bit more Math than Derbyshire offers here, and Riemann's paper is a bit of a read as he makes a lot of assumptions on the part of the reader (he of course assumes you're a Mathematician), this makes the paper relatively short, but means you need to be up on your Complex Analysis, Elementary and Analytic Number Theory help to. We used Apostal's excellent Analytic Number Theory and I found Edward's Riemann Zeta Function to be extremely helpful too; it also has a copy of the original paper.

    To conclude I highly recommend this book by Derbyshire as a great starting point to Riemann's and Number Theory in general. It was for me!
    30 people found this helpful
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  • L. Lopatin
    5.0 out of 5 stars So difficult but worth it
    Reviewed in the United States on February 21, 2025
    Format: KindleVerified Purchase
    I graduated with an undergrad math degree over 20 years ago. I could not follow the math in the book.

    Having said that, it’s a fantastic glimpse at the history of mathematics and one of its main characters.
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  • Arie Pieter Vander Stroom
    4.0 out of 5 stars Mathematics' Holy Grail
    Reviewed in the United States on December 12, 2010
    Format: PaperbackVerified Purchase
    Prime numbers are the most mysterious numbers in mathematics and have mystified mankind since counting was invented. Already in 300 BC Euclid demonstrated that an infinitude of prime numbers exists. In 230 BC, 70 years after Euclid, Eratosthenes of Cyrene developed the famous sieve method for finding Prime numbers. After the Greeks, little happened with the study of prime numbers until the 17th century when Fermat (from the famous Fermat Theorem) got engaged. From then on all the famous Mathematicians like Euler, Gauss, Leibniz, etc. struggled with these special numbers. Primes are the atoms of the number system, because every other number can be built by multiplying primes together. Unfortunately there is no periodic table for the primes -- they are maddeningly capricious. They clump together like buddies on some regions of the number line, but in other areas, nary a prime can be found. So number theorists can't even roughly predict where the next prime will occur. Here the notion of unpredictability raises its ugly head again; remember Heisenberg's uncertainty principle and chaos theory! This book is about the Riemann hypothesis, which only indirectly deals with Prime Numbers. The Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the distribution of the zeros of the Riemann Zeta Function which states that all non-trivial zeros of the Riemann zeta function have real part 1/2. This sounds like abracadabra but the beauty of the Riemann hypothesis (once it is proved) is that it will provide answers on how many Prime Numbers can be found in a specific interval and it will provide a probability function on where they can be found. In the search for the proof a whole new part of mathematics, analytic number theory, had to be invented. But Prime numbers and the Riemann Zeta function also have unexpected links to other sciences like Chaos theory and Quantum Mechanics. Chaos theory applies to physical systems so sensitive to their starting conditions that they are impossible to predict. In the late 1980s however, it was found that when averaged out over many different chaotic systems, the energy level spacings of chaotic systems fit the Riemann spacings with stunning precision. Also in early in the 20th century, mathematicians made a daring conjecture: that the Riemann zeros could correspond to the energy levels of a quantum mechanical system. Quantum mechanics deals with the behavior of tiny particles such as electrons. Crucially, its equations work with complex numbers, but the energy of a physical system is always measured by a real number. So energy levels form an infinite set of numbers lying along the real axis of the complex plane--a straight line. This sounds like Riemann's zeros. It is getting even more interesting since recently it has been determined that in a chaotic system, an object usually moves unpredictably, but sometimes its path will cycle back on itself in a "periodic orbit". It is thought that the right quantum system will have an infinite collection of periodic orbits, one for each prime number. This sounds like Nietzsche's Eternal returns and Godel's Closed Time Curves. Those who believe that mathematics holds the key to the Universe might do well to ponder a question that goes back to the ancients: What secrets are locked within the primes? This book is not an easy read for those without a good understanding of higher mathematics but it gives a great tour though this ongoing and exciting journey in finding the Holy Grail in Mathematics, Physics and perhaps even Metaphysics.
    2 people found this helpful
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Top reviews from other countries

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  • Palle
    5.0 out of 5 stars Pleasant introduction to the Riemann hypothesis
    Reviewed in Sweden on March 31, 2025
    Format: PaperbackVerified Purchase
    The book is a piece of good journalism, written as a popular book on mathematics should be. The book is a model when it comes to serious popularization of mathematics. Derbyshire goes some way toward helping the non-mathematician understand what the statement of the hypothesis means. From the very start, he gives multiple illustrative examples, allowing the reader to grasp just enough before moving on to the next concept.

    The author starts from the very bottom, reminding the reader about the most elementary mathematical facts, such as power laws. Slowly, he climbs up the steep gradient of difficulty, engaging himself at the end in trying to make visual the actual graph of the Riemann zeta-function and discuss the infinite series, conditionally convergent, from which you can recapture the prime-counting function.

    I would recommend the book to anyone interested in mathematics and who has some basic mathematical knowledge.

    To understand the Riemann hypothesis better, this is the "easiest" book. Derbyshire does not present the really difficult aspects of the hypothesis, such as the L-functions. To learn more, I recommend the "The Study of Bernard Riemann's 1859 paper" by Terrence P Murphy. A much more advanced book (for Graduates) is "Riemann's Zeta Function" By H.M. Edwards.
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  • Mark Williams
    4.0 out of 5 stars Excellent easy read for maths enthusiasts.
    Reviewed in Australia on April 16, 2023
    Format: PaperbackVerified Purchase
    Easy style prose with minimum formal maths speak, prepares the reader to comprehend the progressive essential steps to understand the Riemann Hypothesis. The author provides (and mostly proves) the underlying maths theorems and concepts (e.g. power series, limits, functions) necessary to progressively move closer to the actual hypothesis. A very affordable, enjoyable and clever presentation providing access to this "greatest of all time mathematical problem" for the amateur or lay mathematician. Somewhat let down with paper type, print contrast, type face and font size more akin to a cheap romantic paperback than what you normally expect for a maths book.
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  • Berna
    5.0 out of 5 stars Excelente
    Reviewed in Mexico on May 5, 2017
    Format: PaperbackVerified Purchase
    Yo tenía la versión de Kindle de este libro pero resulta tedioso y a veces despistaste tener que regresar a las gráficas y ecuaciones en páginas anteriores. En la versión física no tuve ese problema.
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  • ktwki
    5.0 out of 5 stars リーマン予想－その数学的内容、人物、歴史
    Reviewed in Japan on October 2, 2004
    Format: PaperbackVerified Purchase
    この本のテーマは「リーマン予想」という約１５０年間未解決の数学上の超難問である。一方、２０００年に懸けられた１００万ドルのミレニアム懸賞と、今年６月に解決された（？）、で「旬」なテーマでもある。しかしテーマにもかかわらず、この本は実に読みやすい本だ。著者がどう書けば読みやすい本になるかを完全に把握している。奇数章は数学、偶数章は人物と歴史、という構成も飽きさせない。数学は広い読者を対象に、数列や微積分の基礎から説明されているが、一方、各章、各節に何が書かれているかがつねに明らかにされている本なので、知っている人はどこまで飛ばせば良いかがすぐ判る。英語も実に明快だ（もちろん難しい単語は辞書で引くとして）。文系、理系を問わず、数学に何か心惹かれる人には必読の本であろう。リーマン予想からこんなにも幅広く豊かな数学が育まれてきたのか、と感銘を受ける。また、歴史を背景にした数学者群像も魅力だ。ところで本筋とは関係ないが「オブジェクト」を知っているコンピュータ技術者には、思わずニヤッとさせられるオマケが隠されている。
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  • Cliente Amazon
    5.0 out of 5 stars Excelente
    Reviewed in Spain on March 21, 2017
    Format: PaperbackVerified Purchase
    Soy físico y creo que es un libro interesantísimo tanto para principiantes como para gente con carrera científica. Los capítulos de historia de Gauss, Euler y Riemann son también extremadamente interesantes. Derbyshire consigue transmitir al lector de una manera entretenida y fluida conceptos que no son triviales de entender.
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