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

4.06 of 5 stars 4.06  ·  rating details  ·  1,718 ratings  ·  93 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 pe ...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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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
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
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
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!
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
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
Nishant Pappireddi
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
Ollie Ford
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.
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
Saran Neti
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
a capitoli alternati, uno di storia pura e uno di divulgazione matematica, Derbyshire ripercorre passo dopo passo la storia di Riemann, della sua tesi e di quello che forse il pi grande problema matematico ancora aperto ai giorni nostri. Proprio per la sua particolare struttura, un libro amabile sia da chi non vuole vedere matematica che non sia 2+2, sia da chi gli unici numeri che vuole vedere sono quelli delle formule, sia da chi invece interessato ad entrambe le facce della medaglia. Non l ...more
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
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 topi ...more
Dan Cohen

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
Thomas Paul
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
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 non-practit ...more
Fraser Kinnear
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
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
Gives a really easy introduction to the Riemann Zeta Function and the Riemann Hypothesis. It's a nice book to "vacation" in but does leave out the reality that true understanding of the Zeta Function requires knowledge in complex analysis, a non-trivial subject. However, it does a good job introducing the main ideas and tying it together with the history around the subject. The average reader will be satisfied, but those interested in the mathematics will not and should not.
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
Josh Hamacher
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
Το βιβλίο χωρίζεται σε δύο μέρη στην ουσία, ιστορικό και επιστημονικό, τα οποία παρουσιάζονται εναλλάξ σε κάθε κεφάλαιο. Μπορεί κανείς είτε να διαβάσει μόνο το ιστορικό μέρος είτε μόνο το επιστημονικό και δεν θα νιώθει ότι δεν έχει βγάλει άκρη. Ή ανάλογα τα κέφια, αυτό που έκανα κι εγώ, διάβαζα μια τα ιστορικά μία τα μαθηματικά και μετά γυρνούσα πίσω να διαβάσω αυτό που μου είχε μείνει.
Charles Jeffrey
The mathematics surrounding the Riemann conjecture is beyond most, myself included, but the story of the pursuit to prove the conjecture is gripping, and the incredible characters involved (Reimann, Euler, and others) are superbly brought forward in the book by John Derbyshire. I have read it twice and will likely pick it up for a third read in a year or so. Can't wait.
Bowman Dickson
Hmm, I found this interesting overall - loved some of the historical sections about mathematicians and loved just getting a feel for in general how a singular problem from one little function has plagued mathematicians for a few centuries now. Not sure who the audience is. He explained ridiculously simple math and then slipped a lot of steps as we got further up the abstraction latter. I mean, the guy explained properties of exponents, which is ridiculous because there is NO WAY someone who does ...more
Pawel Mucha
I am wondering if the one who will find the answer will say that he started thinking on it after reading this book, that would be astonishing what kind of power is laying under popular science books.

Well done on this book which was outstanding throughout both presentation of math and in its history.
Dan Caldwell
I loved this book about a fascinating mathematical problem and the mind-blowing, beautiful connections between the central problem and a spectacular array of other mathematical ideas. Well-written and great to read.
However, people deserve to know that the author was fired from the conservative National Review for white supremacist statements and even writes for VDARE, a white nationalist anti-immigration group.
I scoured the book critically for expressions of his racist position, and I could find
This is a really engaging and interesting discussion of the a Prime Number Theorem and the Riemann Hypothesis. The author does a good job providing clear explanations of very complicated concepts from higher mathematics.
Emma Glaisher
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
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Currently living on Long Island, New York
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“I tell you, with complex numbers you can do anything.” 8 likes
“Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.” 0 likes
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