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Prime Obsession: Bernhard Riemann and the…

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in… (original 2003; edition 2003)

by John Derbyshire

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7481018,576 (4.07)5
Title:Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Authors:John Derbyshire
Info:Joseph Henry Press (2003), Edition: Second printing, Hardcover, 448 pages
Tags:math, history of science, biography, 19th century

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Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire (2003)


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Showing 1-5 of 9 (next | show all)
An excellent coverage of the Riemann Hypothesis for the non-mathematician. ( )
  jsburbidge | Jan 12, 2016 |
Seeing as how this is my first exposure to the RH, and I'm only fairly capable in math, I can't say whether or not this is the best place to start. I feel like I have a good sense about this great mathematical problem, which is due in part to Derbyshire's simple explanations. However, I think the way the book was edited may have caused a lot of confusion. I thought it a bit erratic, with too many tangents and I didn't like being constantly referred back to old chapters. ( )
  palaverofbirds | Mar 29, 2013 |
One of the most irritating narrators ever. The history chapters were fascinating and the math itself was fine, but his explanations were pedantic, patronizing, and self-absorbed. ( )
  pale_fire | Feb 24, 2013 |
"This isn't magic. There's a reason this stuff works," my high school math teacher used to say. Of course, there are some contentions, hypotheses, in math where we don't know if they work, if they are true.

For professional mathematicians, one of the most important of these is the Riemann Hypothesis. Everlasting fame amongst mathematicians, and, incidentally, a million dollars is waiting for the person who can nail the truth of the "RH" down.

Unlike some famous math problems, the gist of the RH is not readily apparent to most non-mathematicians. Derbyshire has to spend some time explaining what is meant by "All non-trivial zeros of the zeta function have real part one-half." And, as someone whose formal math instruction ended with four years of high school math and who reads the very occasional popular math book by Gleick, Peterson, or Paulos, I'm pretty much the target audience Derbyshire pitches that explanation to.

The book's style reminded me of the science histories of James Burke. But where Burke's work is a pinball version of history, caroming from person to person, theory to theory, Derbyshire's is a train of mathematical explanation covering the work leading up to, and proceeding from, the RH. Occasionally, Derbyshire stops at some station, pulls up the blind, and looks at some area of tangential interest: famous mathematicians including Gauss, Hilbert, Russell, Dyson, and Turing (who thought RH untrue and attempted to build a computing device to disprove it); German educational reforms of the early 19th century; the Cambridge Five spies; and, most often, since this book is ostensibly a biography of him, the life of Bernhard Riemann. But it's not long before we're back on that math train again. This is not to shortchange the non-math interludes of the book. Derbyshire's quick asides gave me a lot of ideas for further reading. And, if less than half of the book's 422 pages cover Riemann's life, you still get some idea of his protean mind so important not only to mathematics but modern physics.

Derbyshire's claim that, if you don't understand the RH after he explains it you never will, seems credible. I won't claim I immediately followed his chain of explanations the first time around. But that had more to do with trying to read this book in 15 minute intervals over a week rather than Derbyshire's prose. Upon reviewing many sections again, things became clearer.

The book briefly notes some of the consequences of RH, practical and theoretical. A lot of math is based on the assumption it's true. And the RH may have some mysterious relation to the world of quantum physics. In the commercial and military worlds, where encryption methods based on prime numbers are important, the RH, which has to do with the distribution of primes, may have significant importance if proved true.

I think one of the best things about this book is that, briefly, in a simple way, a non-mathematician like me can get some small idea of the excitement mathematicians feel upon discovering some curious pattern in the world of numbers.

The only complaint I have with this book is its format. Is it too much to ask that, in the age of computerized typesetting and with an author whose footnotes are all worth reading, that we put those footnotes at the bottom of the relevant page and not at the end of the book? ( )
1 vote RandyStafford | Nov 29, 2011 |
Well that was thoroughly enjoyable; John Derbyshire’s ‘Prime Obsession’ recounts the story of the Riemann Hypothesis a piece of math that was brilliantly intuitive back in 1859 when Bernard Riemann first presented it and is still unproven despite being close to the heart of large swathes of Math and Physics. John Derbyshire kept warning me that the Math towards the end of the book would have to be taken on trust and sure enough in the last two chapters I was lost; however I did get a distinct flavor of the cooking and I felt that I knew not only something of the big picture but a great deal about the people behind the Math. There is plenty of character in this story and some excellent anecdotes, I would not hesitate to recommend it to anyone with solid High School Math but I suspect that the readership is self selecting and quite probably it is those with a firm math interest who will plum for this mathematically erudite (and simply erudite!) account of the prime of our mathematical lives. ( )
  BeesleSR | Feb 23, 2009 |
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Amazon.com Amazon.com Review (ISBN 0452285259, Paperback)

Bernhard Riemann was an underdog of sorts, a malnourished son of a parson who grew up to be the author of one of mathematics' greatest problems. In Prime Obsession, John Derbyshire deals brilliantly with both Riemann's life and that problem: proof of the conjecture, "All non-trivial zeros of the zeta function have real part one-half." Though the statement itself passes as nonsense to anyone but a mathematician, Derbyshire walks readers through the decades of reasoning that led to the Riemann Hypothesis in such a way as to clear it up perfectly. Riemann himself never proved the statement, and it remains unsolved to this day. Prime Obsession offers alternating chapters of step-by-step math and a history of 19th-century European intellectual life, letting readers take a breather between chunks of well-written information. Derbyshire's style is accessible but not dumbed-down, thorough but not heavy-handed. This is among the best popular treatments of an obscure mathematical idea, inviting readers to explore the theory without insisting on page after page of formulae.

In 2000, the Clay Mathematics Institute offered a one-million-dollar prize to anyone who could prove the Riemann Hypothesis, but luminaries like David Hilbert, G.H. Hardy, Alan Turing, André Weil, and Freeman Dyson have all tried before. Will the Riemann Hypothesis ever be proved? "One day we shall know," writes Derbyshire, and he makes the effort seem very worthwhile. --Therese Littleton

(retrieved from Amazon Thu, 12 Mar 2015 18:16:02 -0400)

(see all 2 descriptions)

This is the story of a riddle posed in 1859 and the man behind it. The Riemann hypothesis - that there must be a general rule for calculating how many prime numbers there are up to a given point - continues to elude the finest mathematical minds and produce creative and bold mathematics.… (more)

(summary from another edition)

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