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Dr. Riemann's Zeros Paperback – 10 Sep 2003
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The only book about the search for a proof to the Riemann Hypothesis.
'An insider's view of the highly competitive, fascinating world of mathematics' --John Cornwell, Sunday Times
In 1859 Bernhard Riemann, a shy German mathematician, wrote an eight-page article, suggesting an answer to a problem that had long puzzled mathematicians. For the next 150 years, the world's mathematicians have longed to confirm the Riemann hypothesis. So great is the interest in its solution that in 2001, an American foundation offered a million-dollar prize to the first person to demonstrate that the hypothesis is correct. Karl Sabbagh's book paints vivid portraits of the mathematicians who spend their days and nights on the race to solve the problem.See all Product description
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For a start, he seems to have a shaky grasp of who he is writing for. Anybody who picks up this book in the first place is likely to be a bit of a geek, and such a person will not be satisfed with the way Sabbagh frequently refuses to explain things on the grounds that he thinks that the reader will not be interested, or won't be able to follow them; so for example, when he talks about an attempt to prove "something called the parallel postulate", he neglects to explain what the parallel postulate is. It's not even a very difficult subject to explain, but people who read popular books about maths do so partly in order to pick up a bit of math, and Sabbagh's careful focus on the personalities of the people he's talking about and his lack of interest in handing over chunks of carefully digested and clearly explained theory means that this book is extremely light in weight.
So in the end, as with so many books of popular science, the interested reader is forced to throw the book away and go straight back to the bookshop in search of stuff in the Further Reading list. I am now very interested in the Riemann Hypothesis, not so much in the stories Sabbagh had to tell about it.
Professor Marcus du Sautoy, in "The Music of the Primes", tried to tell the story of the history of our investigation of the primes, without doing any maths. Imagine trying to appreciate the genius of Stanley Kubrick, say, without watching any of his films. It didn't satisfy me. Sabbagh didn't chicken out. He explained the maths - not all of it, and using many helpful analogies, but he did enough maths to challenge many laymen. But I love the maths, and enjoyed this book which contained not just the history of this idea, and some of the maths, but Sabbagh also interviewed many of the leading mathematicians today who are intrigued by the problem, and in the process asked them many questions about how they work, how they approach the problem, about maths and creativity.
If you have A-level maths, you should get most of it. If you haven't, he uses lots of analogies. And there is much to enjoy in the book besides the M-word - very clever men talking about creativity.
However, a few pages later on p.69 Sabbagh exhibits an exponential equation with quotes from G.H. Hardy suggesting the solution for x is somewhere between 63 & 67.
This is easily seen to be completely wrong. I doubt that Hardy would make such a mistake so I assume there a typo somewhere or Sabbagh has transcribed something incorrectly.
The actual solution to the equation as printed is x=0.100524 to 6 decimals.
(I have not been able to find the source of the equation so do not know where the error arises.)
The scientific implications of the hypothesis (which would have made fascinating reading) are barely touched upon, e.g the connection with Quantum Mechanics, the implications to encryption codes etc.
There is a book covering the same material, called “Prime Obsession” by John Derbyshire which is far superior to this book, sorry....