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Title: The Music of the Primes : Searching to Solve the Greatest Mystery in Mathematics by Marcus du Sautoy ISBN: 0-06-621070-4 Publisher: HarperCollins Pub. Date: 29 April, 2003 Format: Hardcover Volumes: 1 List Price(USD): $24.95 |
Average Customer Rating: 4.6 (15 reviews)
Rating: 3
Summary: way too little substance
Comment: What I learned from this book could probably have been much better communicated through a well-written magazine article. There's very little mathematics and very little history. Even worse, what's in this book struck me as a little too simplistic to be altogether true. I'm no expert, but the concept of primes as the 'atoms' of mathematics seems a bit exaggerated. Though clearly an important result for number theory, I also wonder whether the Riemann hypothesis (which has to do with zeros along the critical line of a zeta function) has really single-handedly been responsible for as much mathematical progression as the author claims. My sense is that the author was willing to leave out many details and exaggerate others in order to increase the drama of his story. Lastly, and I'll grant that this is just my taste, I don't quite understand the author's need to invent and stick with non-standard phrases. Once introduced, would it really have been a big deal to move from 'clock arithmetic' to 'modular arithmetic' or from 'sea-level' to 'zero'? Good books that are popular and true to mathematics exist (see Singh's 'Fermat's Enigma' or Nasar's 'A Beautiful Mind'). I don't think this is one of them.
Rating: 5
Summary: An exciting book
Comment: This is a marvelous book. It fulfills the promises of its titles, and so much more. "The Music of the Spheres" starts with the fascination of prime numbers and, using the analogy of music, leads to "Searching to Solve the Greatest Mystery in Mathematics," the Riemann Hypothesis, so that a layperson can understand the search. Then it explains a relevance to internet commerce and to quantum physics, among other topics.
Even the blurbs on the back cover are true. "He presents the personalities and lives of history's greatest mathematicians with the same vividness and brilliance as he presents their ideas." "No matter what your mathematical IQ, you will enjoy reading 'The Music of the Primes.'"
Rating: 5
Summary: CAUTION! This book may bring out your PRIMal passion!!
Comment: (...)
This twelve chapter book by Oxford mathematics professor, Marcus du Sautoy, introduces the reader to the fascinating universe of prime numbers. At the same time, we enter the world of the mathematician, a world unknown to most readers.
What are prime numbers? A prime is simply a number that cannot be divided by any other number except by one and itself. For example, the primes up to fifty are as follows:
{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47}.
This sequence of fifteen prime numbers and even those primes beyond fifty appear to be random. If you imagine the position of each prime being a note in a musical song, then you get, as this book's title states, "the music of the primes." But for centuries this music was "disorganized noise" since, as mentioned, the prime numbers appeared to be random leaving such questions as these:
(1) How can one predict when the next prime will occur?
(2) Is there a formula that can generate prime numbers?
(3) Is there a pattern to the apparent randomness of primes?
By the mid-1800s, a mathematician named Bernard Riemann (1826-1866), "the Wagner of the mathematical world," came as close as anyone to solving this problem of prime randomness. He presented an educated guess (known as a hypothesis) that the primes may not be really that random and that there actually may be a "harmony" between them and other numbers. In other words the music of the primes may not be as disorganized as once thought. Indeed, "nature [may have] hidden in the primes the music of some mathematical orchestra."
Trouble is that Riemann never proved his hypothesis and ever since, this proof, as this book's subtitle states, has become "the greatest mystery in mathematics." This book is all about the search for that proof. Du Sautoy presents the "prime suspects" (pun intended) in this search to discover the proof of the Riemann Hypothesis. (Note that anyone in today's world that can discover the proof will win a million dollars.)
Du Sautoy describes this quest to find a proof more eloquently: "We [will crisscross] the historical and physical world: Napoleans's Revolutionary France; the neo-humanistic revolution of Germany, from grand Berlin to the medieval streets of [the small town of] Gottingen; the strange alliance between Cambridge [University in England] and India; the isolation of war-torn Norway; the New World, and a new academy founded in Princeton [University] for those brave seekers [seeking the proof] of Riemann's [Hypothesis] expelled from Europe by the ravages of war; and finally to modern Paris and a new [mathematical] language, first [discovered] in a prison cell and which [caused psychological unrest in] the mind of one of its key developers."
In order to keep this quest interesting, du Sautoy presents interesting stories and phenomena along the way. For example, the author describes two species of cicada (large insects) that have prime number life cycles of 13 and 17 years. He goes on to explain why each species chose a prime number of years as the length of their life cycle.
"The story of the primes spreads well beyond the mathematical world" from quantum physics to computer security. With respect to computer security, "The primes now affect all our lives as they protect the world's electronic secrets from the prying eyes of Internet hackers."
There are two things I appreciated about this book. First, the mathematics. You don't have to be a math whiz to read this book (even though I found it helpful to slow down and read the math sections carefully). Important mathematical concepts are explained and complex mathematics is made understandable (which is no small feat). All this is aided by graphs and tables. Enough math is presented (actually more math than I expected is presented) so that the reader has a clear understanding of relevant concepts. (Some people think that not enough math is presented. Personally, I don't understand this. As the book's subtitle states, this book is about a search and not solely about complex mathematics. If I wanted a book on complex mathematics, I would have bought one.) Second, du Sautoy's enthusiasm comes through as he details the search for a proof. For me, this enthusiasm was infectious and I found myself caught up in the story.
Finally, this book has more than twenty-five black-and-white photographs and more than fifteen helpful graphs and tables. There is a "Further Reading" section "for those who have been stimulated to dig deeper into [this] subject." Also, there is a list of informative Internet sites.
In conclusion, this is a book for those who not only have a prime obsession but also for those who have a general interest in mathematics and its mysteries. This is the prime book to read if you want to understand the music of prime numbers and to follow the mathematical search "to solve the greatest mystery in mathematics." Also, you can read this book anytime not just in prime time!
(...)
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Title: Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire ISBN: 0309085497 Publisher: Joseph Henry Press Pub. Date: 23 April, 2003 List Price(USD): $27.95 |
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Title: The Riemann Hypothesis: The Greatest Unsolved Problem in Mathematics by Karl Sabbagh ISBN: 0374250073 Publisher: Farrar Straus & Giroux Pub. Date: 30 April, 2003 List Price(USD): $25.00 |
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Title: Gamma : Exploring Euler's Constant by Julian Havil ISBN: 0691099839 Publisher: Princeton Univ Pr Pub. Date: 17 March, 2003 List Price(USD): $29.95 |
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Title: Riemann's Zeta Function by Harold M. Edwards ISBN: 0486417409 Publisher: Dover Pubns Pub. Date: 13 June, 2001 List Price(USD): $14.95 |
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Title: The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time by Keith J. Devlin ISBN: 0465017290 Publisher: Basic Books Pub. Date: 15 October, 2002 List Price(USD): $26.00 |
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