Rating: 
Summary: CAUTION! This book may bring out your PRIMal passion!!
Review: (...)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! (...)
Rating:
Summary: CAUTION! This book may bring out your PRIM(E)al passion!!
Review: +++++
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 Bernhard Riemann (1826-1866), "the Wagner [or Mozart] 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" 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 book to read anytime (not just in prime time) if you want to understand the music of prime numbers and to follow the mathematical search "to solve the greatest mystery in mathematics."
+++++.
Rating:
Summary: Fun and satisfying
Review: Clear, fun, with quite a bit of humor, and more mathematical detail than I thought I could possibly get through. I enjoyed reading this in tandem with the recent books on the Riemann hypothesis by Derbyshire and Sabbagh. If you liked either of those, this one will also be very satisfying for you.
Rating:
Summary: The Music of the Primes
Review: I guarantee you will enjoy this book. Written for the layperson; scientist; mathematician; student and housewife. I would come home from work and start reading this wonderful book and I found myself carried away into an imaginary landscape of fields of numbers (not boring numbers) but a world of the 5th dimension. Real as our world but connected through a language of The Music of the Primes. You will discover with astonishment the power mathematics has in our simple daily lives, that surrounds us everywhere. For the student: expect to be inspirated to go back to that math class that you told yourself, "I just can't do it." Du Sautoy makes numbers and math fun again but it is not a math book. He takes you on a journey into the hearts and minds of the greatest Mathematicians that ever lived and you feel their failures and their times of Eureka! I would love to sit in Du Sautoy's class. The book reads like an adventure. I truly wish textbooks were like this and believe they can be.
Rating:
Summary: The Music of the Primes
Review: I guarantee you will enjoy this book. Written for the layperson; scientist; mathematician; student and housewife. I would come home from work and start reading this wonderful book and I found myself carried away into an imaginary landscape of fields of numbers (not boring numbers) but a world of the 5th dimension. Real as our world but connected through a language of The Music of the Primes. You will discover with astonishment the power mathematics has in our simple daily lives, that surrounds us everywhere. For the student: expect to be inspirated to go back to that math class that you told yourself, "I just can't do it." Du Sautoy makes numbers and math fun again but it is not a math book.
He takes you on a journey into the hearts and minds of the greatest Mathematicians that ever lived and you feel their failures and their times of Eureka! I would love to sit in Du Sautoy's class. The book reads like an adventure. I truly wish textbooks were like this and believe they can be.
Rating: 
Summary: Worth reading but immensely frustrating.
Review: Neat historic and personality stuff and mathematical overview, but if you like and want to learn the math, the book is very frustrating and somewhat offensive. Du Satoy omits almost all mathematial rigor, and most mathematical detail.
He frequently uses metaphors, usually without ever telling what the real mathematical terms are. To use a metaphor of my own, it reads sort of like, "If you think of numbers as flocks of birds, and prime numbers as differently colored birds, then the Riemann Hypothesis is like a fish." Something neat is going on, but I don't know what it is.
He never actually tells what the Riemann Hypothesis is in clear terms, or even what Li(x) is in the Prime Number Theorem.
I also dislike many of the metaphors themselves. After a while I couldn't stand it any more, and skipped every paragraph containing the words "clock calculator," which he uses instead of "modular number systems." Even as metaphors go, it's horrible. Calculators are little boxy things with number keys on them, and are nothing like modular number systems. Later in the book, I skipped paragraphs which said "quantum drum." I never did figure out what he meant by this.
This could all have been so easily fixed by a short appendix with the actual equations, or even by a list of references. (The book does have references, but they're also non-mathematical, and furthermore they aren't described beyond their titles.)
He even has a website for the book, where this additional information could have gone, but it's just more of the same. It's also, by the way, of the "pretty is more important than navigable" school of website design.
An appendix to the book with a timeline and a list of the mathematicians and their accomplishments would have also been invaluable--how much of this book will you remember in six months?
He sometimes plays fast and loose with mathematical details, e.g., referring to complex numbers as imaginary numbers. It probably doesn't matter, but you have to wonder what else you can't trust.
And some of the stuff, presented without explanation, just doesn't make sense. For instance, (I'm not making this up, though I am paraphrasing): "Ramanujan sent Hardy a letter which said 1+2+3+... = -1/12. At first Hardy and Littlewood thought this was the work of an idiot, but then they realized it said 1+2+3+... = -1/12, and he was actually brilliant." (pp.135-137, paperback edition)
Every once in a while there was some unambiguous math. I liked Euler's product for changing the zeta function into a product of series of reciprocal powers of primes, and how for the harmonic series this simplifies down to a proof that there are infinitely many primes. (p.81). I also like, and am astounded by and don't understand, the equation which generates all the primes but is useless on p.200.
Another neat thing I took from the book was the evidence that individual, unique genius exists, that ideas aren't just out there waiting to be discovered by the next mathematician who comes along. Riemann knew stuff which still isn't know to this day (and he apparently wrote it down, in a black book which disappeappeared but might still exist somewhere). It was nice to have confirmation of this, since it turns up in science fiction ("if we destroy all his notes, the human race will never rediscover this"). I was always skeptical, but I guess it's true.
The main reason I gave the book four stars is that it made me interested enough to want to find another book and look up the real math.
Rating:
Summary: Fascinating look at the most formidable issue in mathematics
Review: The Music of the Primes is an absolutely fascinating look at the most formidable challenge in mathematics today - the Riemann hypothesis. Much of the book is dedicated to detailing the efforts of mathematicians since Reimann, who have endeavored to prove his hypothesis. These chapters provide biographies of the mathematicians who have tried, all in vein, to solve the puzzle. Even though du Sautoy does his best to make the mathematics in the book understandable to those without an advanced math background, some of the equations and ideas can be difficult to understand at times. But that is at most, about 5% of the book. He does though do an impressive job of explaining the mathematical concepts in an understandable manner. The Music of the Primes is a great book and a fascinating read, something that is rarely stated about a book on an advanced mathematical topic.
Rating:
Summary: Fascinating look at the most formidable issue in mathematics
Review: The Music of the Primes is an absolutely fascinating look at the most formidable challenge in mathematics today - the Riemann hypothesis. Much of the book is dedicated to detailing the efforts of mathematicians since Reimann, who have endeavored to prove his hypothesis. These chapters provide biographies of the mathematicians who have tried, all in vein, to solve the puzzle. Even though du Sautoy does his best to make the mathematics in the book understandable to those without an advanced math background, some of the equations and ideas can be difficult to understand at times. But that is at most, about 5% of the book. He does though do an impressive job of explaining the mathematical concepts in an understandable manner. The Music of the Primes is a great book and a fascinating read, something that is rarely stated about a book on an advanced mathematical topic.
Rating:
Summary: An exciting book
Review: 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:
Summary: You Must Read This Book
Review: Warning! This book could change your life. A well written history of the relationship between the strange, seemingly random series of prime numbers. An essential read for anyone interested in the why and wherefore of the construction of a naturally occuring number series.
| 
