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The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics (P.S.) (Englisch) Taschenbuch – 14. August 2012

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Taschenbuch, 14. August 2012
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Produktbeschreibungen

Pressestimmen

“An amazing book! Hugely enjoyable. Du Sautoy provides a stunning journey into the wonderful world of primes.” (Oliver Sacks)

“This fascinating account, decoding the inscrutable language of the mathematical priesthood, is written like the purest poetry.” (Simon Winchester, author of The Professor and the Madman)

“This is a wonderful book about one of the greatest remaining mysteries in mathematics.” (Amir Aczel, author of Fermat's Last Theorem and The Riddle of the Compass)

“No matter what your mathematical IQ, you will enjoy reading The Music of the Primes.” (Keith Devlin, Stanford University, author of The Millennium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time)

“Exceptional. ... A book that will draw readers normally indifferent to the subject deep into the adventure of mathematics.” (Booklist (starred review))

“[A] lively history. . . . A must for math buffs.” (Kirkus Reviews)

“Fascinating.” (Washington Post Book World)

Synopsis

A history of mathematics from the cutting-edge of present-day research, this book tells the story of the most idiosyncratic and most fundamental numbers in pure mathematics, the primes. When counting, primes (numbers only divisible by one and themselves) appear without any reason or rhythm. To a non-mathematician this may seem an oddity. To scientists the key to this seeming randomness, called the Riemann Hypothesis, is one of the most important enigma within mathematics. The Riemann Hypothesis has significance beyond maths - it is the basis for all internet and e-commerce security and has been named as one of the questions of the 21st century, with a reward of a million US dollars to the person who can crack it. It also has ramifications within quantum mechanics, chaos theory and the future of computing. At the heart of the hypothesis is the study of prime numbers, the fundamental building blocks of mathematics. In "The Music of the Primes", mathematician Matthew de Sautoy recounts the history of these elusive numbers, including the work of Euclid, Ramanujan, Odlyzko, the formation of RSA encryption, as well as reports first hand from the far reaches of today's research. -- Dieser Text bezieht sich auf eine andere Ausgabe: Taschenbuch.

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Format: Taschenbuch Verifizierter Kauf
The Music of maths — through the times
From its atoms, its reasons and rhymes:
You will hear it, indeed
Once you started to read
Marcus du Sautoy’s book on the Primes.

Friday afternoon a colleague lent me his copy of the above mentioned book (in a German translation). Once I started to read it I couldn't stop and just finished it half an hour before writing this. In the meantime I ordered an English copy.
For all those of you interested in maths and its history: It's a great one, you'll probably enjoy reading!

See also: Thread in the forum of: OEDILF, The Aardvark & Armadillo, Book Reviews In Limerick Form (BRILF)
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Format: Kindle Edition Verifizierter Kauf
The sound of the primes is very interesting, sometimes surprising but most of the time just pleasure to listen to. The book is written by an insider with a great talent to describe complicated mathematical matter in a simple way without losing the essential. I have read the book with great joy. Unfortunately, the electronic version of the book doesn’t not display the many figures the text it is referring to! I have tried different devices without success. That’s why I have deleted one star in my overall judgment.
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Die hilfreichsten Kundenrezensionen auf Amazon.com (beta)

Amazon.com: 4.6 von 5 Sternen 54 Rezensionen
46 von 48 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Prime Fascination 28. Juli 2003
Von Rob Hardy - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
One of the attractions of number theory is that it has to do with the counting numbers; if you can get from one to two and then to three, you are well on your way to hitting all the subject matter of "The Queen of Mathematics." All those numbers can be grouped into two simple categories. The composite numbers, like 15, are formed by multiplying other numbers together, like 3 and 5. The prime numbers are the ones like 17 that cannot be formed by multiplying, except by themselves and 1. Those prime numbers have held a particular fascination for mathematicians; they are the atoms from which the composites are made, but they have basic characteristics that no one yet has fully fathomed. We know a lot about prime numbers, because mathematicians have puzzled over them for centuries. We know that as you count higher and higher, the number of primes thin out, but Euclid had a beautiful proof that there is no largest prime. However, the primes seem to show up irregularly, without pattern. Can we tell how many primes are present below 1,000,000 for instance, without counting every one? How about even higher limits? Speculating about the flow of primes led eventually to the Riemann Hypothesis, the subject of _The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics_ (HarperCollins) by mathematician Marcus du Sautoy. The counting numbers turn out to be astonishingly complicated, and Du Sautoy knows that egghead number theorists will understand these complications better than we nonmathematicians, but he invites us to consider at a layman's level the importance of the particular quest of proving the Riemann Hypothesis. He is convincing in his demonstration that it is worth knowing what all the effort is about.
Bernhard Riemann, a mathematician at the University of Gottingen, introduced a "zeta function," and proposed that when this particular function equals zero, all the zeros will wind up on a specific line when graphed on the complex plane. Further effort has shown that there are millions of zero points on that line, just as the hypothesis says, and no zero points have been found off the line. Neither of these facts makes a proof, however. Du Sautoy wisely shows some of the enormously complex technicalities of the speculations and computations, but makes no attempts to try to get the reader to comprehend the hypothesis at the level he does. There are a number of reasons that the proof is so important. Right now there are a large number of tentative proofs of important mathematical ideas; they are all based on the Riemann Hypothesis being true, but of course, it has not itself been proved. A proof would tell us more about the prime distribution and finding primes, and this subject has become vital since cryptography, including how you privately send your credit card number across the internet, is based on prime numbers and the difficulty of factoring two big primes multiplied together. The way the Riemann zeros are distributed seems to mirror the patterns quantum physicists find among the energy levels of the nuclei of heavy atoms; in proving Riemann, we may have a closer understanding of fundamental reality.
With the Riemann Hypothesis central to a lot of mathematical effort, Du Sautoy is able to bring in a lot of side issues, such as Turing's attempt to find a program that would attack the proof, the four color map theorem and computer proofs in general, Gödel's Incompleteness Theorem, and much more. The mathematics, such as it is, is leavened by portraits of mathematicians, who range from conventional to very peculiar. A good deal is said about the dashing Italian mathematician Enrico Bombieri who rocked the mathematical world with the announcement that the Riemann Hypothesis had finally been proved. There was jubilation over the announcement until mathematicians realized that the e-mail bore the date 1 April. He could not have picked a better theme for an April Fool's joke; all the mathematicians were eager to see this one proof finally nailed down. Readers who take du Sautoy's entertaining tour can get an idea of why all the effort is being expended on the proof, and what elation there will be if it is ever found.
23 von 23 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen du Sautoy is Prime Time Player 16. Juni 2003
Von NotToto - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
This is an exceptionally interesting book on the nature of prime numbers. The author succeeds on two fronts, he makes an incredibly vexing mathematical problem understandable to the lay person, AND he successfully explains most of the attacks against the problem for the last 150 years in a way that is both intrigueing and understandable. This is NOT a book with pages and pages of formulae, but it does contain a rich description of this problem which helps make it accessible to the curious mind.
The author has provided an excellent index at the back of the book for people that want to delve further. In addition, the author mentions several websites in the book that are helpful. The book contains many interviews with people currently working in the field to solve this problem .. but what I found most interesting, was how far ahead of his time Riemann himself was. The fact that he was able to come up with this hypothesis way before the advent of modern computational equipment and the ability to compute the zeroes necessary in the formula ... truly marks him as a unique mind. What would he be like if he lived today, with our supercomputers and other aids to computation?
I felt the book was very thought provoking on several fronts, the author's style was quite accessible, and it was enjoyable reading.
37 von 41 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen The good, the bad, and the ugly 8. Juni 2005
Von P. Wung - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe Verifizierter Kauf
As the previous reviewers have already noted, du Sautoy does a great job bringing together the history of research that has been done on prime numbers, especially the Riemann Hypothesis and anything that pertains to that problem. I had not heard of the physics connection until I read this book and I did enjoy reading about it. The coverage is also very comprehensive and very thorough.

The bad is the purple prose that du Sautoy resorts to in order to make the material accessible to the lay reader. i think perhaps he underestimates his audience -to some a fatal flaw, to others a grating annoyance. My opinion is somewhere in between. It is rather difficult to express higher mathematics in a language other than in the mathematical language. I thought he did a pretty decent job with many of the concepts but I wonder what Simon Singh could have done with the same information. For example, du Sautoy's explanation of the RSA encryption method was lightweight and confusing. I think I had to read the pages four or five times before I saw how he was trying to explain the method. I am not a mathematician but I do have extensive background in mathematics, so if I got confused, what happens to the average reader?

The ugly is the way he flits around in his narrative. There is never any sense of when he is done talking about one development and the beginning of another. the history of the mathematicians were cursory at best. I understand that the purpose is to explore the idea of primes and their frequency but I agree also that the history and quirks of the mathematicians are interesting sidenotes that help the narrative move along, but don't leave the reader hanging!!!

regardless, I would recommend the book because of the expanse of mathemtical ground covered and the interesting concept introduced. I like the concept, I just did not care for the execution.
16 von 16 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen I'd give this book 6 stars if I could 18. Mai 2006
Von Brian Michalowski - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
Mathematical texts are seldom page-turners, but du Sautoy has written a book that's difficult to put down. He describes the history of the Riemann Hypothesis as an unfolding mystery, and there are genuine cliffhangers that leave you wondering what twists and turns the plot is about to take.

My favorite part of the book, though, consists of the characters. Instead of dryly listing each mathematician's achievement, du Sautoy describes their personalities and quirks. If you have a background in math, you'll have heard of most of the mathematicians in this book, but perhaps not known which were womanizers, which were rivals with each other, and which were just plain nuts. I'd wager that this is the first math text ever written to start with the description of an April Fool's prank.

This plot and character development means there's not as much space for technical explanations as one might like, and du Sautoy consistently avoids technical details to emphasize the ideas behind them instead. For me this was fine, since it's given me the motivation to read a more technical book, but folks who are interested only in the math behind the Riemann Hypothesis and nothing more would be happier selecting another text.
14 von 16 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Worth reading but immensely frustrating. 31. Dezember 2004
Von Dan Bloch - Veröffentlicht auf Amazon.com
Format: Gebundene Ausgabe
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.
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