The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics (P.S.)

This is a fantastic history book on the efforts of some of the greatest mathematical (and physicist's )minds from Gauss and Riemann to Selberg and Alain Connes in their efforts to crack one of the most beautiful problems: the distribution of prime numbers. Some of the greatest insights in mathematics and in science are when somebody makes an unexpected link between two different areas. This is what the genius of Riemann suggested connecting the prime numbers to the zeroes of a function of complex variable. The conjectured location of the zeroes of this function, the Riemann Hypothesis, is the only unsolved problems of Hilbert's list and has become, with all the honours, one of the Millenium problems, worth one million dollars, but that is nothing compared to the instant glory acquired by whoever can solve it. Unlike the other famous problem, Fermat's Last Theorem, many theorems depend on the Hypothesis. The book reads like a thriller and indeed some of the anecdotes are those of thriller, like the mysteries still contained in the remaining unpublished papers of Riemann, the Nachlass, and the disappearance of one of his notebooks and the destruction of a large number of his notes by his housekeeper. Another example is André Weil being accused of espionage in Finland for writing mathematical letters to Russian colleagues, being condemned to death and being spared of the death sentence by a chance dinner of the Police Chief with Nevalinna (a Finish mathematician) the night before the execution. Billions of zeroes are known to be in the critical line and even we know that a high percentage are there, but we cannot prove with absolute certainty that they are all there. And, as Littlewood, showed, great empirical evidence is not a guarantee of mathematical certainty. It was interesting to learn that there is a formula that outputs (when the value is positive) all primes and only primes. This is a highly recommended book for all people interested in mathematics, although some college level of this subject will make it easier to digest.

This book is a very enjoyable read that gives a lot of background information on the key players of number theory. I've seen reviews criticizing the fact that there is very little math in this book. While this is true, one shouldn't see it as a math book but a history book. Unfortunately the Kindle version is missing the illustrations. I don't quite understand this omission. Otherwise, the book is a page turner goes well with other books on the subject, as it adds so much to the names behind those amazing theorems and conjectures.

A brilliant summary regarding prime numbers, with the best explanation in general terms of the Riemann Hypothesis and its implications that I have yet come across. The many biographical inclusions of pioneering mathematicians makes for added interest, and extends to computing and cryptography, finally embracing quantum chaos. First published in 2003, this is still a very modern book by Marcus du Sautoy, and at Amazon;s price of just $10.17 US, why wouldn't you include it in your library? A great read.

Highly recommend this book to people who are interested in math! I read it as an undergraduate --it was a great read!

Great book for its exact way of describing the progress in mathematics. The zeta of Riemann born as statistical interpretation of number of primes in an interval. In 1800 many mathematical researchers follow this position, trying to show it, particularly Gauss and Hilbert. But a true proof looks like very difficult to find. In 1900 this proof is tried at computer as for the theorem of 4-colours, but without important results. Finally in last years Connes has used those questions for the problem of the renormalizzazion of the quantum space. That produces the translation of the concepts from geometry to algebra.

Great read for math and non-math types. Many mathematicians lives seems sad and lonely. But there's the rush of discovering something. Riemann's housekeeper: argh! It does read like a detective novel. Clever writing.

An excellent history of the mathematic fraternity over the past three or four centuries. The Riemann hypothesis being the one major challenge for the other mathematicians to prove right or wrong. The author follows a step by step timeline with the prodigious attempts in each period explained in detail. Easy to read and follow if you are mathematically inclined and difficult to put it down.

This book is great in tracking the history of the Riemann hypothesis, the Mathematicians who approached it, and related issues. However personally I wanted to understand more about the math behind the Riemann hypothesis, but it seems this book is not intended for this. Overall it was a nice book to read.

Fascinating story about the prime numbers, thoroughly enjoyed every page.

Great book. Clearly and beautifully written.

I bought this for my mathematician son-in-law a year or so ago, and borrowed it to read last week. It's a brisk description of efforts made by mathematicians to understand the way in which the prime numbers (2, 3, 5, 7, 11, 13...) are distributed. This problem was originally looked at by Euclid (who proved there were infinitely many primes), but work on how they're distributed started with Gauss, who suggested the formula N/log(N) for their asymptotic distribution. This led onto Riemann's investigation using his zeta function, and his hypothesis (that the real part of all non-trivial zeros of the zeta function is 1/2). There's a deep connection between the hypothesis and the distribution of primes, but - so far - the hypothesis has resisted all attempts to prove it. There's a cavalcade of mathematicians featured in this book: from Gauss and Riemann through Hilbert, Hardy, Littlewood, Ramanujan, Erdos and Turing to Jon Keating (whom I heard speak about proving the Riemann hypothesis at a conference in Sydney around twenty years ago). The author does a good job of explaining the mathematics and the way in which each discovery builds on previous work to move the subject forward: he describes this memorably as a "mathematical relay race" [p102]. He also makes the link between pure research in prime numbers and commercial applications such as encryption. Thus, there's a lengthy digression on the RSA cryptosystem, which relies on the difficulty of of factoring the product of two large prime numbers - this would be made much easier if the distribution of primes was known. I enjoyed reading this book. Of course, the explanation of the mathematics has had to be simplified for the lay reader, but the author uses some nice analogies ("sea level" for the Riemann zeros, for example) which convey much of the sense, and is good on the personalities and interactions of the people working in this most abstruse of fields. Recommended.

Great book

This book shows that Mathematics is the base for all advanced sciences. I enjoyed reading it