Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers by Dan Rockmore (PDF)

Description

For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐OK, let’s just stipulate that this guy loves mathematics–me, I’m just oddly fascinated with a topic so esoteric that it takes a graduate degree just to decipher the several alphabets that have been sacrificed to the needs of mathematical symbology. It appears as though I am not alone.However, Dr. Rockmore is staking out a different turf than the other books. His goal seems not to be geared towards explaining the difficult topics so much as giving a lay reader an introduction to the various issues that pertain to the problem of the Riemann Hypothesis. Metaphor and simile are not the best tools for describing higher mathematics. My only criticism of this book is that while it touches on everything it actually explains very little. At first, having read the Sabbagh and Derbyshire books, this was frustrating; however, it becomes clear that the purpose of this book is very different.”Stalking the Riemann Hypothesis” is more in the nature of “Einstein’s Dreams” by Alan Lightman. It is more an attempt to convey the mathematician’s wonder and curiosity than an understanding of the underlying science; seen in this light, I felt the book succeeded.

⭐This is another fine book on the Riemann Hypothesis that, in my view, strongly complements the volumes by John Derbyshire and Marcus du Sautoy. Readers of the book should have some prior exposure to the Riemann Hypothesis (including a basic understanding of complex variables), some understanding of linear algebra, and a modicum of understanding of quantum physics. I say this because, unlike for Derbyshire and du Sautoy, the mathematics underlying the Riemann Hypothesis are more talked about than developed. The strengths of the book are (1) the author’s strong historical perspective, (2) his ability to make extremely esoteric mathematical concepts understandable (and fun!), and (3)a better discussion than provided by either Derbyshire or du Sautoy of the connection between the distribution of the zeta zeroes and the distribution of the prime numbers — in short, why it is that the Riemann Hypothesis is viewed amongst mathematicians as being so important.

⭐This is the latest and we hope the last book on theRH at least until the thing is solved. It is notat all clear what audience the author was aimingfor but if he is afraid even to spell out suchbasics as the euler product, then clearly the wholeenterprise is doomed. The first third of the book -in which the maxim ‘a picture (formula) is worth athousand words’ is inverted – is essentiallya total loss. The only redeeming features are sectionson the connection to quantum chaos and to random matrices.Still, considering the resources available to the author,one expected much more.

⭐Rockmore’s narrative couched within all the historical background of Riemann and his contemporaries was not only interesting but it provided a path to understand all the why’s of the Zeta function, Fourier Analysis, Complex Analysis … and so much more. Most enjoyable with sufficient technical rigor to challenge even the enlightened.

⭐I greatly enjoyed Prof. Rockmore’s clear, non-jargon laden prose. He explains abstract, yet extremely important mathematical ideas with lucidity. I recommend this book highly.

⭐This book is not only a review of the issues, personalities and history of this great problem, but also an assessment of why it matters. A fascinating read.

⭐This wasn’t any good as a hardback and reissuing itin paperback doesn’t change matters.To get an idea of what you are in for, see the reviewsof the hardback version.Bottom line: don’t waste your money.

⭐good book

⭐An enjoyable mathematical romp, but I became increasingly concerned about Rockmore’s reliability with detail and accuracy. He states (p41) that the natural log of 1000000 is about 13, whereas even many A-level pupils can see that the answer is 6 times log10, which is about 6 times 2.3, or 13.8; and on page 57 he seems to think that log10 is about 3. How far can I take on trust any other results, especially of calculations for which simple mental checks are not available?Historical detail leaves much to be desired. Who is John Barrow (page 47), predecessor of Isaac Newton? Rockmore has invented a hybrid of John Wallis and Isaac Barrow! Again, how far can we accept other such historical detail?Heisenberg’s ‘uncertainty principle’ (a misnomer if ever there was one – even Heisenberg referred to ‘indeterminacy’ rather than ‘uncertainty’, a subtle difference) gets an airing, but what a surprise to find the usual ‘popular science book’ fob-off in ‘explaining’ it, rather than a correct explanation. I admit that at this point I was worried that Rockmore himself didn’t understand, especially when you read about so many other demanding technicalities elsewhere in the book.Some folk might say it’s a foolhardy enterprise to attempt popularising the Riemann Hypothesis. A bit like explaining long division to a child who can barely count. But this book is quite readable and gives a revealing insight into the daily lives of professional mathematicians. I found it more enjoyable than some comparable efforts, but it doesn’t achieve the fabulous excitement of Derbyshire’s book (which requires some basic algebraic dexterity).

⭐Excellent

⭐I have read some more books on the Riemann hypothesis (the music of the primes / obssessed with primes). I really adore all of them. I like this book most because it really goes into some of the latest research. It makes the trip from EUler to Gauss to Riemann but also goes way further than montgommery. The onyl thing I don’t like is that for some reason the author didn’t want to include any formula. Sometimes this makes for some cumbersome sentences that would have been far easier to understand in formula form. But his is certainly very highly recommended reading for the mathematically interested.

⭐Excellent book. I liked it very much.

⭐bien bien très intéressant , c’est toute la recherche actuelle des matheux avec les fonctions L et les fonctions elliptiques. C’est le point de rencontre de l’algèbre, de la topologie, de la géométrie et de l’arithmétique

⭐

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