Product Description

This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.

Customer Reviews (1)

Not all papers are in English
I enjoyed reading the book which gave me more appreciation of how some of the important results relating the to Riemann Hypothesis are derived.However, I was disappointed that not all of the included reference papers were in English. I think these could have all been translated. ... Read more

Product Description
Since 1859, when the shy German mathematician Bernhard Riemann wrote an eight-page article giving a possible answer to a problem that had tormented mathematical minds for centuries, the world's greatest mathematicians have been fascinated, infuriated, and obsessed with proving the Riemann hypothesis. They speak of it in awed terms and consider it to be an even more difficult problem than Fermat's last theorem, which was finally proven by Andrew Wiles in 1995.

In The Riemann Hypothesis, acclaimed author Karl Sabbagh interviews some of the world's finest mathematicians who have spent their lives working on the problem--and whose approaches to meeting the challenges thrown up by the hypothesis are as diverse as their personalities.

Wryly humorous, lively, accessible and comprehensive, The Riemann Hypothesis is a compelling exploration of the people who do math and the ideas that motivate them to the brink of obsession--and a profound meditation on the ultimate meaning of mathematics.
... Read more

Customer Reviews (20)

Others deserve learning about complexity too
Karl Sabbagh has done his job well. He never pretended to be a master at this topic. He pretended to give the layman as myself access to the intricate and complex mind of a genius. This is what divulgation is about.

I do not understand those hard ratings or much less comments like "which I could probably do here ultra-briefly if I had a charge number for a couple of hours". It is as if I buy a children's book on physics and complain about the depth of its concepts. Some wise pedagogue would say I was completely confused on what divulgation is about.

If you think you can enlighten our small minds on this matter dedicating a couple hours, I suggest you send a manuscript to the press. I shall be happy to buy it and rate it afterwards.

In scientific literature there ought to be room for books that can be understood by more than one hundred people. Sometimes complexity is an added feature that does not add value...

The fact that I am not an expert at math does not make me a conceptual handicapped. I think this book is a good entrance to the topic. In my case it has triggered the purchase of other deeper approaches.

Well done Karl!!!

Eh
There are a few mistakes:
1) p. 133 In the smallest n-digit primes sequence, there are incorrect 8th and 11th members.
2) p. 190 The values of the Mobius function are listed from one to ten, the 7th is incorrect (should be -1)
3) p. 206 The inline formula for the gamma function is incorrect. It reads "Gamma(n) = n * Gamma(n-1)" but should read "Gamma(n) = (n-1) * Gamma(n-1)".

There is also a fuzzy explanation which contradicts another explanation of T. H. White's "everything not forbidden is compulsory" (p. 185). Sabbagh claims that Gell-Mann says this is how the laws of physics work--that if something is predicted to exist by a theory, then it exists somewhere. Kip Thorne clearly explains in 'Black Holes & Time Warps' that this is not how the laws of physics work. From the book, "Many of the things permitted by the laws of physics are so highly improbable that in practice they will never happen." (p 137) It may be that I misunderstood Sabbagh's writing or that Sabbagh misunderstood Gell-Mann. Nevertheless there is something going on here that doesn't match up.

Other than that, the book was pretty good. It didn't quite give me the dose of mathematics I was looking for, but then again I always ask for more than I can handle. It was very readable.

Where's the Beef?
Nice to have a book to read on the mathematical history and personalities hooked on the search.Way too soft on what the search is for and actual progress in any direction.Has an appendix with some current effort at a proof but without any surrounding discussion it's hardly worth the effort.

The Riemann Hypothesis for non-mathematicians
The book is really about the search for solutions to the Riemann Hypothesis, and contains lots of stories about mathematicians, and mathematical topics. It also includes a wide variety of tangential topics, such as the resolution of previously unsolved problems: the Bierbach Conjecture and Fremat's Last Theorem.

While intended as an accessible account of the Riemann Zeta Function and the Riemann Hypothesis for the non-mathematician, it uses overly trite and simplistic descriptions of basic mathematical concepts such as prime numbers, complex numbers, and zeros of functions, while glossing over more advanced concepts, such as L-functions, Hilbert Spaces, and Random Matrices. Clearly, this was written by a mathematical novice.

YOU can understand the Riemann Hypothesis....after this commercial break.
I'm halfway through this book and am getting very frusturated.The beginning chapters did a very good job laying out the foundations of the RH.You begin to think you may, finally, be able to understand what the RH is about.However, I am realizing that less and less of the book is actually about the RH or the RZF the farther I progress.An entire chapter will waste space describing a mathematician (physical appearance, quirky behavorial traits), his unrelated contributions to math, and either a vague description of the work he is doing to prove the RH or some opinion on whether it will be solved or not. The book has devolved into irritating tangents unrelated to my understanding of the RH/RZF...clever math poems, crap about Fermats theorem, etc.I would even be forgiving if he was describing the life and times of Riemann himself.There are plenty of cute little math stories here, but I didnt waste $14.00 on a book about the RH to NOT read about the RH.I want every single chapter to build on the previous, start slow, explain the concepts, and raise the bar.If you get stuck, too bad...research the web and pick the book up later.Thats what I wanted here, and this book is turning out to be a letdown.
There is very good information for someone completely new to the concept of the RH or RZF, but this book is 4 chapters of useful material spread out into an entire book filled with math-related lore.I appreciate what Sabbagh is trying to do here, but lets be realistic.This is a very advanced mathematical concept; you can't hand-hold someone through this from start to finish.At some point he should challenge the reader and escalate the difficulty of the book, but this does not appear to happen.Instead we get a smoke-screen...a cliffhanger.Would I recommend this book?Only to those who have absolutely no understanding of what the RH/RZF is and want a springboard to something else. ... Read more

Product 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. ... Read more

Customer Reviews (14)

If God gave us the integers why were prime numbers included?
When Albert Einstein sought the mathematics to bring his general theory of relativity to life, he found his solution in the works of none other than Bernard Reimann.

And although Reimann died young (at 39) apparently the special math necessary for relativity was not Reimann's only masterstroke.

He also developed a theta function or formula for predicting the placement of prime numbers in the number line.As you may recall from elementary mathematics, prime numbers are those numbers only divisible by themselves and one.

Though casual thought on the matter may initially lead one to conclude that prime numbers would eventually be exhausted (indeed the higher you go the more rare they do become) mathematical proofs dating back to Euclid show that like the integer line they accompany they go on forever.

But again figuring out how they can be located algorithmically within that forever was long a mathematics holy grail until 1859 when Bernard Reimann posited a hypothesis for locating them.His hypothesis or zeta function involves incredibly complicated mathematics certainly beyond the scope of this book so if you want to understand it you may do better to read Reimann's Zeta Function.

However if you want the outlines of search that goes from ancient Greece all the way to modern times, this book makes quick accessible reading.

Lacks clarity and focus
I don't know what it is with the latest books trying to popularize certain branches of contemporary and modern science, but it seems to me that poetic and decorated language now sells better than scientific clarity and educational value. This book serves more as a general overview into a wide range of more or less related open and solved problems in mathematics and physics rather than an interesting introduction into the problem of prime number distribution and the Riemann hypothesis. The many analogies, which are often explained in too much detail, do not only distract from the main topic, but often lack a considerable amount of relevance. In several cases they don't even lead to any meaningful conclusion for the particular problem at hand. Near the end of the book, the author somewhat succeeds to "close the circle", but overall this work leaves much to be desired. In my opinion a great opportunity to explain the book's topic to a general audience was missed.

Not surprising to read other reviews here
How do you write a book about mathematics and numbers without any? I got lost in the sea of abstract forced analogies and ended up more confused, irritated, and lost than I had when I began reading the book. 80 pages into the book, I give up and will read Derbyshire's book, about which I have read good things.

Disclaimer: I am not a mathematician by training but have a science/engineering background. Even if I did not understand all the details, I had hoped the book would at least grip my attention and make me want to learn more.

What a contrast (and a frustrating one at that) attempting to read this book was...especially considering I just finished reading QED - The strange theory of light and matter by Richard Feynman. There couldn't be two contrasting writing styles!

A diverging book!
I felt very irritated by reading this book. Many analogies and side stories lead to loose the focused main subject. Stories always diverge, never converge to any meaningful understanding. Avoiding equations and narrative description of the content of equations rather makes even difficult to understand. Simply showing equations is much better. A very badly organized poor book

forget it
This wasn't any good as a hardback and reissuing it
in paperback doesn't change matters.
To get an idea of what you are in for, see the reviews
of the hardback version.
Bottom line: don't waste your money. ... Read more

Product Description
This book unlocks the mystery of Riemann Hypothesis in simple high school mathematics. The author emphasizesreal world applications and initiates the solution based on real analysis and technical basis rather than complex(and imaginary) mathematics. By little discipline, anybodywith mathematics proficiency, with the help of knowledge revealed in this book, can attain the leadership position in digital age. ... Read more

Customer Reviews (2)

Legendary Solution/ Colossal Engineering Feat
Engineering Analysis, Advanced Engineering Analysis are typical engineering mathematics courses in Engineering Graduate Schools. While engineering professionals may not have time, patience or background to delve around the applied or pure mathematics required to fully realize many practical engineering applications, generally the texts used for Engineering Analysis are Advanced Engineering Mathematics by Kreyszig or Advanced Engineering Mathematics by Wylie. To know what is truly required beyond these texts distinguishes pro engineer from novice. This book fills this huge gap and hence is worth it's weight in gold.

I don't know what is the aim of the writer writing that book!!!!
When I received the book, I felt excited.
But how disappointed I am when I open the book.
This book just packed with equations without explanation
and how the equations are derived. To simplify my comment:
if you should know how to derive those equations,
your mathamatical knowledge is much higher than requiring
that book, if you do not know what these equations are,
then you should not read this book. So I cannot suggest
a reason to buy this book !!!!! ... Read more

Product Description
This volume contains the proceedings of the conference ""Casimir Force, Casimir Operators and the Riemann Hypothesis- Mathematics for Innovation in Industry and Science"" held in November 2009 in Fukuoka (Japan). The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry ... Read more

Product Description
The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function. ... Read more

Customer Reviews (1)

did he really do it?
I am not a professional mathematician, and of course I may have misunderstood ... but in this book the author appears to claim to have proved the most important and famous outstanding problem in mathematics: the Riemann Hypothesis.

After all, he says in the Summary at the end that his equations show that all the zeroes of the zeta function have real part 1/2, which sounds exactly like the Riemann Hypothesis ....

Now, his formulae look impressively profound and significant to me, with lots of cool-looking symbols and Greek letters, but what bothers me is ... why haven't I read about this in the New York Times? Because if the author really has solved the Riemann Hypothesis, it would seem to have merited at least a mention, and more likely a front-page article, in the Good Gray Lady.

So I'm starting to wonder .... could this be another one of those embarrassing episodes ... well, enough said.



... Read more

Product Description
Chapters: Riemann Zeta Function, Dirichlet's Theorem on Arithmetic Progressions, Generalized Riemann Hypothesis, Langlands Program, Dirichlet Character, Weil Conjectures, Polylogarithm, Basel Problem, Hurwitz Zeta Function, Zeta Function Universality, Lindelöf Hypothesis, Apéry's Constant, Birch and Swinnerton-Dyer Conjecture, Zeta Constant, Apéry's Theorem, Euler Product, Artin L-Function, Hecke Character, Riesz Function, Subgroup Growth, Lerch Zeta Function, Explicit Formula, Multiplication Theorem, Hilbert-pólya Conjecture, Dirichlet Series, Zeta Function Regularization, Proof of the Euler Product Formula for the Riemann Zeta Function, Local Zeta-Function, Hasse-weil Zeta Function, Rational Zeta Series, Riemann-siegel Theta Function, Shimura Variety, Dirichlet Eta Function, Dirichlet L-Function, Functional Equation, Riemann-siegel Formula, Selberg Class, Stark Conjectures, Brumer-stark Conjecture, Selberg Zeta Function, Clausen Function, Li's Criterion, Special Values of L-Functions, Riesz Mean, Dedekind Zeta Function, Montgomery's Pair Correlation Conjecture, Ramanujan-petersson Conjecture, P-Adic L-Function, Dirichlet Beta Function, Ihara Zeta Function, Lefschetz Zeta Function, Siegel Zero, Stieltjes Constants, Artin-mazur Zeta Function, Hadjicostas's Formula, Weil's Criterion, Riemann Xi Function, Prime Zeta Function, Fekete Polynomial, Chowla-mordell Theorem, Multiple Zeta Function, Zetagrid, Equivariant L-Function, Grand Riemann Hypothesis, Goss Zeta Function, Minakshisundaram-Pleijel Zeta Function, Epstein Zeta Function. Source: Wikipedia. Pages: 298. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In mathematics, the Riemann hypothesis, proposed by Bernhard Riemann (1859), is a conjecture about the distribution of the zeros of the Riemann zeta-function which states that all non...More: http://booksllc.net/?id=19344125 ... Read more

Product Description
Whether you are a student at Princeton University, MIT, or just an enthusiastic science fiction reader trying to get some more information on Wikipedia, you might be interested in the famous Riemann Hypothesis. Well, this book may give you everything you want. Not only because it deals with this mathematical mystery. It also tells you about things like cars, music, time traveling, higher dimensional spaces, and much more.

For more than a century scientists have tried to solve the mystery behind the Riemann Hypothesis. But up to today nobody has been able to come up with a definitive proof. This is bad news since large parts of mathematics seem to be built on quicksand as long as the proof of the Riemann Hypothesis is still hanging in the air. A mathematics institute in the US even offers a million dollars to the one solving the mystery. In this book someone actually proves the Riemann Hypothesis. In a completely new graphical way. Believe me; the guys in this story are getting really rich. ... Read more

Product Description
Purchase includes free access to book updates online and a free trial membership in the publisher's book club where you can select from more than a million books without charge. Chapters: P Versus Np Problem, Poincaré Conjecture, Millennium Prize Problems, Riemann Hypothesis, Hodge Conjecture, Navier-stokes Existence and Smoothness, Birch and Swinnerton-Dyer Conjecture, Yang-mills Existence and Mass Gap. Excerpt:Millennium Prize Problems In mathematics , the Birch and Swinnerton-Dyer conjecture relates the rank of the abelian group of points over a number field of an elliptic curve E to the order of the zero of the associated L-function L ( E , s ) at s = 1. Specifically, it is conjectured that the Taylor expansion of L ( E , s ) at s = 1 is where c is not zero and r is the rank of E over the field of rational numbers . As of 2010, it has been proven only in special cases, all of rank less than or equal to 1. It has been an open problem for around 40 years, and has stimulated much research; its status as one of the most challenging mathematical questions has become widely recognized. It is one of the Millennium Prize Problems listed by the Clay Mathematics Institute , which has offered a $ 1,000,000 prize for the first correct proof. Background In 1922 Louis Mordell proved Mordell's theorem : the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite sub-set of the rational points on the curve, from which all further rational points may be generated. If the number of rational points on a curve is infinite then some point in a finite basis must have infinite order. The number of independent basis points with infinite order is called the rank of the curve, and is an important invariant property of an elliptic curve. If the rank of an elliptic curve is 0, then the curve has only a finite number of rational points. On the other hand, if the rank of the curve is greater than 0, then the curve has an... ... Read more

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One of the Millennium prize problems has haunted mathematicians since Bernhard Riemann propounded it in 1859; I take up suggestions here by physicist Freemon Dyson and others that the solution may reside not in abstract mathematics, but in the most fundamental domain of nature—that of quantum mechanics. I propose that the orbits of the oscillatory nucleus of the hydrogen atom may, in fact, be fundamentally related to the distribution of the prime numbers and to Riemann's hypothesis. ... Read more

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How many prime numbers up to 10?2, 3, 5, and 7 are the four prime numbers up to 10.Lehmer have listed the prime numbers up to 10,006,721, and we can count with his list.A supercomputer was used to count how many primes are up to a Billion times a Trillion.But isnt there some formula to replace counting?In 1859 Riemann derived -assuming the Riemann Hypothesis- the Formula for the Count of the Primes up to a given number.The Riemann Hypothesis enables us to compute an infinite series in the formula, at the infinitely many zeros of the Riemann Zeta function on the line 1/2+iy.The Riemann Hypothesis Series can only be approximated by its partial sums, which converge unpredictably.The approximation of the Hypothesis Series, and of the Count of the Primes up to a number, may improve by the use of many zeta zeros.We use Riemanns Formula to approximate the number of Primes up to a(Billion)x(Trillion)=10^21. ... Read more

Product Description
This digital document is an article from Journal of Mathematics and Statistics, published by Science Publications on January 1, 2009. The length of the article is 5553 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available immediately after purchase. You can view it with any web browser.

From the author: Key words: Riemann hypothesis, zeta function, gamma function, errors, prime, asymptote, integral

Citation Details
Title: A numerical test on the Riemann hypothesis with applications.
Author: N.K. Oladejo
Publication: Journal of Mathematics and Statistics (Magazine/Journal)
Date: January 1, 2009
Publisher: Science Publications
Volume: 5Issue: 1Page: 47(7)

Distributed by Gale, a part of Cengage Learning ... Read more

Product Description
This digital document is an article from New Criterion, published by Thomson Gale on November 1, 2005. The length of the article is 1090 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available in your Amazon.com Digital Locker immediately after purchase. You can view it with any web browser.

Citation Details
Title: Hypothesis finxit.(Stalking the Riemann Hypothesis)(Book Review)
Author: John Derbyshire
Publication: New Criterion (Magazine/Journal)
Date: November 1, 2005
Publisher: Thomson Gale
Volume: 24Issue: 3Page: 71(3)

Article Type: Book Review

Distributed by Thomson Gale ... Read more

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Chapters: Analytic Geometry, Homological Algebra, Bézout's Theorem, Generalized Riemann Hypothesis, Motive, Dessin D'enfant, Glossary of Arithmetic and Diophantine Geometry, Hodge Structure, Smooth Function, Nakayama Lemma, Resolution of Singularities, Algebraic K-Theory, Grassmannian, Valuation, Gröbner Basis, Calabi-yau Manifold, Chow Ring, Cotangent Complex, Algebraic Variety, Crystalline Cohomology, Esquisse D'un Programme, Macdonald Polynomial, Hilbert Scheme, Flat Module, Algebraic Geometry and Analytic Geometry, Homogeneous Polynomial, Quantum Cohomology, Gromov-witten Invariant, Drinfel'd Module, General Position, Ample Line Bundle, Milnor Number, Flip, Generic Property, Minimal Model Program, Hilbert's Arithmetic of Ends, Regular Local Ring, Adjunction Formula, Néron-tate Height, Pseudoholomorphic Curve, Codimension, Injective Sheaf, Characteristic Set, Kähler Manifold, Conifold, Dévissage, Rational Mapping, Arakelov Theory, Hasse-weil Zeta Function, Cohen-macaulay Ring, Algebraic Stack, List of Algebraic Geometry Topics, Lefschetz Theorem on (1,1)-Classes, A¹ Homotopy Theory, Adequate Equivalence Relation, Italian School of Algebraic Geometry, Fondements de La Géometrie Algébrique, Standard Conjectures on Algebraic Cycles, Shimura Variety, Algebraic Space, Cone of Curves, Hyperkähler Manifold, Deformation Theory, Noncommutative Algebraic Geometry, Flat Topology, Descent, Excellent Ring, Stable Vector Bundle, Finite Morphism, Amoeba, Tropical Geometry, Canonical Singularity, Complete Intersection, Tangent Cone, N!-Conjecture, Conic Bundle, Irreducible Component, Canonical Ring, Residue Field, Abstract Algebraic Variety, Inverse Image Functor, Kähler Differential, Formal Scheme, Grothendieck's Galois Theory, Mnev's Universality Theorem, Jacobian Conjecture, Local Parameter, Period, Differential of the First Kind, Positive Form, Zariski Tangent Space, Schubert Variety, Generic Point, Noetherian Topological Space, Néron ...More: http://booksllc.net/?id=1997 ... Read more

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This digital document is an article from Science News, published by Science Service, Inc. on September 27, 2008. The length of the article is 684 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available immediately after purchase. You can view it with any web browser.

Citation Details
Title: Quantum physics may offer clues to solving prime number problem: electron energy levels linked to Riemann hypothesis.(Numbers)
Author: Davide Castelvecchi
Publication: Science News (Magazine/Journal)
Date: September 27, 2008
Publisher: Science Service, Inc.
Volume: 174Issue: 7Page: 14(1)

Distributed by Gale, a part of Cengage Learning ... Read more

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"Excerpt from the book..."

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[formula] [formula] die Componenten der Geschwindigkeit sind, mit der eine
Flüssigkeit parallel zur [formula]-Ebene strömt. Wir mögen uns diese
Flüssigkeit zwischen zwei Ebenen eingeschlossen denken, die parallel zur
[formula]-Ebene verlaufen, oder auch uns vorstellen, dass die Flüssigkeit
als unendlich dünn
... Read more

Customer Reviews (1)

Unreadable! Formulas are missing
You can see already from the sample text that all the formulas in the original text are replaced by "[formula]". A mathematical textbook with the formulas removed is worthless, don't waste your money on this. Honestly, I expect a little more quality control in the Kindle store. ... Read more