Stalking The Riemann Hypothesis

If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights.

Stalking The Riemann Hypothesis

Author: Daniel Nahum Rockmore

Publisher: Random House

ISBN: 1446483622

Page: 304

View: 265

Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.

Stalking the Riemann Hypothesis

If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights.

Stalking the Riemann Hypothesis

Author: Dan Rockmore

Publisher: Vintage

ISBN: 9780099429944

Page: 288

View: 350

Like a hunter who sees 'a bit of blood' on the trail, that's how Princeton mathematician Peter Sarnak describes the feeling of chasing an idea that seems to have a chance of success. If this is so, then the jungle of abstractions that is mathematics is full of frenzied hunters these days. They are out stalking big game: the resolution of 'The Riemann Hypothesis', seems to be in their sights. The Riemann Hypothesis is about the prime numbers, the fundamental numerical elements. Stated in 1859 by Professor Bernhard Riemann, it proposes a simple law which Riemann believed a 'very likely' explanation for the way in which the primes are distributed among the whole numbers, indivisible stars scattered without end throughout a boundless numerical universe. Just eight years later, at the tender age of thirty-nine Riemann would be dead from tuberculosis, cheated of the opportunity to settle his conjecture. For over a century, the Riemann Hypothesis has stumped the greatest of mathematical minds, but these days frustration has begun to give way to excitement. This unassuming comment is revealing astounding connections among nuclear physics, chaos and number theory, creating a frenzy of intellectual excitement amplified by the recent promise of a one million dollar bounty. The story of the quest to settle the Riemann Hypothesis is one of scientific exploration. It is peopled with solitary hermits and gregarious cheerleaders, cool calculators and wild-eyed visionaries, Nobel Prize-winners and Fields Medalists. To delve into the Riemann Hypothesis is to gain a window into the world of modern mathematics and the nature of mathematics research. Stalking the Riemann Hypothesis will open wide this window so that all may gaze through it in amazement.

The Riemann Hypothesis

... have been written to introduce the Riemann hypothesis to the general public. ... Dan Rockmore's Stalking the Riemann Hypothesis: The Quest to Find the ...

The Riemann Hypothesis

Author: Peter Borwein

Publisher: Springer Science & Business Media

ISBN: 0387721258

Page: 533

View: 558

The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.

What Are the Arts and Sciences

The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas.

What Are the Arts and Sciences

Author: Dan Rockmore

Publisher: Dartmouth College Press

ISBN: 1512601039

Page: 376

View: 935

What constitutes the study of philosophy or physics? What exactly does an anthropologist do, or a geologist or historian? In short, what are the arts and sciences? While many of us have been to college and many aspire to go, we may still wonder just what the various disciplines represent and how they interact. What are their origins, methods, applications, and unique challenges? What kind of people elect to go into each of these fields, and what are the big issues that motivate them? Curious to explore these questions himself, Dartmouth College professor and mathematician Dan Rockmore asked his colleagues to explain their fields and what it is that they do. The result is an accessible, entertaining, and enlightening survey of the ideas and subjects that contribute to a liberal education. The book offers a doorway to the arts and sciences for anyone intrigued by the vast world of ideas.

The Book Review Digest

Rowse , T. Number study See Number theory Number theory See also Galois
theory Rockmore , D. N. Stalking the Riemann hypothesis Numbers , Natural See
also Numbers , Prime Numbers , Prime Rockmore , D. N. Stalking the Riemann ...

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All the Math You Missed

There is also the recent The Riemann Hypothesis [191] by Roland van der Veen and ... Dan Rockmore's Stalking the Riemann Hypothesis: The Quest to Find the ...

All the Math You Missed

Author: Thomas A. Garrity

Publisher: Cambridge University Press

ISBN: 1009006207

Page:

View: 870

Beginning graduate students in mathematical sciences and related areas in physical and computer sciences and engineering are expected to be familiar with a daunting breadth of mathematics, but few have such a background. This bestselling book helps students fill in the gaps in their knowledge. Thomas A. Garrity explains the basic points and a few key results of all the most important undergraduate topics in mathematics, emphasizing the intuitions behind the subject. The explanations are accompanied by numerous examples, exercises and suggestions for further reading that allow the reader to test and develop their understanding of these core topics. Featuring four new chapters and many other improvements, this second edition of All the Math You Missed is an essential resource for advanced undergraduates and beginning graduate students who need to learn some serious mathematics quickly.

The Joy of x

For more emphasis on the latest developments but still at a very accessible level, see D. Rockmore, Stalking the Riemann Hypothesis (Pantheon, 2005), ...

The Joy of x

Author: Steven Strogatz

Publisher: Houghton Mifflin Harcourt

ISBN: 0547517661

Page: 336

View: 745

“Delightful . . . easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!”—Scientific American Many people take math in high school and promptly forget much of it. But math plays a part in all of our lives all of the time, whether we know it or not. In The Joy of x, Steven Strogatz expands on his hit New York Times series to explain the big ideas of math gently and clearly, with wit, insight, and brilliant illustrations. Whether he is illuminating how often you should flip your mattress to get the maximum lifespan from it, explaining just how Google searches the internet, or determining how many people you should date before settling down, Strogatz shows how math connects to every aspect of life. Discussing pop culture, medicine, law, philosophy, art, and business, Strogatz is the math teacher you wish you’d had. Whether you aced integral calculus or aren’t sure what an integer is, you’ll find profound wisdom and persistent delight in The Joy of x.

The Best Writing on Mathematics 2013

In his book Stalking the Riemann Hypothesis, mathematician and computer scientist Dan Rockmore describes that meeting: As Dyson ...

The Best Writing on Mathematics 2013

Author: Mircea Pitici

Publisher: Princeton University Press

ISBN: 0691160414

Page: 272

View: 880

This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2013 makes available to a wide audience many articles not easily found anywhere else--and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Philip Davis offers a panoramic view of mathematics in contemporary society; Terence Tao discusses aspects of universal mathematical laws in complex systems; Ian Stewart explains how in mathematics everything arises out of nothing; Erin Maloney and Sian Beilock consider the mathematical anxiety experienced by many students and suggest effective remedies; Elie Ayache argues that exchange prices reached in open market transactions transcend the common notion of probability; and much, much more. In addition to presenting the year's most memorable writings on mathematics, this must-have anthology includes a foreword by esteemed mathematical physicist Roger Penrose and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us--and where it is headed.

The Pythagorean Theorem

Despite numerous attempts, the conjecture remains unproved. ... and Dan Rockmore, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime ...

The Pythagorean Theorem

Author: Eli Maor

Publisher: Princeton University Press

ISBN: 0691196885

Page: 280

View: 166

An exploration of one of the most celebrated and well-known theorems in mathematics By any measure, the Pythagorean theorem is the most famous statement in all of mathematics. In this book, Eli Maor reveals the full story of this ubiquitous geometric theorem. Although attributed to Pythagoras, the theorem was known to the Babylonians more than a thousand years earlier. Pythagoras may have been the first to prove it, but his proof—if indeed he had one—is lost to us. The theorem itself, however, is central to almost every branch of science, pure or applied. Maor brings to life many of the characters that played a role in its history, providing a fascinating backdrop to perhaps our oldest enduring mathematical legacy.

The New Criterion

... 89 ; Hypothesis finxit a review of Stalking the Riemann Hypothesis by Dan
Rockmore ( BOOKS ) , Nov . , 71 Donoghue , Denis Defeating the poem on
teaching poetry , April , 14 Downing , Ben Duff Cooper ' s game book a review of
The Duff ...

The New Criterion

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Pythagoras Legacy

Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers. New York: Vintage. Rudman, Peter S. 2010. The Babylonian Theorem: The ...

Pythagoras  Legacy

Author: Marcel Danesi

Publisher: Oxford University Press

ISBN: 0192593781

Page: 160

View: 753

As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of science, engineering, and even philosophy. A so called ", mathematics has guided and stimulated many aspects of human innovation down through the centuries. In this book, Marcel Danesi presents a historical overview of the ten greatest achievements in mathematics, and dynamically explores their importance and effects on our daily lives. Considered as a chain of events rather than isolated incidents, Danesi takes us from the beginnings of modern day mathematics with Pythagoras, through the concept of zero, right the way up to modern computational algorithms. Loaded with thought-provoking practical exercises and puzzles, Pythagoras' Legacy allows the reader to apply their knowledge and discover the significance of mathematics in their everyday lives.

The Mathematical Function Computation Handbook

Stalking the Riemann Hypothesis: the Quest to Find the Hidden Law of Prime Numbers. Vintage Books, New York, NY, USA, 2006. ISBN 0-375-72772-8 (paperback); ...

The Mathematical Function Computation Handbook

Author: Nelson H.F. Beebe

Publisher: Springer

ISBN: 3319641107

Page: 1115

View: 526

This highly comprehensive handbook provides a substantial advance in the computation of elementary and special functions of mathematics, extending the function coverage of major programming languages well beyond their international standards, including full support for decimal floating-point arithmetic. Written with clarity and focusing on the C language, the work pays extensive attention to little-understood aspects of floating-point and integer arithmetic, and to software portability, as well as to important historical architectures. It extends support to a future 256-bit, floating-point format offering 70 decimal digits of precision. Select Topics and Features: references an exceptionally useful, author-maintained MathCW website, containing source code for the book’s software, compiled libraries for numerous systems, pre-built C compilers, and other related materials; offers a unique approach to covering mathematical-function computation using decimal arithmetic; provides extremely versatile appendices for interfaces to numerous other languages: Ada, C#, C++, Fortran, Java, and Pascal; presupposes only basic familiarity with computer programming in a common language, as well as early level algebra; supplies a library that readily adapts for existing scripting languages, with minimal effort; supports both binary and decimal arithmetic, in up to 10 different floating-point formats; covers a significant portion (with highly accurate implementations) of the U.S National Institute of Standards and Technology’s 10-year project to codify mathematical functions. This highly practical text/reference is an invaluable tool for advanced undergraduates, recording many lessons of the intermingled history of computer hardw are and software, numerical algorithms, and mathematics. In addition, professional numerical analysts and others will find the handbook of real interest and utility because it builds on research by the mathematical software community over the last four decades.

An Invitation to Modern Number Theory

[Roc] D. Rockmore, Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers, Pantheon, New York, 2005.

An Invitation to Modern Number Theory

Author: Steven J. Miller

Publisher: Princeton University Press

ISBN: 0691215979

Page:

View: 706

In a manner accessible to beginning undergraduates, An Invitation to Modern Number Theory introduces many of the central problems, conjectures, results, and techniques of the field, such as the Riemann Hypothesis, Roth's Theorem, the Circle Method, and Random Matrix Theory. Showing how experiments are used to test conjectures and prove theorems, the book allows students to do original work on such problems, often using little more than calculus (though there are numerous remarks for those with deeper backgrounds). It shows students what number theory theorems are used for and what led to them and suggests problems for further research. Steven Miller and Ramin Takloo-Bighash introduce the problems and the computational skills required to numerically investigate them, providing background material (from probability to statistics to Fourier analysis) whenever necessary. They guide students through a variety of problems, ranging from basic number theory, cryptography, and Goldbach's Problem, to the algebraic structures of numbers and continued fractions, showing connections between these subjects and encouraging students to study them further. In addition, this is the first undergraduate book to explore Random Matrix Theory, which has recently become a powerful tool for predicting answers in number theory. Providing exercises, references to the background literature, and Web links to previous student research projects, An Invitation to Modern Number Theory can be used to teach a research seminar or a lecture class.

Stalking White Crows

Imagine that she has a dream in which she solves the Riemann Hypothesis in mathematics. However great the dream accomplishment might make her feel, ...

Stalking White Crows

Author: Jack Crittenden

Publisher: John Hunt Publishing

ISBN: 1789042194

Page: 328

View: 797

How making up our minds and the makeup of our minds can help us live better and die better. We live in a climate where feelings trump reason and evidence. Lies are treated as “alternative facts.” At the same time, it seems our culture does not want us to treat altered or higher states of consciousness seriously. Focusing both on evidence and on such states of consciousness can reorient our attitudes. Jack Crittenden asks the reader to think about life after death, about the basis of morality and the essence of spirituality, about the meaning of happiness, about the path of dying, and about the proper role of work in our lives and how education connects to that role. What if our memories, thoughts, and whole personality lived on after we died? What if morality were based on reasons and evidence and not on God and sacred texts? What if happiness lies not in what we think, how we feel, and what we long for, but in living in the present and in the dying of the self itself? Experiences of and the evidence on altered and higher states of consciousness can lead us to better lives and better deaths.

Asymptotic Analysis of Differential Equations

See “Stalking the Riemann Hypothesis” by Dan Rockmore, Pantheon (2005). Thus it appears that the zeros of the zeta function are given by the eigenvalues of ...

Asymptotic Analysis of Differential Equations

Author: R. B. White

Publisher: World Scientific

ISBN: 1848166079

Page: 405

View: 358

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

The Nature of Computation

Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers. Pantheon Books, 2005. [505] [714] Yurii Rogozhin.

The Nature of Computation

Author: Cristopher Moore

Publisher: Oxford University Press

ISBN: 0199233217

Page: 985

View: 146

The boundary between physics and computer science has become a hotbed of interdisciplinary collaboration. In this book the authors introduce the reader to the fundamental concepts of computational complexity and give in-depth explorations of the major interfaces between computer science and physics.

The Bloch Kato Conjecture for the Riemann Zeta Function

Let us choose a geometric point S : SpecK – S and let 2,5 be the stalk of 2, at S. We consider 2,5 as a finite set with a continuous Galois action.

The Bloch   Kato Conjecture for the Riemann Zeta Function

Author: John Coates

Publisher: Cambridge University Press

ISBN: 1316241300

Page:

View: 915

There are still many arithmetic mysteries surrounding the values of the Riemann zeta function at the odd positive integers greater than one. For example, the matter of their irrationality, let alone transcendence, remains largely unknown. However, by extending ideas of Garland, Borel proved that these values are related to the higher K-theory of the ring of integers. Shortly afterwards, Bloch and Kato proposed a Tamagawa number-type conjecture for these values, and showed that it would follow from a result in motivic cohomology which was unknown at the time. This vital result from motivic cohomology was subsequently proven by Huber, Kings, and Wildeshaus. Bringing together key results from K-theory, motivic cohomology, and Iwasawa theory, this book is the first to give a complete proof, accessible to graduate students, of the Bloch–Kato conjecture for odd positive integers. It includes a new account of the results from motivic cohomology by Huber and Kings.