Prime Obsession Bernhard Riemann And The Greatest Unsolved Problem In Mathematics

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Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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Author by : John Derbyshire
Languange Used : English, France, Spanish, Italia and chinese
Page : 429
Isbn : 0309512573
Identifier : 9780309512572
Release : 2003-04-29
Publisher by : Joseph Henry Press
Category : Science
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Description : Read Now Prime Obsession by John Derbyshire and you can download with pub, pdf, txt, doc, and more file format with free account. in august 1859 bernhard riemann, a little-known 32-year old mathematician, presented a paper to the berlin academy titled: "on the number of prime numbers less than a given quantity." in the middle of that paper, riemann made an incidental remark — a guess, a hypothesis. what he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. today, after 150 years of careful research and exhaustive study, the question remains. is the hypothesis true or false? riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic — defining a precise formula to track and identify the occurrence of prime numbers. but it is that incidental remark — the riemann hypothesis — that is the truly astonishing legacy of his 1859 paper. because riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows — subtle variations in the distribution of those prime numbers. brilliant for its clarity, astounding for its potential consequences, the hypothesis took on enormous importance in mathematics. indeed, the successful solution to this puzzle would herald a revolution in prime number theory. proving or disproving it became the greatest challenge of the age. it has become clear that the riemann hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. the making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the hypothesis. in a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. hunting down the solution to the riemann hypothesis has become an obsession for many — the veritable "great white whale" of mathematical research. yet despite determined efforts by generations of mathematicians, the riemann hypothesis defies resolution. alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, prime obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. posited a century and a half ago, the riemann hypothesis is an intellectual feast for the cognoscenti and the curious alike. not just a story of numbers and calculations, prime obsession is the engrossing tale of a relentless hunt for an elusive proof — and those who have been consumed by it.

Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics

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Author by : John Derbyshire
Languange Used : English, France, Spanish, Italia and chinese
Page : 446
Isbn : 0309085497
Identifier : 9780309085496
Release : 2003-04-15
Publisher by : Joseph Henry Press
Category : Science
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Description : Read Now Prime Obsession by John Derbyshire and you can download with pub, pdf, txt, doc, and more file format with free account. in august 1859 bernhard riemann, a little-known 32-year old mathematician, presented a paper to the berlin academy titled: "on the number of prime numbers less than a given quantity." in the middle of that paper, riemann made an incidental remark â€" a guess, a hypothesis. what he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. today, after 150 years of careful research and exhaustive study, the question remains. is the hypothesis true or false? riemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic â€" defining a precise formula to track and identify the occurrence of prime numbers. but it is that incidental remark â€" the riemann hypothesis â€" that is the truly astonishing legacy of his 1859 paper. because riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows â€" subtle variations in the distribution of those prime numbers. brilliant for its clarity, astounding for its potential consequences, the hypothesis took on enormous importance in mathematics. indeed, the successful solution to this puzzle would herald a revolution in prime number theory. proving or disproving it became the greatest challenge of the age. it has become clear that the riemann hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. the making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the hypothesis. in a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. hunting down the solution to the riemann hypothesis has become an obsession for many â€" the veritable "great white whale" of mathematical research. yet despite determined efforts by generations of mathematicians, the riemann hypothesis defies resolution. alternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, prime obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. posited a century and a half ago, the riemann hypothesis is an intellectual feast for the cognoscenti and the curious alike. not just a story of numbers and calculations, prime obsession is the engrossing tale of a relentless hunt for an elusive proof â€" and those who have been consumed by it.

Dr. Riemann's Zeros

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Author by : Karl Sabbagh
Languange Used : English, France, Spanish, Italia and chinese
Page : 289
Isbn :
Identifier : CHI:76308988
Release : 2003
Publisher by : Atlantic Books (UK)
Category : Number theory
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Description : Read Now Dr Riemann S Zeros by Karl Sabbagh and you can download with pub, pdf, txt, doc, and more file format with free account. in 1859 bernhard riemann, a shy german mathematician, gave an answer to a problem that had long puzzled mathematicians. although he couldn't provide a proof, riemann declared that his solution was 'very probably' true. for the next one hundred and fifty years, the world's mathematicians have longed to confirm the riemann hypothesis. so great is the interest in its solution that in 2001, an american foundation offered a million-dollar prize to the first person to demonstrate that the hypothesis is correct. in this book, karl sabbagh makes accessible even the airiest peaks of maths and paints vivid portraits of the people racing to solve the problem. dr. riemann's zeros is a gripping exploration of the mystery at the heart of our counting system.

Unknown Quantity A Real and Imaginary History of Algebra

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Author by : John Derbyshire
Languange Used : English, France, Spanish, Italia and chinese
Page : 390
Isbn : 030909657X
Identifier : 9780309096577
Release : 2006-06-02
Publisher by : National Academies Press
Category : Science
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Description : Read Now Unknown Quantity by John Derbyshire and you can download with pub, pdf, txt, doc, and more file format with free account. prime obsession taught us not to be afraid to put the math in a math book. unknown quantity heeds the lesson well. so grab your graphing calculators, slip out the slide rules, and buckle up! john derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "here is the story of algebra." with this deceptively simple introduction, we begin our journey. flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. our first encounter with algebraic arithmetic takes us back 38 centuries to the time of abraham and isaac, jacob and joseph, ur and haran, sodom and gomorrah. moving deftly from abel's proof to the higher levels of abstraction developed by galois, we are eventually introduced to what algebraists have been focusing on during the last century. as we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. this dramatic shift in thinking revolutionized mathematics. written for those among us who are unencumbered by a fear of formulae, unknown quantity delivers on its promise to present a history of algebra. astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.

Stalking The Riemann Hypothesis

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Author by : Daniel Nahum Rockmore
Languange Used : English, France, Spanish, Italia and chinese
Page : 304
Isbn : 1446483622
Identifier : 9781446483626
Release : 2011-06-08
Publisher by : Random House
Category : Science
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Description : Read Now Stalking The Riemann Hypothesis by Daniel Nahum Rockmore and you can download with pub, pdf, txt, doc, and more file format with free account. 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 Great Mathematical Problems

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Author by : Ian Stewart
Languange Used : English, France, Spanish, Italia and chinese
Page : 340
Isbn : 1847653510
Identifier : 9781847653512
Release : 2013-03-07
Publisher by : Profile Books
Category : Mathematics
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Description : Read Now The Great Mathematical Problems by Ian Stewart and you can download with pub, pdf, txt, doc, and more file format with free account. there are some mathematical problems whose significance goes beyond the ordinary - like fermat's last theorem or goldbach's conjecture - they are the enigmas which define mathematics. the great mathematical problems explains why these problems exist, why they matter, what drives mathematicians to incredible lengths to solve them and where they stand in the context of mathematics and science as a whole. it contains solved problems - like the poincar conjecture, cracked by the eccentric genius grigori perelman, who refused academic honours and a million-dollar prize for his work, and ones which, like the riemann hypothesis, remain baffling after centuries. stewart is the guide to this mysterious and exciting world, showing how modern mathematicians constantly rise to the challenges set by their predecessors, as the great mathematical problems of the past succumb to the new techniques and ideas of the present.

Prime Numbers and the Riemann Hypothesis

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Author by : Barry Mazur
Languange Used : English, France, Spanish, Italia and chinese
Page : 150
Isbn : 9781107499430
Identifier : 1107499437
Release : 2016-04-11
Publisher by : Cambridge University Press
Category : Mathematics
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Description : Read Now Prime Numbers And The Riemann Hypothesis by Barry Mazur and you can download with pub, pdf, txt, doc, and more file format with free account. prime numbers are beautiful, mysterious, and beguiling mathematical objects. the mathematician bernhard riemann made a celebrated conjecture about primes in 1859, the so-called riemann hypothesis, which remains to be one of the most important unsolved problems in mathematics. through the deep insights of the authors, this book introduces primes and explains the riemann hypothesis. students with minimal mathematical background and scholars alike will enjoy this comprehensive discussion of primes. the first part of the book will inspire the curiosity of a general reader with an accessible explanation of the key ideas. the exposition of these ideas is generously illuminated by computational graphics that exhibit the key concepts and phenomena in enticing detail. readers with more mathematical experience will then go deeper into the structure of primes and see how the riemann hypothesis relates to fourier analysis using the vocabulary of spectra. readers with a strong mathematical background will be able to connect these ideas to historical formulations of the riemann hypothesis.

The Millennium Prize Problems

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Author by : James A. Carlson
Languange Used : English, France, Spanish, Italia and chinese
Page : 165
Isbn : 9780821836798
Identifier : 082183679X
Release : 2006-01
Publisher by : American Mathematical Soc.
Category : Mathematics
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Description : Read Now The Millennium Prize Problems by James A. Carlson and you can download with pub, pdf, txt, doc, and more file format with free account. on august 8, 1900, at the second international congress of mathematicians in paris, david hilbert delivered his famous lecture in which he described twenty-three problems that were to play an influential role in mathematical research. a century later, on may 24, 2000, at a meeting at the college de france, the clay mathematics institute (cmi) announced the creation of a us$7 million prize fund for the solution of seven important classic problems which have resisted solution. the prize fund is divided equally among the seven problems. there is no time limit for their solution. the millennium prize problems were selected by the founding scientific advisory board of cmi--alain connes, arthur jaffe, andrew wiles, and edward witten--after consulting with other leading mathematicians. their aim was somewhat different than that of hilbert: not to define new challenges, but to record some of the most difficult issues with which mathematicians were struggling at the turn of the second millennium; to recognize achievement in mathematics of historical dimension; to elevate in the consciousness of the general public the fact that in mathematics, the frontier is still open and abounds in important unsolved problems; and to emphasize the importance of working towards a solution of the deepest, most difficult problems. the present volume sets forth the official description of each of the seven problems and the rules governing the prizes. it also contains an essay by jeremy gray on the history of prize problems in mathematics.

The Distribution of Prime Numbers

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Author by : A. E. Ingham
Languange Used : English, France, Spanish, Italia and chinese
Page : 114
Isbn : 9780521397896
Identifier : 0521397898
Release : 1990-09-28
Publisher by : Cambridge University Press
Category : Mathematics
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Description : Read Now The Distribution Of Prime Numbers by A. E. Ingham and you can download with pub, pdf, txt, doc, and more file format with free account. originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. despite being long out of print, it remains unsurpassed as an introduction to the field.

Riemann's Zeta Function

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Author by : Harold M. Edwards
Languange Used : English, France, Spanish, Italia and chinese
Page : 315
Isbn : 9780486417400
Identifier : 0486417409
Release : 2001
Publisher by : Courier Corporation
Category : Mathematics
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Description : Read Now Riemann S Zeta Function by Harold M. Edwards and you can download with pub, pdf, txt, doc, and more file format with free account. superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “on the number of primes less than a given magnitude,” and traces developments in theory inspired by it. topics include riemann's main formula, the prime number theorem, the riemann-siegel formula, large-scale computations, fourier analysis, and other related topics. english translation of riemann's original document appears in the appendix.

Prime Numbers and Computer Methods for Factorization

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Author by : Hans Riesel
Languange Used : English, France, Spanish, Italia and chinese
Page : 464
Isbn : 9780817682989
Identifier : 0817682988
Release : 2011-11-23
Publisher by : Springer Science & Business Media
Category : Mathematics
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Description : Read Now Prime Numbers And Computer Methods For Factorization by Hans Riesel and you can download with pub, pdf, txt, doc, and more file format with free account. from the original hard cover edition: in the modern age of almost universal computer usage, practically every individual in a technologically developed society has routine access to the most up-to-date cryptographic technology that exists, the so-called rsa public-key cryptosystem. a major component of this system is the factorization of large numbers into their primes. thus an ancient number-theory concept now plays a crucial role in communication among millions of people who may have little or no knowledge of even elementary mathematics. hans riesel’s highly successful first edition of this book has now been enlarged and updated with the goal of satisfying the needs of researchers, students, practitioners of cryptography, and non-scientific readers with a mathematical inclination. it includes important advances in computational prime number theory and in factorization as well as re-computed and enlarged tables, accompanied by new tables reflecting current research by both the author and his coworkers and by independent researchers. the book treats four fundamental problems: the number of primes below a given limit, the approximate number of primes, the recognition of primes and the factorization of large numbers. the author provides explicit algorithms and computer programs, and has attempted to discuss as many of the classically important results as possible, as well as the most recent discoveries. the programs include are written in pascal to allow readers to translate the programs into the language of their own computers. the independent structure of each chapter of the book makes it highly readable for a wide variety of mathematicians, students of applied number theory, and others interested in both study and research in number theory and cryptography. ​

The Riemann Hypothesis The Greatest Unsolved Problem in Mathematics

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Author by : Karl Sabbagh
Languange Used : English, France, Spanish, Italia and chinese
Page : 340
Isbn : 9780374250072
Identifier : 0374250073
Release : 2003
Publisher by : Macmillan
Category : Mathematics
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Description : Read Now The Riemann Hypothesis by Karl Sabbagh and you can download with pub, pdf, txt, doc, and more file format with free account. an accessible meditation on the ultimate meaning of mathematics draws on the famous eight-page riemann hypothesis publication and the ongoing contest to prove his answer true and support his idea about the distribution of prime numbers.