Prime Obsession

Prime Obsession

Author: John Derbyshire

Publisher: Joseph Henry Press

Published: 2003-04-15

Total Pages: 447

ISBN-13: 0309141257

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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.


The Life of Ludwig van Beethoven (Complete)

The Life of Ludwig van Beethoven (Complete)

Author: Alexander Wheelock Thayer

Publisher: Library of Alexandria

Published: 2020-09-28

Total Pages: 1474

ISBN-13: 146558322X

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If for no other reasons than because of the long time and monumental patience expended upon its preparation, the vicissitudes through which it has passed and the varied and arduous labors bestowed upon it by the author and his editors, the history of Alexander Wheelock Thayer’s Life of Beethoven deserves to be set forth as an introduction to this work. His work it is, and his monument, though others have labored long and painstakingly upon it. There has been no considerable time since the middle of the last century when it has not occupied the minds of the author and those who have been associated with him in its creation. Between the conception of its plan and its execution there lies a period of more than two generations. Four men have labored zealously and affectionately upon its pages, and the fruits of more than four score men, stimulated to investigation by the first revelations made by the author, have been conserved in the ultimate form of the biography. It was seventeen years after Mr. Thayer entered upon what proved to be his life-task before he gave the first volume to the world—and then in a foreign tongue; it was thirteen more before the third volume came from the press. This volume, moreover, left the work unfinished, and thirty-two years more had to elapse before it was completed. When this was done the patient and self-sacrificing investigator was dead; he did not live to finish it himself nor to see it finished by his faithful collaborator of many years, Dr. Deiters; neither did he live to look upon a single printed page in the language in which he had written that portion of the work published in his lifetime. It was left for another hand to prepare the English edition of an American writer’s history of Germany’s greatest tone-poet, and to write its concluding chapters, as he believes, in the spirit of the original author. Under these circumstances there can be no vainglory in asserting that the appearance of this edition of Thayer’s Life of Beethoven deserves to be set down as a significant occurrence in musical history. In it is told for the first time in the language of the great biographer the true story of the man Beethoven—his history stripped of the silly sentimental romance with which early writers and their later imitators and copyists invested it so thickly that the real humanity, the humanliness, of the composer has never been presented to the world. In this biography there appears the veritable Beethoven set down in his true environment of men and things—the man as he actually was, the man as he himself, like Cromwell, asked to be shown for the information of posterity. It is doubtful if any other great man’s history has been so encrusted with fiction as Beethoven’s. Except Thayer’s, no biography of him has been written which presents him in his true light. The majority of the books which have been written of late years repeat many of the errors and falsehoods made current in the first books which were written about him. A great many of these errors and falsehoods are in the account of the composer’s last sickness and death, and were either inventions or exaggerations designed by their utterers to add pathos to a narrative which in unadorned truth is a hundredfold more pathetic than any tale of fiction could possibly be. Other errors have concealed the truth in the story of Beethoven’s guardianship of his nephew, his relations with his brothers, the origin and nature of his fatal illness, his dealings with his publishers and patrons, the generous attempt of the Philharmonic Society of London to extend help to him when upon his deathbed.


History Algebraic Geometry

History Algebraic Geometry

Author: Jean Dieudonné

Publisher: CRC Press

Published: 1985-05-30

Total Pages: 202

ISBN-13: 9780412993718

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This book contains several fundamental ideas that are revived time after time in different guises, providing a better understanding of algebraic geometric phenomena. It shows how the field is enriched with loans from analysis and topology and from commutative algebra and homological algebra.


Galileo Unbound

Galileo Unbound

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.


Journey Through Genius

Journey Through Genius

Author: William Dunham

Publisher: Penguin Books

Published: 1991-08

Total Pages: 324

ISBN-13:

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Like masterpieces of art, music, and literature, great mathematical theorems are creative milestones, works of genius destined to last forever. Now William Dunham gives them the attention they deserve. Dunham places each theorem within its historical context and explores the very human and often turbulent life of the creator — from Archimedes, the absentminded theoretician whose absorption in his work often precluded eating or bathing, to Gerolamo Cardano, the sixteenth-century mathematician whose accomplishments flourished despite a bizarre array of misadventures, to the paranoid genius of modern times, Georg Cantor. He also provides step-by-step proofs for the theorems, each easily accessible to readers with no more than a knowledge of high school mathematics. A rare combination of the historical, biographical, and mathematical, Journey Through Genius is a fascinating introduction to a neglected field of human creativity. “It is mathematics presented as a series of works of art; a fascinating lingering over individual examples of ingenuity and insight. It is mathematics by lightning flash.” —Isaac Asimov


A History of the Theories of Aether and Electricity

A History of the Theories of Aether and Electricity

Author: Edmund Taylor Whittaker

Publisher: Forgotten Books

Published: 2017-09-16

Total Pages: 492

ISBN-13: 9781528264624

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Excerpt from A History of the Theories of Aether and Electricity: From the Age of Descartes to the Close of the Nineteenth Century Newton shows that rays Obtained by double refraction have sides his Objections to the undulatory theory. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.


An Introduction to the Theory of the Riemann Zeta-Function

An Introduction to the Theory of the Riemann Zeta-Function

Author: S. J. Patterson

Publisher: Cambridge University Press

Published: 1995-02-02

Total Pages: 176

ISBN-13: 9780521499057

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An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro