The Music of the Primes

Searching to Solve the Greatest Mystery in Mathematics
Author: Marcus du Sautoy
Publisher: Harper Collins
ISBN: 0060935588
Category: Mathematics
Page: 335
View: 8812

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An examination of the Riemann Hypothesis considers the modern implications of its solution, noting its potential impact on business, science, and other fields and describing the million-dollar prize currently being offered to whomever can crack its code. Reprint.

Prime Obsession

Bernhard Riemann and the Greatest Unsolved Problem in Mathematics
Author: John Derbyshire
Publisher: Joseph Henry Press
ISBN: 0309141257
Category: Science
Page: 446
View: 3726

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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.

Stalking the Riemann Hypothesis

The Quest to Find the Hidden Law of Prime Numbers
Author: Dan Rockmore
Publisher: Vintage
ISBN: 0307427943
Category: Mathematics
Page: 304
View: 8848

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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. From the Trade Paperback edition.

The Great Unknown

Seven Journeys to the Frontiers of Science
Author: Marcus du Sautoy
Publisher: Penguin
ISBN: 0735221812
Category: Science
Page: 464
View: 667

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“An engaging voyage into some of the great mysteries and wonders of our world." --Alan Lightman, author of Einstein’s Dream and The Accidental Universe “No one is better at making the recondite accessible and exciting.” —Bill Bryson Brain Pickings and Kirkus Best Science Book of the Year Every week seems to throw up a new discovery, shaking the foundations of what we know. But are there questions we will never be able to answer—mysteries that lie beyond the predictive powers of science? In this captivating exploration of our most tantalizing unknowns, Marcus du Sautoy invites us to consider the problems in cosmology, quantum physics, mathematics, and neuroscience that continue to bedevil scientists and creative thinkers who are at the forefront of their fields. At once exhilarating, mind-bending, and compulsively readable, The Great Unknown challenges us to consider big questions—about the nature of consciousness, what came before the big bang, and what lies beyond our horizons—while taking us on a virtuoso tour of the great breakthroughs of the past and celebrating the men and women who dared to tackle the seemingly impossible and had the imagination to come up with new ways of seeing the world.

Prime Numbers

The Most Mysterious Figures in Math
Author: David Wells
Publisher: John Wiley & Sons
ISBN: 9781118045718
Category: Mathematics
Page: 288
View: 6134

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A fascinating journey into the mind-bending world of prime numbers Cicadas of the genus Magicicada appear once every 7, 13, or 17 years. Is it just a coincidence that these are all prime numbers? How do twin primes differ from cousin primes, and what on earth (or in the mind of a mathematician) could be sexy about prime numbers? What did Albert Wilansky find so fascinating about his brother-in-law's phone number? Mathematicians have been asking questions about prime numbers for more than twenty-five centuries, and every answer seems to generate a new rash of questions. In Prime Numbers: The Most Mysterious Figures in Math, you'll meet the world's most gifted mathematicians, from Pythagoras and Euclid to Fermat, Gauss, and Erd?o?s, and you'll discover a host of unique insights and inventive conjectures that have both enlarged our understanding and deepened the mystique of prime numbers. This comprehensive, A-to-Z guide covers everything you ever wanted to know--and much more that you never suspected--about prime numbers, including: * The unproven Riemann hypothesis and the power of the zeta function * The "Primes is in P" algorithm * The sieve of Eratosthenes of Cyrene * Fermat and Fibonacci numbers * The Great Internet Mersenne Prime Search * And much, much more

Prime Numbers and the Riemann Hypothesis


Author: Barry Mazur,William Stein
Publisher: Cambridge University Press
ISBN: 1107101921
Category: Mathematics
Page: 150
View: 7622

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This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

The Great Mathematical Problems


Author: Ian Stewart
Publisher: Profile Books
ISBN: 1847653510
Category: Mathematics
Page: 340
View: 2039

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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.

The Riemann Hypothesis

The Greatest Unsolved Problem in Mathematics
Author: Karl Sabbagh
Publisher: Macmillan
ISBN: 9780374250072
Category: Mathematics
Page: 340
View: 7892

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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.

The Number Mysteries

A Mathematical Odyssey through Everyday Life
Author: Marcus du Sautoy
Publisher: St. Martin's Press
ISBN: 9780230120280
Category: Mathematics
Page: 272
View: 7535

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Every time we download music, take a flight across the Atlantic or talk on our cell phones, we are relying on great mathematical inventions. In The Number Mysteries, one of our generation's foremost mathematicians Marcus du Sautoy offers a playful and accessible examination of numbers and how, despite efforts of the greatest minds, the most fundamental puzzles of nature remain unsolved. Du Sautoy tells about the quest to predict the future—from the flight of asteroids to an impending storm, from bending a ball like Beckham to forecasting population growth. He brings to life the beauty behind five mathematical puzzles that have contributed to our understanding of the world around us and have helped develop the technology to cope with it. With loads of games to play and puzzles to solve, this is a math book for everyone.

Uncle Petros and Goldbach's Conjecture


Author: Apostolos Doxiadis
Publisher: Faber & Faber
ISBN: 057129569X
Category: Fiction
Page: 224
View: 5953

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Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.

Riemann's Zeta Function


Author: Harold M. Edwards
Publisher: Courier Corporation
ISBN: 9780486417400
Category: Mathematics
Page: 315
View: 9786

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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.

Problem-Solving and Selected Topics in Number Theory

In the Spirit of the Mathematical Olympiads
Author: Michael Th. Rassias
Publisher: Springer Science & Business Media
ISBN: 1441904956
Category: Mathematics
Page: 324
View: 796

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The book provides a self-contained introduction to classical Number Theory. All the proofs of the individual theorems and the solutions of the exercises are being presented step by step. Some historical remarks are also presented. The book will be directed to advanced undergraduate, beginning graduate students as well as to students who prepare for mathematical competitions (ex. Mathematical Olympiads and Putnam Mathematical competition).

Fermat’s Last Theorem


Author: Simon Singh
Publisher: HarperCollins UK
ISBN: 0007381999
Category: Science
Page: 368
View: 9375

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‘I have a truly marvellous demonstration of this proposition which this margin is too narrow to contain.’

The Riemann Hypothesis

The Greatest Unsolved Problem in Mathematics
Author: Karl Sabbagh
Publisher: Farrar, Straus and Giroux
ISBN: 9780374529352
Category: Mathematics
Page: 352
View: 5365

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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.

The Routledge Handbook of Corpus Linguistics


Author: Anne O'Keeffe,Michael McCarthy
Publisher: Routledge
ISBN: 1135153620
Category: Education
Page: 740
View: 2583

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The Routledge Handbook of Corpus Linguistics provides a timely overview of a dynamic and rapidly growing area with a widely applied methodology. Through the electronic analysis of large bodies of text, corpus linguistics demonstrates and supports linguistic statements and assumptions. In recent years it has seen an ever-widening application in a variety of fields: computational linguistics, discourse analysis, forensic linguistics, pragmatics and translation studies. Bringing together experts in the key areas of development and change, the handbook is structured around six themes which take the reader through building and designing a corpus to using a corpus to study literature and translation. A comprehensive introduction covers the historical development of the field and its growing influence and application in other areas. Structured around five headings for ease of reference, each contribution includes further reading sections with three to five key texts highlighted and annotated to facilitate further exploration of the topics. The Routledge Handbook of Corpus Linguistics is the ideal resource for advanced undergraduates and postgraduates.

The Man who Loved Only Numbers

The Story of Paul Erdös and the Search for Mathematical Truth
Author: Paul Hoffman
Publisher: Fourth Estate (GB)
ISBN: 9781857028294
Category: Mathematicians
Page: 301
View: 5888

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The biography of a mathematical genius. Paul Erdos was the most prolific pure mathematician in history and, arguably, the strangest too. 'A mathematical genius of the first order, Paul Erdos was totally obsessed with his subject -- he thought and wrote mathematics for nineteen hours a day until he died. He travelled constantly, living out of a plastic bag and had no interest in food, sex, companionship, art -- all that is usually indispensible to a human life. Paul Hoffman, in this marvellous biography, gives us a vivid and strangely moving portrait of this singular creature, one that brings out not only Erdos's genius and his oddness, but his warmth and sense of fun, the joyfulness of his strange life.' Oliver Sacks For six decades Erdos had no job, no hobbies, no wife, no home; he never learnt to cook, do laundry, drive a car and died a virgin. Instead he travelled the world with his mother in tow, arriving at the doorstep of esteemed mathematicians declaring 'My brain is open'. He travelled until his death at 83, racing across four continents to prove as many theorems as possible, fuelled by a diet of espresso and amphetamines. With more than 1,500 papers written or co-written,

Birth of a Theorem

A Mathematical Adventure
Author: Cédric Villani
Publisher: Farrar, Straus and Giroux
ISBN: 0374710236
Category: Biography & Autobiography
Page: 272
View: 3139

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In 2010, French mathematician Cédric Villani received the Fields Medal, the most coveted prize in mathematics, in recognition of a proof which he devised with his close collaborator Clément Mouhot to explain one of the most surprising theories in classical physics. Birth of a Theorem is Villani's own account of the years leading up to the award. It invites readers inside the mind of a great mathematician as he wrestles with the most important work of his career. But you don't have to understand nonlinear Landau damping to love Birth of a Theorem. It doesn't simplify or overexplain; rather, it invites readers into collaboration. Villani's diaries, emails, and musings enmesh you in the process of discovery. You join him in unproductive lulls and late-night breakthroughs. You're privy to the dining-hall conversations at the world's greatest research institutions. Villani shares his favorite songs, his love of manga, and the imaginative stories he tells his children. In mathematics, as in any creative work, it is the thinker's whole life that propels discovery—and with Birth of a Theorem, Cédric Villani welcomes you into his.

Men of Mathematics


Author: E.T. Bell
Publisher: Simon and Schuster
ISBN: 1476784256
Category: Mathematics
Page: 608
View: 2987

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From one of the greatest minds in contemporary mathematics, Professor E.T. Bell, comes a witty, accessible, and fascinating look at the beautiful craft and enthralling history of mathematics. Men of Mathematics provides a rich account of major mathematical milestones, from the geometry of the Greeks through Newton’s calculus, and on to the laws of probability, symbolic logic, and the fourth dimension. Bell breaks down this majestic history of ideas into a series of engrossing biographies of the great mathematicians who made progress possible—and who also led intriguing, complicated, and often surprisingly entertaining lives. Never pedantic or dense, Bell writes with clarity and simplicity to distill great mathematical concepts into their most understandable forms for the curious everyday reader. Anyone with an interest in math may learn from these rich lessons, an advanced degree or extensive research is never necessary.