The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics

Overview

In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved?one that baffles mathematicians to this day.

Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the ...

See more details below
Paperback (Reprint)
$13.37
BN.com price
(Save 10%)$14.99 List Price

Pick Up In Store

Reserve and pick up in 60 minutes at your local store

Other sellers (Paperback)
  • All (18) from $5.59   
  • New (9) from $7.99   
  • Used (9) from $5.59   
Sending request ...

Overview

In 1859, German mathematician Bernhard Riemann presented a paper to the Berlin Academy that would forever change mathematics. The subject was the mystery of prime numbers. At the heart of the presentation was an idea that Riemann had not yet proved—one that baffles mathematicians to this day.

Solving the Riemann Hypothesis could change the way we do business, since prime numbers are the lynchpin for security in banking and e-commerce. It would also have a profound impact on the cutting edge of science, affecting quantum mechanics, chaos theory, and the future of computing. Leaders in math and science are trying to crack the elusive code, and a prize of $1 million has been offered to the winner. In this engaging book, Marcus du Sautoy reveals the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it.

Read More Show Less

Editorial Reviews

Oliver Sacks
“An amazing book! Hugely enjoyable. Du Sautoy provides a stunning journey into the wonderful world of primes.”
Simon Winchester
“This fascinating account, decoding the inscrutable language of the mathematical priesthood, is written like the purest poetry.”
Amir Aczel
“This is a wonderful book about one of the greatest remaining mysteries in mathematics.”
Keith Devlin
“No matter what your mathematical IQ, you will enjoy reading The Music of the Primes.”
Booklist (starred review)
“Exceptional. ... A book that will draw readers normally indifferent to the subject deep into the adventure of mathematics.”
Washington Post Book World
“Fascinating.”
Booklist
"Exceptional. ... A book that will draw readers normally indifferent to the subject deep into the adventure of mathematics."
The New York Times
[du Sautoy] is an insider, a research mathematician. He walks the walk and talks the talk. His discussion of mathematics is figurative and elliptical, as when mathematicians talk to one another. — James Alexander
The Los Angeles Times
Number theorist Marcus du Sautoy's book The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics compares the pattern the primes make to music. At first they seem to appear at random, like a kind of noise, but under analysis display a more musical structure. — Ben Yandell
Publishers Weekly
The quest to bring advanced math to the masses continues with this engaging but quixotic treatise. The mystery in question is the Riemann Hypothesis, named for the hypochondriac German mathematician Bernard Reimann (1826-66), which ties together imaginary numbers, sine waves and prime numbers in a way that the world's greatest mathematicians have spent 144 years trying to prove. Oxford mathematician and BBC commentator du Sautoy does his best to explain the problem, but stumbles over the fact that the Riemann Hypothesis and its corollaries are just too hard for non-tenured readers to understand. He falls back on the staples of math popularizations by shifting the discussion to easier math concepts, offering thumbnail sketches of other mathematicians and their discoveries, and occasionally overdramatizing the sedentary lives of academics (one is said to be a "benign Robespierre" whose non-commutative geometry "has instilled terror" in his colleagues). But du Sautoy makes the most of these genre conventions. He is a fluent expositor of more tractable mathematics, and his portraits of math notables-like the slipper-shod, self-taught Indian Srinivasa Ramanujan, a mathematical Mozart who languished in chilly Oxford-are quite vivid. His discussion of the Riemann Hypothesis itself, though, can lapse into metaphors ("By combining all these waves, [Riemann] had an orchestra that played the music of the primes") that are long on sublime atmospherics but short on meaningful explanation. The consequences of the hypothesis-a possible linkage to "quantum chaos," implications for internet data encryption-may seem less than earth-shaking to the lay reader, but for mathematicians, the Riemann Hypothesis may be the "deepest and most fundamental problem" going. 40 illustrations, charts and photos. (Apr.) Copyright 2003 Reed Business Information.
Library Journal
Thanks to a proof by Euclid, mathematicians have known for more than 2000 years that there is no limit to the population of prime numbers; they extend to infinity. However, work continues to be done on the distribution of the primes, and much of that work now centers on efforts to prove the Riemann hypothesis. Bernhard Riemann was a great 19th-century German mathematician who offered in an 1859 paper an admittedly unproven conjecture relating some zero values of a "zeta function" to the distribution of primes. The importance of this abstruse speculation for modern research is demonstrated in a recent online search of Mathematical Reviews for the term "Riemann hypothesis"; 1403 publications were found. Now there are three more books to add to the numerous studies. Derbyshire, a mathematician by training, a member of the Mathematical Association of America, and a novelist (Seeing Calvin Coolidge in a Dream), first takes readers through well-organized mathematical fundamentals in order to give them a good understanding of Riemann's discovery and its consequences. Interspersed with the hardcore math, other chapters profile Reimann the man and trace the history of mathematics in relation to his still-unproven hypothesis. Derbyshire shows how after 150 years, the world's greatest minds still haven't found a solution. Because this book does not sugarcoat complex ideas, readers lacking at least college-level math will be hard-pressed to understand some parts. Still, this volume is highly recommended for academic and larger public libraries as an excellent introduction for nonspecialists. Du Sautoy is the only professional research mathematician among these three authors, but he does not confront his readers with very many equations or other bits of mathematical apparatus. Instead, he offers nicely done verbal descriptions of the essence of the hypothesis and the efforts to prove it. Like Derbyshire, he intersperses items from math history and from the work and interactions of current researchers. Du Sautoy's book has much to offer for most academic and public libraries, especially to readers of very limited math background. Sabbagh (A Rum Affair) has written several books on a variety of topics, not all science-related. His latest emphasizes anecdotes from contemporary mathematicians who have studied Riemann's hypothesis. Indeed, he pays so much attention to a particularly idiosyncratic mathematician, ignored by the two other authors, that in his quest for human-interest material, he seems to lose sight of serious mathematical issues. Sabbagh's discussion of the actual mathematics is not so well organized, and much of it is relegated to a series of appendixes. His book is most useful in giving readers a feel for how research mathematicians live, work, and interrelate in the 21st century. Only libraries seeking comprehensive coverage of mathematics will need to get the Sabbagh work.-Jack W. Weigel, Ann Arbor, MI Copyright 2003 Reed Business Information.
Kirkus Reviews
A Royal Society research fellow takes the Riemann Hypothesis, reputedly the most difficult of all math problems, as the focus for his lively history of number theory. Du Sautoy (Mathematics/Oxford) begins in 1900 with German mathematician David Hilbert's famous address to the International Congress of Mathematicians in Paris, where Hilbert offered 23 unsolved problems as challenges to his colleagues. Among them was the Reimann Hypothesis, which concerns the distribution of prime numbers; it is the only one still unsolved. Greek mathematicians knew that the primes are infinite in number and distributed randomly in the set of natural numbers. Two centuries ago, Carl Friedrich Gauss offered a formula to estimate how many primes lie below any given number; in 1859, Gauss's student, Bernhard Riemann, refined that estimate, based on the incredibly complex Zeta function, but died without proving his hypothesis. With a minimum of equations and mathematical symbols, du Sautoy outlines the progress each succeeding generation has made on the problem. Along the way, readers meet G.H. Hardy and J.E. Littlewood, the twin beacons of the Cambridge math department between the world wars; Ramanujan, the self-taught Indian clerk who claimed that his ideas were given to him by his family goddess; and Atle Selberg, who survived the Nazi occupation of Norway to become a leading light at Princeton's Institute for Advanced Studies. Alan Turing, the father of modern computers, tried to devise a program to attack the Riemann Hypothesis; now the primes are the key to cryptography. A Boston businessman has offered a million-dollar reward for a proof, although few mathematicians seem to need additional incentive totackle the Everest of mathematical problems. Du Sautoy keeps the story moving and gives a clear sense of the way number theory is played in his accessible text. (See Karl Sabbagh’s The Riemann Hypothesis, p. 369, which covers similar territory but spotlights current mathematicians searching for a Riemann proof.) A must for math buffs.
Read More Show Less

Product Details

  • ISBN-13: 9780062064011
  • Publisher: HarperCollins Publishers
  • Publication date: 8/14/2012
  • Series: P.S. Series
  • Edition description: Reprint
  • Pages: 335
  • Sales rank: 218,938
  • Product dimensions: 5.38 (w) x 7.82 (h) x 0.86 (d)

Meet the Author

Marcus du Sautoy is a professor of mathematics and the Simonyi Professor for the Public Understanding of Science at Oxford University. He is a frequent contributor on mathematics to The Times, The Guardian, and the BBC, and he lives in London.

Read More Show Less

Read an Excerpt

The Music of the Primes

Searching to Solve the Greatest Mystery in Mathematics
By Marcus du Sautoy

HarperCollins

ISBN: 0066210704


Chapter One


Who Wants To Be a Millionaire?

'Do we know what the sequence of numbers is? Okay, here, we can do it in our heads .. fifty-nine, sixty-one, sixty-seven ... seventy-one ... Aren't these all prime numbers?' A little buzz of excitement circulated through the control room. Ellie's own face
momentarily revealed a flutter of something deeply felt, but this was quickly replaced by a sobriety, a fear of being carried away, an apprehension about appearing foolish, unscientific.

- Carl Sagan, Contact

One hot and humid morning in August 1900, David Hilbert of the University of Göttingen addressed the International Congress of Mathematicians in a packed lecture hall at the Sorbonne, Paris. Already recognised as one of the greatest mathematicians of the age, Hilbert had prepared a daring lecture. He was going to talk about what was unknown rather than what had already been proved. This went against all the accepted conventions, and the audience could hear the nervousness in Hilbert's voice as he began to lay out his vision for the future of mathematics. 'Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?' To herald the new century, Hilbert challenged the audience with a list of twenty-three problems that he believed should set the course for the mathematical explorers of the twentieth century.

The ensuing decades saw many of the problems answered, and those who discovered the solutions make up an illustrious band of mathematicians known as 'the honours class'. It includes the likes of Kurt Gödel and Henri Poincaré, along with many other pioneers whose ideas have transformed the mathematical landscape. But there was one problem, the eighth on Hilbert's list, which looked as if it would survive the century without a champion: the Riemann Hypothesis.

Of all the challenges that Hilbert had set, the eighth had a special place in his heart. There is a German myth about Frederick Barbarossa, a much-loved German emperor who died during the Third Crusade. A legend grew that he was still alive, asleep in a cavern in the Kyffhäuser Mountains. He would awake only when Germany needed him. Somebody allegedly asked Hilbert, 'If you were to be revived like Barbarossa, after five hundred years, what would you do?' His reply: 'I would ask, "Has someone proved the Riemann Hypothesis?"'

As the twentieth century drew to a close, most mathematicians had resigned themselves to the fact that this jewel amongst all of Hilbert's problems was not only likely to outlive the century, but might still be unanswered when Hilbert awoke from his five-hundred-year slumber. He had stunned the first International Congress of the twentieth century with his revolutionary lecture full of the unknown. However, there turned out to be a surprise in store for those mathematicians who were planning to attend the last Congress of the century.

On April 7, 1997, computer screens across the mathematical world flashed up some extraordinary news. Posted on the website of the International Congress of Mathematicians that was to be held the following year in Berlin was an announcement that the Holy Grail of mathematics had finally been claimed. The Riemann Hypothesis had been proved. It was news that would have a profound effect. The Riemann Hypothesis is a problem which is central to the whole of mathematics. As they read their email, mathematicians were thrilling to the prospect of understanding one of the greatest mathematical mysteries.

The announcement came in a letter from Professor Enrico Bombieri. One could not have asked for a better, more respected source. Bombieri is one of the guardians of the Riemann Hypothesis and is based at the prestigious Institute for Advanced Study in Princeton, once home to Einstein and Gödel. He is very softly spoken, but mathematicians always listen carefully to anything he has to say.

Bombieri grew up in Italy, where his prosperous family's vineyards gave him a taste for the good things in life. He is fondly referred to by colleagues as 'the Mathematical Aristocrat'. In his youth he always cut a dashing figure at conferences in Europe, often arriving in a fancy sports car. Indeed, he was quite happy to fuel a rumour that he'd once come sixth in a twenty-four-hour rally in Italy. His successes on the mathematical circuit were more concrete and led to an invitation in the 1970s to go to Princeton, where he has remained ever since. He has replaced his enthusiasm for rallying with a passion for painting, especially portraits.

But it is the creative art of mathematics, and in particular the challenge of the Riemann Hypothesis, that gives Bombieri the greatest buzz. The Riemann Hypothesis had been an obsession for Bombieri ever since he first read about it at the precocious age of fifteen. He had always been fascinated by properties of numbers as he browsed through the mathematics books his father, an economist, had collected in his extensive library. The Riemann Hypothesis, he discovered, was regarded as the deepest and most fundamental problem in number theory. His passion for the problem was further fuelled when his father offered to buy him a Ferrari if he ever solved it - a desperate attempt on his father's part to stop Enrico driving his own model.

According to his email, Bombieri had been beaten to his prize. 'There are fantastic developments to Alain Connes's lecture at IAS last Wednesday,' Bombieri began. Several years previously, the mathematical world had been set alight by the news that Alain Connes had turned his attention to trying to crack the Riemann Hypothesis. Connes is one of the revolutionaries of the subject, a benign Robespierre of mathematics to Bombieri's Louis XVI. He is an extraordinarily charismatic figure whose fiery style is far from the image of the staid, awkward mathematician. He has the drive of a fanatic convinced of his world-view, and his lectures are mesmerising. Amongst his followers he has almost cult status ...

(Continues...)



Excerpted from The Music of the Primes by Marcus du Sautoy
Excerpted by permission. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.

Read More Show Less

Table of Contents

1 Who Wants To Be a Millionaire? 1
2 The Atoms of Arithmetic 19
3 Riemann's Imaginary Mathematical Looking-Glass 59
4 The Riemann Hypothesis: From Random Primes to Orderly Zeros 84
5 The Mathematical Relay Race: Realising Riemann's Revolution 102
6 Ramanujan, the Mathematical Mystic 132
7 Mathematical Exodus: From Gottingen to Princeton 148
8 Machines of the Mind 175
9 The Computer Age: From the Mind to the Desktop 204
10 Cracking Numbers and Codes 224
11 From Orderly Zeros to Quantum Chaos 255
12 The Missing Piece of the Jigsaw 288
Acknowledgements 315
Further Reading 317
Illustration and Text Credits 323
Index 325
Read More Show Less

First Chapter

The Music of the Primes
Searching to Solve the Greatest Mystery in Mathematics

Chapter One

Who Wants To Be a Millionaire?

'Do we know what the sequence of numbers is? Okay, here, we can do it in our heads .. fifty-nine, sixty-one, sixty-seven ... seventy-one . . . Aren't these all prime numbers?' A little buzz of excitement circulated through the control room. Ellie's own face momentarily revealed a flutter of something deeply felt, but this was quickly replaced by a sobriety, a fear of being carried away, an apprehension about appearing foolish, unscientific.
-- Carl Sagan, Contact

One hot and humid morning in August 1900, David Hilbert of the University of Göttingen addressed the International Congress of Mathematicians in a packed lecture hall at the Sorbonne, Paris. Already recognised as one of the greatest mathematicians of the age, Hilbert had prepared a daring lecture. He was going to talk about what was unknown rather than what had already been proved. This went against all the accepted conventions, and the audience could hear the nervousness in Hilbert's voice as he began to lay out his vision for the future of mathematics. 'Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?' To herald the new century, Hilbert challenged the audience with a list of twenty-three problems that he believed should set the course for the mathematical explorers of the twentieth century.

The ensuing decades saw many of the problems answered, and those who discovered the solutions make up an illustrious band of mathematicians known as 'the honours class'. It includes the likes of Kurt Gödel and Henri Poincaré, along with many other pioneers whose ideas have transformed the mathematical landscape. But there was one problem, the eighth on Hilbert's list, which looked as if it would survive the century without a champion: the Riemann Hypothesis.

Of all the challenges that Hilbert had set, the eighth had a special place in his heart. There is a German myth about Frederick Barbarossa, a much-loved German emperor who died during the Third Crusade. A legend grew that he was still alive, asleep in a cavern in the Kyffhäuser Mountains. He would awake only when Germany needed him. Somebody allegedly asked Hilbert, 'If you were to be revived like Barbarossa, after five hundred years, what would you do?' His reply: 'I would ask, "Has someone proved the Riemann Hypothesis?"'

As the twentieth century drew to a close, most mathematicians had resigned themselves to the fact that this jewel amongst all of Hilbert's problems was not only likely to outlive the century, but might still be unanswered when Hilbert awoke from his five-hundred-year slumber. He had stunned the first International Congress of the twentieth century with his revolutionary lecture full of the unknown. However, there turned out to be a surprise in store for those mathematicians who were planning to attend the last Congress of the century.

On April 7, 1997, computer screens across the mathematical world flashed up some extraordinary news. Posted on the website of the International Congress of Mathematicians that was to be held the following year in Berlin was an announcement that the Holy Grail of mathematics had finally been claimed. The Riemann Hypothesis had been proved. It was news that would have a profound effect. The Riemann Hypothesis is a problem which is central to the whole of mathematics. As they read their email, mathematicians were thrilling to the prospect of understanding one of the greatest mathematical mysteries.

The announcement came in a letter from Professor Enrico Bombieri. One could not have asked for a better, more respected source. Bombieri is one of the guardians of the Riemann Hypothesis and is based at the prestigious Institute for Advanced Study in Princeton, once home to Einstein and Gödel. He is very softly spoken, but mathematicians always listen carefully to anything he has to say.

Bombieri grew up in Italy, where his prosperous family's vineyards gave him a taste for the good things in life. He is fondly referred to by colleagues as 'the Mathematical Aristocrat'. In his youth he always cut a dashing figure at conferences in Europe, often arriving in a fancy sports car. Indeed, he was quite happy to fuel a rumour that he'd once come sixth in a twenty-four-hour rally in Italy. His successes on the mathematical circuit were more concrete and led to an invitation in the 1970s to go to Princeton, where he has remained ever since. He has replaced his enthusiasm for rallying with a passion for painting, especially portraits.

But it is the creative art of mathematics, and in particular the challenge of the Riemann Hypothesis, that gives Bombieri the greatest buzz. The Riemann Hypothesis had been an obsession for Bombieri ever since he first read about it at the precocious age of fifteen. He had always been fascinated by properties of numbers as he browsed through the mathematics books his father, an economist, had collected in his extensive library. The Riemann Hypothesis, he discovered, was regarded as the deepest and most fundamental problem in number theory. His passion for the problem was further fuelled when his father offered to buy him a Ferrari if he ever solved it -- a desperate attempt on his father's part to stop Enrico driving his own model.

According to his email, Bombieri had been beaten to his prize. 'There are fantastic developments to Alain Connes's lecture at IAS last Wednesday,' Bombieri began. Several years previously, the mathematical world had been set alight by the news that Alain Connes had turned his attention to trying to crack the Riemann Hypothesis. Connes is one of the revolutionaries of the subject, a benign Robespierre of mathematics to Bombieri's Louis XVI. He is an extraordinarily charismatic figure whose fiery style is far from the image of the staid, awkward mathematician. He has the drive of a fanatic convinced of his world-view, and his lectures are mesmerising. Amongst his followers he has almost cult status ...

The Music of the Primes
Searching to Solve the Greatest Mystery in Mathematics
. Copyright © by Marcus du Sautoy. Reprinted by permission of HarperCollins Publishers, Inc. All rights reserved. Available now wherever books are sold.
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
Sort by: Showing all of 2 Customer Reviews
  • Anonymous

    Posted December 13, 2003

    Excelent introduction to Reimann Hypothesis

    Excelent book written in plain English perfectly understandable for non natural speaking people. Gives an overview over the Reimann Hypothesis (RH) and applications of it. The math is not profound so everybody can read and understand the book. It explains very well the relation between the Reimann Hypothesis and the distribituin of the prime numbers. It is fascinating the way the author presents the severall mathematicians that tried to prove the RH and the way they have approach it.

    Was this review helpful? Yes  No   Report this review
  • Anonymous

    Posted September 6, 2010

    No text was provided for this review.

Sort by: Showing all of 2 Customer Reviews

If you find inappropriate content, please report it to Barnes & Noble
Why is this product inappropriate?
Comments (optional)