The Music of the Primes: Searching to Solve the Greatest Mystery in Mathematics by Marcus du Sautoy

Apr 15, 2009 Jafar rated it 3 of 5 stars

Well, aren’t prime numbers really fascinating? If you’re rolling your eyes, then you should read this book.

The main subject of the book is the Riemann Hypothesis. You have to be patient if you don’t know what it is. It takes about 100 pages of the book to get to the point where it (sort of) tells you what it is. There’s a particular complex function called zeta function. The zeros of this function can be used to correct a formula by Gauss that approximates the number of prime numbers less than...more

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Mar 31, 2013 Rosa rated it 4 of 5 stars · review of another edition

El libro empieza genial y se mantiene genial durante al menos el 80%. Marcus du Satoy sabe transmitir la pasi��n que se nota que siente por la hip��tesis de Riemann y logra explicar algo tan complicado a un p��blico bastante amplio. Personalmente yo ech�� de menos alg��n contenido un poco m��s t��cnico pero entiendo que en un libro as�� estar��a fuera de lugar. La narraci��n temporal recorriendo parte de la historia de las matem��ticas relativa a la hip��tesis de Riemann y posterior lucha en la...more

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Mar 19, 2013 Huw Evans rated it 4 of 5 stars

Shelves: science

Prime numbers are unique; they can only be divided by themselves and the number one. They crop up irregularly as you count upwards and are seemingly wholly unpredictable in their occurrence. There is an infinite number of them and they appear to be as important in life, the universe and everything as the numbers in the Fibonacci series.

There seems to be an inherent need in mathematics to rationalise and predict with a level of accuracy that goes beyond the normal. Only if the sun can be proved t...more Prime numbers are unique; they can only be divided by themselves and the number one. They crop up irregularly as you count upwards and are seemingly wholly unpredictable in their occurrence. There is an infinite number of them and they appear to be as important in life, the universe and everything as the numbers in the Fibonacci series.

There seems to be an inherent need in mathematics to rationalise and predict with a level of accuracy that goes beyond the normal. Only if the sun can be proved to have risen every day for an infinite number of days will a mathematician be happy to tell you that the sun rises. He may not be able to tell you why it rises or what the impact of its rising is but he will be happy to tell you that, under certain circumstances, it will rise every morning.

In 1859 Bernard Reimann published his hypothesis on prime numbers; that the real part of any non trivial zero of the Riemann zeta function is 1/2. It was apparently proven by Riemann himself but the proof was never found, reportedly burned by his housekeeper when tidying up after his death. Since then many mathematicians have devoted their efforts to providing enough evidence that this is true. Even with the advent of supercomputers and the finding of prime numbers with a million digits, which still fulfil the hypothesis, it has not been proven satisfactorily. Attempts to disprove it have been equally unsuccessful by not finding a single prime number that doesn't behave in this way.

So far, so good. I am not a mathematician and, even now, I could not explain to you the derivation and use of a zeta function - there may be none for all I know. This is a book as much about mathematicians as it is about their subject matter, and they are every bit as fascinating. These are people who are so driven by the abstract that they seem to want to find the rules that govern even the most random events using a language that has evolved in huge leaps to the point of being unrecognisable by ordinary men.

Marcus de Sautoy speaks clearly throughout this book and the mathematics is not overpowering. In fact I found the most interesting section was the application of prime number mathematics to internet security and cryptography. At the end of the book, I confess, no mathematical light had clicked on in my head and some of even the most basic stuff left me puzzled but, overall, this is an impressive, erudite and coherent read.(less)

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Jan 12, 2012 Maurizio Codogno rated it 2 of 5 stars · review of another edition

Shelves: finished, math, biografie

(vedi http://xmau.com/notiziole/arch/200502... per altri commenti)
Negli ultimi anni vanno di moda i libri che raccontano i grandi problemi che la matematica ha incontrato nel corso degli anni: i racconti usano meno formule possibili - e lo si può capire - e sono anche romanzati, secondo lo stile portato al successo da Eric Temple Bell che non si è peritato di portare alle future generazioni delle biografie di grandi matematici piuttosto esagerate. Con questo libro (Marcus du Sautoy, L'enigma dei...more

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Oct 14, 2011 Bill Ward rated it 3 of 5 stars · review of another edition

Shelves: math, history, geeky-history

This book was at its heart a biography of the Reimann Hypothesis, and of the mathematicians who worked on trying to prove or disprove it over the years. I really liked the way that it showed the relationships among the people involved, and how the centers of number theory research shifted from Paris to Göttingen to Princeton, and how this was caused in large part by the geopolitics of the area (Napoleon and Hitler in particular).

But this book has a serious flaw. The math was really dumbed down...more

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Jan 29, 2011 Matteo rated it 4 of 5 stars · review of another edition

Un libro avvincente come un giallo, costruito su una delle più tenaci sfide della matematica moderna, la dimostrazione dell'ipotesi di Riemann, congetturata nel 1859, forse dimostrata da Riemann stesso, ma distrutta da una domestica troppo solerte nel fuoco di un camino, o persa nelle pagine di un quaderno nero smarrito per beghe familiari degli eredi.
Il lettore è accompagnato attraverso la storia della matematica per cogliere il fascino e la sfida dei numeri primi, in un percorso divulgativo e...more

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Sep 24, 2009 Noel Bush rated it 5 of 5 stars Recommends it for: anyone

I'm most grateful to this book for finally enabling me to understand the Riemann Hypothesis. My love for math was derailed in high school when I got in over my head, and ever since it's always such a pleasure for me to find something that can help me taste some of that world that I missed out on. This book does a wonderful job of taking you through the development of some very cool math by telling the stories of the people who made important discoveries. You get a very clear sense of how mathema...more

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May 02, 2010 Aaron Humphrey rated it 4 of 5 stars · review of another edition

I was fascinated with prime numbers myself for years. Many of my classmates could (if they had been paying attention) attest to the fact that I spent much of my class time, in high school math and many university courses, factorizing random 7- and 8-digit numbers, often when I really should have been paying attention and taking notes. I had the primes up to at least 200 memorized. I often wondered if there were easier ways to factorize, and I'm still not convinced there are, though apparently th...more I was fascinated with prime numbers myself for years. Many of my classmates could (if they had been paying attention) attest to the fact that I spent much of my class time, in high school math and many university courses, factorizing random 7- and 8-digit numbers, often when I really should have been paying attention and taking notes. I had the primes up to at least 200 memorized. I often wondered if there were easier ways to factorize, and I'm still not convinced there are, though apparently there are easier ways to determine whether a number is prime or not. So this book pricked my interest immediately.

This book covers a lot of different topics about prime numbers, moving quickly into general statements and conjectures, and spends a lot of time at the heart of the prime number problem, the Riemann Hypothesis. It has something to do with a function (the Riemann zeta function) having an infinite number of zeroes on the complex plane, and whether those zeroes are all on the same line or not. The implications of this go over my head (I didn't get that far in complex analysis, sadly), but I gather that proving the Hypothesis could lead to, say, an easy way to generate prime numbers, and thus, potentially, an easy way to break RSA encryption.

It strikes about the right balance between the math and the mathematicians. One seldom thinks of how, for instance, the French Revolution or World War I impact the progress of mathematics (as opposed to, say, physics). As someone who's gone far enough in university math to understand most, if not all, of the concepts in the book, I found it enlightening, though I am both filled with respect for the mathematicians who made the discoveries in the book and more certain I could never really be one of them. I remember seeing some kind of PBSish show on TV (in our hotel room in Orlando) about the Riemann Hypothesis, which was so overdramatized that it felt like "Behind The Math". It spent more time on the failures, the people whose careers were blighted by trying to prove the Hypothesis, not to mention John "Beautiful Mind" Nash's disastrous public breakdown while lecturing on the subject. I enjoyed this much more, but then, I'd rather read a nonfiction book than watch a documentary any day. Maybe not for the faint of math, though I can't really judge.(less)

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Jul 28, 2011 Silvio Curtis rated it 5 of 5 stars · review of another edition

I picked up this book not knowing if the focus would be on math or history of math. It's definitely on the history side, but doesn't assume you know anything much about either one. It's centered on the Riemann Hypothesis, which from what this book says is the longest-standing unsolved math problem of its importance. Bernhard Riemann first proposed it in 1859. The conjecture is that the only complex numbers that give a value of 0 for a certain function have a real part of 1/2, and if true it woul...more

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Apr 23, 2013 Milo22 rated it 5 of 5 stars · review of another edition

Che meraviglia questo saggio! Nonostante la mole non indifferente riesce a conquistare e appassionare il lettore dalla prima all'ultima pagina. Non lasciatevi scoraggiare dall'argomento, perché basta semplicemente essere curiosi e appassionati di questioni scientifiche per poter apprezzare tutta la bellezza nascosta dietro questa branca della matematica e ciò che le gira intorno. Un saggio veramente stimolante, che si legge come un romanzo, e dove l'indagine sull'affascinante mondo dei numeri pr...more

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May 16, 2009 Nina Tandon is currently reading it

I really like the quote from Weber "When the globe is covered with a set of railroads and telegraph wires, this net will render services comparable to those of the nervous system in the human body, partly as a means of transport, partly as a means for the propagation of ideas and sensations with the speed of lightning." For me, having grown up with the internet and extant high-speed transportation systems, I was attracted to physiology because of the analogy I saw between the "outside" and "insi...more

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Apr 08, 2013 Eddy Allen rated it 4 of 5 stars

Shelves: arts-and-historical

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

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Sep 01, 2010 Tim rated it 4 of 5 stars · review of another edition

Shelves: 2010, maths

I have mixed feelings about this book. On the one hand, it is reasonably well written, and provides fascinating insights both into the history of mathematics and into the strange world of modern number theory. As a result, it helped change my view of what maths is, and realise that it should be a fascinating journey of discovery, a million miles away from the dry routine of calculation and prescribed problem-solving I remember from school. On the other hand, I have to admit that most of the math...more

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Dec 07, 2010 Kirsty Darbyshire rated it 3 of 5 stars · review of another edition

Shelves: library-book

This book surprised me. It's mostly about things I learnt on my maths degree and mostly hated at the time. Linking the whole history of the exploration of prime numbers, which mostly comes down to trying to prove the Riemann hypothesis, together with the background and biography of the mathematicians involved, the reasons why they were exploring this problem, and modern day real world applications makes it really interesting though. Wish I'd read it about 18 years ago really.

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May 02, 2013 Tom Hudson rated it 3 of 5 stars

I got a lot out of du Sautoy’s history of mathematics’ greatest unsolved mystery, but I still wish there had been more. A fantastic history of the places and faces of specific mathematical fields of study, it started with some juicy mathematical tidbits explaining the concepts and their importance. But, as the mathematics became more advanced, any attempt to explain the underlying concepts became vaguer and more reliant on unwieldy analogies, almost to the point of blandness.

Calling the Riemann...more I got a lot out of du Sautoy’s history of mathematics’ greatest unsolved mystery, but I still wish there had been more. A fantastic history of the places and faces of specific mathematical fields of study, it started with some juicy mathematical tidbits explaining the concepts and their importance. But, as the mathematics became more advanced, any attempt to explain the underlying concepts became vaguer and more reliant on unwieldy analogies, almost to the point of blandness.

Calling the Riemann Hypothesis an ‘unsolved mystery’ isn’t quite the right terminology. Rather, it is a very strong conjecture regarding the nature of prime numbers that has since become the part of the connective fabric of thousands of other theorems in number theory. The hypothesis has a great deal of evidence to support it but it has never been demonstrated through a connection of axioms, theorems, and other proofs tying it directly into the foundations of mathematical logic. As such, all of the theorems that depend on it are in a similar state of “we have every reason to believe this is true EXCEPT for the most important condition of having proved it to be true.”

The author does a very good job of painting portraits of the figures involved in studying prime numbers and the importance of those special numbers in the pantheon of pure mathematical thought, connecting them also to the practical applications of information security and beyond. The subject, though, is so broad and the specifics so deep, it’s hard not to sense that we are only getting a glimpse into the connectedness of the topics. He also uses analogies to help envision certain concepts, but then opts to refer to those analogies going forward instead of using the accepted mathematical terms (“sea level of a landscape” instead of “the zeroes of the function” or referring to clock calculators instead of modular arithmetic, or the beating of a drum as a metaphor for… I’m not even sure what, because the analogy seemed so flimsy: the distribution patterns of probabilistic functions, I think?). I understand the book is written for laypersons, and while I myself have a certain mathematical knowledge, I am no mathematician. However, I would have enjoyed a little more trust in the reader’s intellect to follow along without constantly falling back on the simpler, almost banal conceptualization of this topic which du Sautoy is clearly.

In the end, it was a worthwhile read, and I learned much about the history of mathematics and SOME of the specifics of the Riemann Hypothesis. I feel, though, that in du Sautoy’s attempt to share his passion, he may have simplified it a step or two too far and some of the magic of mathematics he could have conveyed with more precise language ultimately became lost in translation.
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Nov 02, 2012 Manuel Dominguez rated it 4 of 5 stars · review of another edition

Un libro excepcional.
Repasa de manera fabulosa la evolución de las matemáticas a la luz del rastro dejado por el estudio de los números primos. El hilo de la trama es tan embriagador que en un momento dado te desorienta y en te hace perderte en un alud de personajes que corren desorientados tras los misterios de la función Z de Riemann. Y es posiblemente esta parte la que se hace más espesa por la dificultad del autor de transmitir en lenguaje simple lo que sólo desde el profundo conocimiento de...more

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Apr 11, 2013 Jocelyn rated it 4 of 5 stars

I've been interested in numbers ever since I can remember. Math was always my favorite subject in school, and I majored in it in college. I don't do a lot of math anymore, with the exception of the odd algebra problem on my page a day calendar, but I enjoy reading about the history of math.

A couple of years ago my son gave me a book on the Reimann Hypothesis, Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. It was a fascinating book, but had a lot of math that...more

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Sep 03, 2012 Alex Jones rated it 2 of 5 stars · review of another edition

I think I read this book at the wrong time - if I had read it during GCSEs I'm sure I'd have loved it, during sixth form I'd still have liked it a lot. However, the summer before entering the third year of a maths degree is the wrong time for a pop-maths book. This book details Riemann's famous hypothesis about the prime numbers from before its conception to modern day and it does a good job of telling a historical story. Some details seem like padding and some a little too apocryphal, but it do...more

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Sep 02, 2012 Pallavi rated it 4 of 5 stars

It is with books like these that I wonder why I never chose to study mathematics further. I would like to believe it was due to the abysmal, 'learn-by-rote and don't explore' method that I was forced to follow in the rat-race to pick a career. It is extremely unfortunate that I ended up quitting the subject with quite some vitriol, but it is even more unfortunate that I have begun to discover, a little too late, the very subject's beauty. Well, better late than never, right?
But hey, if I really...more It is with books like these that I wonder why I never chose to study mathematics further. I would like to believe it was due to the abysmal, 'learn-by-rote and don't explore' method that I was forced to follow in the rat-race to pick a career. It is extremely unfortunate that I ended up quitting the subject with quite some vitriol, but it is even more unfortunate that I have begun to discover, a little too late, the very subject's beauty. Well, better late than never, right?
But hey, if I really hated mathematics, I should have never looked again at a book that extolled it. Maybe I wanted to redeem myself? Nah! Some part of me probably wanted to give it another chance despite the fact that it always tried to bring me down (all those damn exams!).
Anyway, it was with some haughtiness that I gave into this book. "Stupid mathematicians-I thought-trying to build something really difficult out of something as simple as 1,2,3...stupid theorems, stupid proofs that ended with 'hence proved'"-the rants in my head wouldn't end. I never saw the beauty of primes, never thought them special, actually I never really thought of them after high school. It didn't help that the book is written by a professor of mathematics who gushes over the subject somewhat unabashedly and with seemingly low regard for other disciplines. Sample this- "Those names [certain mathematicians] will live long after we have forgotten the likes of Aeschylus, Goethe and Shakespeare". This is just an absurd argument to me and something I completely disagree with. Really intelligent, well-read people will remember both mathematicians and bards alike, not to mention other significant scientists and artists. A really small point, but it began to put me off the writing, until I began to really get into why the Riemann Hypothesis is such a big deal and the interesting history of mathematics (I think the history more than the math part of it was interesting to me until a certain point and then maths soon began to catch up).
It was interesting to get into the minds of these brilliant mathematicians and read about how math played a role in their lives. It was nostalgic reading about the zillions of theorems that I had touched upon in another life and I felt incredibly patriotic reading about the contributions of Indian mathematicians and-believe it or not-a certain quote by an eminent British mathematician that the Indian education system played a huge role in honing his skills! (Wow, was it just me then?)
But most of all, it was fascinating to read about the unknown primal beat and how knowledge of at least a few of the prime numbers' secrets, starting with the Riemann Hypothesis may be linked to quantum theory and eventually a better understanding of the universe. I enjoyed the rare glimpses of humor in the author's writing [for e.g. while referring to the strange case of the autistic twins in Oliver Sacks book The Man Who Mistook His Wife for a Hat & Other Clinical Tales -"Before anyone could find out how they were doing it, the twins were separated at the age of thirty-seven by their doctors, who believed that their private numerological language had been hindering their development. Had they listened to the arcane conversations that can be heard in the common rooms of university maths departments, these doctors would probably have recommended closing them down too"]. However, the constant reminders of monetary benefits to solving problems of such significance were a bit of a turn off. Isn't eternal fame enough?
I feel like this book deserved the 4 stars I gave it, because despite some disagreement with his tone, I overall agreed with Prof. du Sautoy in that I was completely wrong in dismissing mathematics as a boring subject with no value in real life except for simple arithmetic calculations. (less)

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Dec 22, 2012 Hassan Kadhem rated it 5 of 5 stars

The Music of The Primes, a wonderful and amazing journey to the world of prime numbers and patterns

it was at the summer of 2009 when i was first introduced to the beauty and strength of the primes when the instructor asked us to implement some factorization problems in my second programming course, it was at that class where he shed a little light on the true beauty of primes talking about RSA encryption which is discussed in a late chapter of the book. almost one year later, i had the chance t...more The Music of The Primes, a wonderful and amazing journey to the world of prime numbers and patterns

it was at the summer of 2009 when i was first introduced to the beauty and strength of the primes when the instructor asked us to implement some factorization problems in my second programming course, it was at that class where he shed a little light on the true beauty of primes talking about RSA encryption which is discussed in a late chapter of the book. almost one year later, i had the chance to dive deeper in the world of primes while studying Number Theory at another course, and what a world it was!

this book is concerned about prime numbers, exploring them .. and illustrating the most famous problems related to them. some of which were solved, and some remained unsolved till this day. the most famous problem of them all is The Riemann Hypothesis which is discussed all along the book due to its importance, struggles and implications it will have (if solved) on other problems, mathematics and other sciences like physics.

du Sautoy takes the reader into a long journey exposing the ideas of the greatest minds ever, starting from Fermat, moving to Gauss, Riemann, Gödel, the enigma code breaker and father of AI and computing Alan Turing .. and many many others.

Marcus is very good at clarifying scientific concepts, he explains the Riemann Hypothesis really well that you grasp the core of it even if you're not a mathematician. i remember i came across the Riemann Hypothesis before reading this book and i tried to understand it by reading its Wikipedia related articles several times, but without having the slightest of idea about it! not until i read this book i understood what it is really about and realized how big its potential is.

the book explores The Riemann Hypothesis which is mainly a problem of navigating the primes looking for a pattern.

this is a really great book, one of the best i ever read. and i gotta say, du Sautoy's books are better than his documentaries. which reminds me to watch the televised series of this book presented by du Sautoy :D

as written on the back of the book, "A book not to be put down"!
cheers!

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Oct 17, 2012 Elisa Ferrarese rated it 5 of 5 stars · review of another edition

Shelves: read-multiple-times, recommended-my-favorites

Un libro coinvolgente ed affascinante su uno degli aspetti più intriganti della matematica, quello della dimostrazione dell’ipotesi di Reimann.
Il mistero dei numeri primi, così potentemente legati all’essenza stessa della realtà, è capace di avvincere chi è già appassionato di matematica, e forse in grado di far innamorare della matematica chi a scuola non l’ha mai amata.
Di certo questo è il più bel libro sulla matematica che abbia mai letto, racconta l’appassionante storia della matematica, fat...more

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Sep 27, 2011 Jishnu Bhattacharya rated it 5 of 5 stars · review of another edition

Shelves: popular-science, non-fiction

The Music of the Primes is an amazing introduction to the Riemann hypothesis. I'm a bit biased here, since I like math, and have some idea about the subject matter. If you know a bit about prime counting, logarithms, modular arithmetic and quantum mechanics, you can't put this down. Even the people who don't like math might find it interesting, it is so well written. The language is lucid, and even complicated mathematical concepts are presented in a way that is easy to understand. In fact, he n...more

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May 13, 2009 Andrea rated it 5 of 5 stars · review of another edition Recommends it for: Alysia, Gwen, Robbin

Recommended to Andrea by: Sally

Shelves: math, scientific-journalism

You are not going to believe that a book on a math subject would be hard to put down but this book is brilliantly written. I started reading this with doubts I would actually finish and I keep getting hooked into reading the next chapter and the next chapter. The author writes the whole book like this is THE GREATEST treasure hunt ever. He starts out by talking about the million dollar prize for the person who can prove Riemann's Hypothesis. Then he tells the story of how people discovered littl...more

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Jul 27, 2007 Dan rated it 4 of 5 stars Recommends it for: people interested in number theory

As much as I think popular science is as a genre futile and mostly poorly executed, I think popular math nonfiction is very interesting and well done. Popular math nonfiction books are more often accurate while packing a lot of relevant information.

This book is about the history of the Riemann hypothesis, an unproven statement in mathematics that relates a function of complex numbers to the distribution of the primes. Specifically, if the Riemann hypothesis were true, there is a function which p...more

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Jun 12, 2007 graycastle rated it 3 of 5 stars

Shelves: mathporn, nonfiction

This was a lot of fun for me, because I'm one of those who is really interested in math, but has no formal training in it. It's probably best classified as a work of history rather than a work of math; it tracks the history of investigation into prime numbers from the time of Ancient Greece to the present. If you're wondering what's up with that Riemann hypothesis thing, this is a good source; it explains the history of the concept, Riemann's work, and the fallout since. I really like the histor...more

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Sep 10, 2009 Nikos Skantzos rated it 5 of 5 stars

A totally absorbing book for those who enjoy numbers and their curiosities. It made me fall in love with mathematics again. From Euclid to Gauss, Riemann, Hardy, Ramanujan and to the 20th century... Here's the history of the mystic prime numbers. In high school we learned about Euclid's proof of the existence of an infinite number of primes but I admit I feel embarassed I didn't get the ingenuity of it till reading this book. It provides at the same time great biographies of the men behind the s...more

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Jan 06, 2012 Lsanti Santi rated it 4 of 5 stars · review of another edition

Uno dei principali enigmi della matematica spiegato in maniera semplice e chiara. Bello scoprire il mistero della matematica, l'impegno di uomini che vogliono arrivare oltre il limite della conoscenza, le sfide tra menti eccelse per arrivare a nuovi risultati. Coinvolgente e affascinante. Da leggere anche per chi non ha mai amato la matematica come materia di scuola ma non può non restare affascinato dall'importanza dei numeri e dei loro misteri nella vista di tutti noi.

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Jul 08, 2012 Oscar rated it 2 of 5 stars

Shelves: popsci

Mostly a random assortment of anecdotes and biographical fun facts some of which are apocryphal and others which are not all that fascinating. Not very well written or original but it might serve to sate the curiosity of someone not at all familiar with mathematics. Even so it would be better if it actually contained some mathematics or if the book made it clear that the book could as well be about philately or any other field people pursue passionately.

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Feb 21, 2012 Alvin rated it 4 of 5 stars

A great overview of the history behind the Reimann Hypothesis. I learned a few new and surprising things, that a formula for the primes does exist and is formed by the locations of the zeroes on critical line of the zeta function and that at very large numbers, the distribution of the zeroes resembles the eigenvalues of the excitation states of atomic nuclei, a very unexpected connection between the abstract and reality.

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Aug 27, 2011 Christin rated it 5 of 5 stars

Engaging journey through mathematics-the writing style is fantastic and the content interesting. I bought this book with high hopes (a ex-mathlete pursuing abandoned mathematical interest), but then shelved it for over a year. When I picked it up again I was hesitant (i.e. intimidated) but so glad I did! Du Satoy's enthusiasm for the subject matters pours out of every page.

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