The Music of the Primes: Why an Unsolved Problem in Mathematics Matters

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In this remarkable book, Marcus du Sautoy tells a story of eccentric and brilliant men, and of the unquenchable thirst for knowledge that has driven some to madness and others to glory. Illuminating, authoritative, and extremely engaging, The Music of the Primes provides the extraordinary history behind the holy grail of mathematics and the ongoing quest to capture it. The most unsettling thing about these new numbers was working out where they were. There wasn't any room on the number line, which contained places for numbers like 2, -3, pi or e. It was Gauss, Riemann's teacher, who suggested creating a new direction for this new imaginary number i. The ordinary numbers (or real numbers as mathematicians call them) sat on the number line This problem is at the centre of the book. But around it the author builds up a whole cultural history of mathematics. Almost all mathematicians who dealt with prime numbers at some point and made their contributions found their rightful place here. The baton has been handed down over the centuries: Euklid, Euler, Gauss, Riemann, Hilbert, Hardy/Littlewood, Ramanujan, Gödel, Turing, to name but only a few of the best known actors. The book is filled with anecdotal stuff about all of these intriguing characters. In addition, one learns about the current state of cryptography, without which secure Internet communication would not be possible, and in which large prime numbers (100 digits and more) play an essential role.

Music of the Primes Download - OceanofPDF [PDF] The Music of the Primes Download - OceanofPDF

There is a good reason for the religious, even spiritual, interpretation of mathematics - particularly number theory, and especially prime numbers. In the first instance, unlike any other area of human inquiry - even theology - the results obtained in mathematics never change. Euclid’s proofs may be superseded by more general analysis but they are nevertheless entirely correct and need no modification in a world of radically different cosmology and technology.Book Genre: Academic, Biography, History, History Of Science, Mathematics, Music, Nonfiction, Physics, Popular Science, Science

Music of the Primes by Marcus du Sautoy | Goodreads The Music of the Primes by Marcus du Sautoy | Goodreads

Desde Euclides, que demostró que los números primos son infinitos (hoy el más elevado es 2 elevado a 13.466.917 - 1, hallado en 2001 por un estudiante canadiense, un número de cuatro millones de cifras), hasta Euler en San Petersburgo, el trío de Gotinga (Gauss, Riemann, Dirichlet), Cauchy, las series armónicas de Pitágoras, Fourier, Hilbert, Hardy, Skewes, Ramanujan (el matemático Indio de Cambridge, que fue protagonista de una película reciente), Gödel y su teorema de la incompletitud, las máquinas de Touring, la criptografía RSA y la relación entre los primos y la física cuántica. Un recorrido inacabado y muy bien contado. six-sided dice would land exactly one in six times on the prime side. But of course it is very unlikely that a dice thrown 6,000 times will land exactly 1,000 times on the prime side. A fair dice is allowed to over- or under-estimate this score. But was there any way to understand how to get from Gauss's theoretical guess to the way the prime number dice had really landed? Aged 33, Riemann, now I know us mathematicians don’t generally have to do much reading of books so hopefully it will be nice to hear that the book is written in a conversational, digestible way that makes it a fairly light read – I read it on holiday. When I was finding books for my personal statement, the books “about maths” were all very readable and were more for personal interest. When looking at the other kind of maths books, I would recommend sitting at a desk and working through the problems presented and any exercises at the ends of chapters.We take it for granted now that evolutionary biology, among other things, helps us understand human behaviour, but we're not entirely sure why maths matters - if, indeed, it matters at all. Hence books like this, which strain to assert their importance: 'Why an Unsolved Problem in Mathematics Matters'. Hence Marcus du Sautoy, whose combination of brains and charm should soften up even the most wilfully innumerate of readers. Gauss's guess is like the prediction that a six-sided dice thrown 6,000 times lands exactly 1,000 times on the prime side. The heights of Riemann's harmonic waves tell us how far Gauss's guess is from the way the prime number dice really landed, that is, the errors between Gauss's guess and the true number of primes.