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

Product Information

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! 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 Euclid’s proofs may be superseded by more general analysis but they are nevertheless entirely correct and need no modification in a world of radically different cosmology and technology. The fun arises because although mathematicians know primes occur less and less frequently as we progress up the scale of numbers, no one knows how to predict when the next one will be encountered. They can be, and have been, calculated to very large numbers indeed, but they can’t be anticipated, only recognised once they appear.* Or should the term be ‘revealed’?

Music of the Primes by Marcus du Sautoy | Perlego [PDF] The Music of the Primes by Marcus du Sautoy | Perlego

La idea central del libro es la de si los primos siguen un patrón o la naturaleza los elige de manera aleatoria. Riemann conjeturó con una función específica (la función zeta) que los ceros que producía esta función sí tienen que seguir un orden lógico. Su conjetura es uno de los veintitrés problemas que propuso Hilbert en un congreso en la Sorbona en el año 1900. Esta hipótesis sigue eludiendo una demostración válida, y su búsqueda es la que cuenta este libro. Again by adding the heights of all these sine waves together we can see the square shape of the clarinet emerging from the basic sine wave corresponding to the A of the tuning fork. Follow this link to see the way the first five harmonics combine to build up the wave shape created by a clarinet. But most of all, this is the story of a problem, which, since its formulation in 1859 has baffled the greatest of minds - The Riemann Hypothesis.However, I felt more and more at sea as the book went on. Given that I have studied the Riemann Hypothesis at Masters level, and even written an essay on it and the Riemann Zeta Function (in 2019), you would think I’d do better – however, my maths brain has not done well since I gave up in 2021, and I have forgotten so much.

Million dollar question | Science and nature books | The Guardian Million dollar question | Science and nature books | The Guardian

There’s surprisingly little maths in this book about an unsolved maths problem, only a few scattered and rather simple equations and some graphs, all of which should be understandable for non-mathematicians. And even if you don’t, you can still follow the text easily. Marcus du Sautoy works a lot with metaphors, which is frowned upon by real mathematicians, but which help to keep the layman in line. the height of the wave grows like N c. This means the contribution from this harmonic to the error between Gauss's guess and the real number of primes will be N c. So if the Riemann Hypothesis is correct and c is always 1/2, the error will always be N 1/2 (which is just another way of writing the square root of N). If true, the Prime numbers become less frequent as numbers get larger. There are fewer in any interval greater than let’s say 1000, than the same interval less than 1000. This is intuitively obvious since the greater the number the more lesser numbers there that might be divided into it evenly. Interestingly, there is always at least one prime between any number and its double. negative times a negative is always positive. But the French revolution gave mathematicians the courage to think of new ideas. They invented new months and new days of the week, so why not new numbers? So came about the birth of the new number i, the square root of minus one. All the other imaginary numbers were got by taking combinations of this new number with the ordinary numbers, for the book explores The Riemann Hypothesis which is mainly a problem of navigating the primes looking for a pattern.Prime numbers and their distribution have always been one of the more interesting subjects to talk about. This book takes you through the whole journey of starting out with finding the first few prime numbers to trying to find a pattern on how primes are spread through the universe of natural numbers. The list of protagonists include Euclid, Euler, Gauss, Riemann, Polignac, Hilbert, Hardy, Littlewood, Ramanujan, Godel, Turing to name a few. Naturally, the book focuses on one of the most important conjectures ever : The Riemann Hypothesis. 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. Although the book does not delve into any theory, it is tough not to keep reading about each of the protagonists and their achievements on the side. It is tough to get out of the loop. Wikipedia, Numberphile, 3Blue1Brown are some of the resources that I would suggest to go along with the book.

music of the primes - maths The music of the primes - maths

Book Genre: Academic, Biography, History, History Of Science, Mathematics, Music, Nonfiction, Physics, Popular Science, Science The sound of the clarinet, in contrast, is depicted by a sound wave that looks like the crenellations on a castle, which leads to its more closed sound, compared to the sharp note of the violin. In the same way as the violin's characteristic sound is made up of additional harmonic notes, the sound of clarinet too is built by simultaneously playing a combination of sine waves of different called the logarithmic integral, which seemed to give a very good estimate for the number of primes. The graph to the left shows Gauss's function compared to the true number of primes amongst the first 100 numbers. Really a question: Could someone tell me precisely what the ordinate and abscissa are in the three graphs shown? I have and have twice read "The Music of the Primes. Wonderful book, but I want more! I've got Edwards book; it's slow going, though so far I'm making it. I'm quite familiar with Fourier Analysis as applied to engineering and physics, but not to Number Theory. I have a Ph.D. in Applied Math, and am now retired and having fun studying the primes. Di certo questo è il più bel libro sulla matematica che abbia mai letto, racconta l’appassionante storia della matematica, fatta di scoperte e progressi che viaggiano da un capo all’altro del mondo, ma soprattutto la storia di matematici, grandi uomini che competono per arrivare oltre i confini della conoscenza e personaggi spesso affascinanti: Euclide, Gauss, Riemann, Ramanujan, Weil… quanto vorrei poter parlare per un momento con loro!running East-West in this map of imaginary numbers, while the North-South direction corresponded to the imaginary part. So each imaginary number, like -3+4 i, just became a point in this map: go 3 units west and 4 units north. Suddenly a two-dimensional map of the world of imaginary numbers emerged, making these numbers far more tangible. 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). Heawood, Jonathan (August 23, 2003), "Million dollar question: Marcus du Sautoy tries to explain why an unsolved mathematical conundrum matters in The Music of the Primes", The Guardian Un libro muy interesante a ratos sobre la historia de las matemáticas, y en especial la teoría de números y la hipótesis de Riemann. Se lee como una novela de acción y de búsqueda, y por sus páginas circulan las mentes matemáticas más brillantes, pero habla de algo cuya contemplación o entendimiento es sólo para matemáticos expertos (salvo que uno entienda cosas como "...el mismo comportamiento de las diferencias entre pares de valores propios de las matrices aleatorias hermitianas"). De hecho el libro no cuenta con fórmulas matemáticas sino que las describe, como si estuviéramos comentando una obra de arte basándonos en la sombra que deja en el suelo su proyección. Con tanta metáfora, ciertos capítulos son incomprensibles. Pero el esfuerzo divulgativo es notable y en otros capítulos hay verdadera emoción con la brillantez de algunas mentes.