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

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sea-level to create one of the prime number harmonics. The frequency of each harmonic was determined by how far north the corresponding point at sea-level was, and how loud each harmonic sounded was determined by the east-west frequency. A pattern emerges Gowers, W. T. (October 2003), "Prime time for mathematics (review of Prime Obsession and The Music of the Primes)", Nature, 425 (6958): 562, doi: 10.1038/425562a If there is advanced technological life elsewhere in the universe, it would unlikely be Christian, or Muslim, or Jewish, or Buddhist. It would however certainly know the same mathematics that we do. And it would understand the phenomenon of the prime numbers and their significance as much as, perhaps more than, we do. Mathematics is the natural religion of the cosmos; and prime numbers are its central mystery. Lccn 2004270176 Ocr_converted abbyy-to-hocr 1.1.20 Ocr_module_version 0.0.17 Openlibrary OL3319126M Openlibrary_edition the book explores The Riemann Hypothesis which is mainly a problem of navigating the primes looking for a pattern.

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

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.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 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.

The Music of the Primes: Why an Unsolved Problem in

So how fair are the prime number dice? Mathematicians call a dice "fair" if the difference between the theoretical behaviour of the dice and the actual behaviour after N tosses is within the region of the square root of N. The heights of Riemann's harmonics are given by the east-west coordinate of the corresponding point at sea-level. If the east-west coordinate is c then It has been a few years since I stopped my Masters in Maths, and I was starting to miss it. So, this book looked like it would hit the spot. At the start of the book, you get the impression that you will only need to understand what a prime number is, and what an imaginary number is, to fully appreciate the story. And for a fair bit of the book that is true. Particularly at the beginning, where there is a lot more mathematical history than complicated maths.

The Music of the Primes

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

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

Mathematicians feel like characters and the course of history feels like a fictional story beautifully woven by du Sautoy. But Riemann couldn't prove that every point at sea level really lay on this magic leyline (or "critical line", as mathematicians call it) that seemed to be running through his landscape. But he hypothesised they did. And this is what all mathematicians would sell their souls to prove - even without the million dollar prize that has been offered for a solution. The Riemann Hypothesis: 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. 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. Una cosa que no me ha gustado es el abuso que hace a veces el autor de la analogía. Es difícil divulgar sobre matemáticas, y más sobre matemáticas complejas como la teoría de números. Hay que encontrar un equilibrio entre lo demasiado simple y lo demasiado farragoso. Pero al autor, a veces, se va no ya por lo simple sino por lo incomprensible. Cuando habla de la intersección no nula de los números primos y la física cuántica, hace una analogía con "una tambor cuántico", que no queda del todo clara. Pero a partir de ese momento sólo hablará de físicos y matemáticos diversos que investigan sobre tambores cuánticos, así sin comillas. ¿Tambores cuánticos? ¿No podría el autor definir algo más en serio, aunque fuera una vez, a qué se refiere exactamente con un tambor cuántico, y luego ya seguir con la analogía? Otra de estas analogías son las "calculadoras de reloj", que usa sin comillas a lo largo de todo el libro para referirse a la aritmética modular. Como en un reloj de 12 horas 9+4 o es 13 sino 1 (y así nos introduce la aritmética modular), cualquier referencia posterior a la aritmética modular la traviste de calculadoras de reloj. Son dos analogías sobreutilizadas que recuerdo que no me gustaron. En cualquier caso, nadie ha dicho que sea fácil divulgar ideas tan complejas. Su punto de de equilibrio entre lo preciso y lo comprensible para el público está un poco más escorado que el mío.To the right is an animation showing the effect of adding on the first 100 harmonics. Adding on each new wave contorts the smooth graph that little bit more. Riemann realised that by the time you added on the infinitely many waves he had discovered, the resulting graph would be an exact match for the prime number staircase.