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

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The reason the violin doesn't look and sound like the tuning fork is that it is playing, not just an A, but also a combination of different frequencies called the harmonics. We get an additional note for each sine wave that fits exactly along the length of the string. Each additional note beats faster, which means it sounds higher. As the notes get higher they get gradually quieter, Nearly 150 years ago, a German mathematician named Bernard Riemann came as close as anyone has ever come to solving this problem. In 1859 he presented a paper on the subject of prime numbers to the Berlin Academy. At the heart of his presentation was an idea -- a hypothesis -- that seemed to reveal a magical harmony between primes and other numbers. It was an idea that Riemann argued was very likely to be true. But after his death, his housekeeper burned all of his personal papers, and to this day, no one knows whether he ever found the proof. Fantástico libro que narra la (hasta ahora inacabada) épica aventura de la hipótesis de Riemann. Una de las mejores cosas que puede tener un libro es provocar el deseo de saber más sobre un tema, en mi opinión. Y con este libro me he apuntado muchas, muchísimas cosas para luego indagar más. Eso es algo que le agradezco mucho al autor. Comenzamos poco a poco aprendiendo cómo el ministro de educación prusiano, Wilhelm von Humboldt, transformó el sistema educativo del país para dar más cancha a las ciencias básicas, justo cuando nuestro joven Riemann se incorporaba al sistema educativo. Seguimos la vida de Riemann, que comienza a mezclarse con las de Gauss, Euler, Hilbert y una plétora de matemáticos (¡y físicos!) que han contribuido esfuerzos encaminados a la resolución de la hipótesis de Riemann. El relato es fantástico y solo he echado de menos en alguna ocasión un poco más de detalle por parte del autor. Pero la intensidad del relato es mucha y mantiene mucho el interés. Es soberbio. 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 - maths The music of the primes - maths

urn:oclc:851997506 Republisher_date 20141113014332 Republisher_operator [email protected] Scandate 20141112075329 Scanner scribe13.shenzhen.archive.org Scanningcenter shenzhen Worldcat (source edition)

L'ipotesi di Riemann, l'ultimo teorema di Fermat, la congettura di Goldbach, .. sono tutte scoperte che hanno reso immortali i matematici responsabili di aver dissepolto quei tesori nel corso dell'esplorazione dei numeri primi. 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 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’? Riemann had found one very special imaginary landscape, generated by something called the zeta function, which he discovered held the secret to prime numbers. In particular, the points at sea-level in the landscape could be used to produce these special harmonic waves which changed Gauss's graph into the genuine staircase of the primes. Riemann used the coordinates of each point at

The Music of the Primes - Wikipedia

He sets himself quite a task, though. The Music of the Primes is about the search for a formula which will enable mathematicians to understand the distribution of prime numbers. Primes, you will remember, are those numbers divisible only by one and themselves - 2, 3, 5, 7, 11, 13, 17, 19, etc... - although it's not as simple as that 'etcetera' might suggest. While other number sequences continue in predictable ways, primes can still only be located through a laborious process of trial and error. There is no formula for finding the six billionth prime, for instance, although a computer, going through all the other numbers on the way, will get there eventually. The highest prime yet discovered is a number with more than four million digits. But the hypothesis still stands strong. Some believe its time has come while others feel that it'll survive its bicentenary. Some believe it is false where other think that it is true but unprovable. 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. Prime numbers are the very atoms of arithmetic. They also embody one of the most tantalising enigmas in the pursuit of human knowledge. How can one predict when the next prime number will occur? Is there a formula which could generate primes? These apparently simple questions have confounded mathematicians ever since the Ancient Greeks.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. He brings hugely enjoyable writing, full of zest and passion, to the most fundamental questions in the pursuit of true knowledge.' Sunday Times

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

Should you read this? I would say, yes. If you’re interested in the history of maths/science in general (on the basis of a prominent example), I guess it’s hard to come by a presentation that is more simple but has the same high level of seriousness, fun, and sophistication. Keating, Jonathan P. (June 2004), "Review of The Music of the Primes", Physics Today, 57 (6): 63, doi: 10.1063/1.1784279About 160 years ago, Bernhard Riemann came up with a hypothesis about the distribution of prime numbers, which is still unproven to this day. In The Music of the Primes, Marcus du Sautoy takes you through history as various mathematical powerhouses all tried to solve this famous problem.