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

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Edwards, Harold M. (December 2004), "Prime obsession; The Music of the Primes; The Riemann Hypothesis", The Mathematical Intelligencer, 26 (1): 55–59, doi: 10.1007/bf02985403, S2CID 122755808 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’?

The Music of the Primes - Wikipedia

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

A pattern emerges

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. Well, aren’t prime numbers really fascinating? If you’re rolling your eyes, then you should read this book. Riemann died shortly after he made his great conjecture aged only 39. Faced with the mess he left behind, his housekeeper destroyed many of his unpublished scribblings before she was stopped by members of the faculty in Göttingen. Did Riemann have a proof that was lost for eternity in the kitchen fire of his over-zealous housekeeper? We shall never know.

The music of the primes : Marcus Du Sautoy : Free Download The music of the primes : Marcus Du Sautoy : Free Download

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, 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.

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. 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 - University College Oxford

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. 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. 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.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

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