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

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This theorem is important in areas of both pure and applied Maths, as many proofs of the last century rely on the Riemann Hypothesis being true and prime numbers have applications in cryptography or quantum computers. Marcus du Sautoy does a great job of weaving these links into the book. Du Sautoy is a contagious enthusiast, a populist with a staunch faith in the public's intelligence...he has uncovered a wealth of intriguing anecdotes that he has woven into a compelling narrative.' Observer 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! 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. Leutwyler, Kristin (May 2003), "Math's Most Wanted: A trio of books traces the quest to prove the Riemann hypothesis", Scientific American, 288 (5): 94–95, doi: 10.1038/scientificamerican0503-94, JSTOR 26060289

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

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. 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). Prime numbers are those integers which can only be divided without remainder by themselves (or of course by 1). Put another way, as du Sautoy does, prime numbers are the atoms from which all other numbers are composed. 1, 2, 3, and 5 are prime. 4 is merely 2 x 2; and 6 is 2 x 3. 10 is 2 x 5. Prime numbers constitute the periodic table of mathematical elements which can be mixed and matched to form molecules and compounds of enormous size and complexity. If the Riemann Hypothesis is true, it explains why there are no strong patterns in the primes. A zero off Riemann's critical line would cause a strong pattern to be stamped on the primes, as this one harmonic dominated the rest of the harmonics. The Riemann Hypothesis says that we believe this is not the case. The harmonics are in some perfect balance, creating the endless ebb and flow of the

Lccn 2004270176 Ocr_converted abbyy-to-hocr 1.1.20 Ocr_module_version 0.0.17 Openlibrary OL3319126M Openlibrary_edition 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.

BBC Two - The Music of the Primes

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. About 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. Un libro coinvolgente ed affascinante su uno degli aspetti più intriganti della matematica, quello della dimostrazione dell’ipotesi di Reimann. Riemann was very shy as a schoolchild and preferred to hide in his headmaster's library reading maths books rather than playing outside with his classmates. It was while reading one of these books that Riemann first learnt about Gauss's guess for the number of primes one should encounter as one counts higher and higher. Based on the idea of the prime number dice, Gauss had produced a function, Mathematicians feel like characters and the course of history feels like a fictional story beautifully woven by du Sautoy.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. frequencies. This time the sine waves must fit the length of the clarinet but be open at one end, closed at the other. This results in the clarinet choosing a different sequence of harmonic notes to those favoured by the violin. 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. 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.