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

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Connes is one of the revolutionaries of the subject, a benign Robespierre of mathematics to Bombieri’s Louis XVI. It is a story of strange journeys, last-minute escapes from death and the unquenchable thirst for knowledge.

The Music of the Primes by Marcus du Sautoy | Goodreads

In science, it has critical ramifications in Quantum Mechanics, Chaos Theory, and the future of computing. Sautoy does an excellent job of delivering the history with plenty of mathematical depth, and revealing the humanity of the people behind those walls. Modern mathematical proofs are notoriously long-winded (Andrew Wiles's proof of Fermat's last theorem occupied several hundred pages of typescript) and was composed of innumerable digressions. 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.

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 liturgy and art of the Roman Church has no advantage over the aesthetic wonder of the Euler Identity, which connects worlds even further apart than Heaven and Earth. Somebody allegedly asked Hilbert, ‘If you were to be revived like Barbarossa, after five hundred years, what would you do? In school we spend our time learning the scales and time signatures of this music, without knowing what joys await us if we can master these technical exercises.

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

He had always been fascinated by properties of numbers as he browsed through the mathematics books his father, an economist, had collected in his extensive library. Desde Euclides, que demostró que los números primos son infinitos (hoy el más elevado es 2 elevado a 13.

While academic subjects such as science, history and psychology have successfully descended from the ivory towers, and turned abstract theories into bestselling books and television programmes, maths is still lurking shyly in the cloisters.

The music of the primes | plus.maths.org

Considered to be even more difficult and more important than Fermat's Last Theorem, Riemann's solution would serve as a periodic table in charting the entire mathematical universe. Riemann has assumed that the zeros of a certain (admittedly rather complex) function, the Zeta-function, all lie on a certain critical line. It is the idea that brings together many other areas of science and has ramifications within Quantum Mechanics, Chaos Theory and the future of computing. There are an infinite number of these zeros, so one cannot simply determine and check them all with the help of a super computer, because even the most powerful computer cannot perform an infinite number of calculations in a finite time.

Had the alien culture transmitted the previous ten years of alien winning lottery numbers, Ellie couldn’t have distinguished them from the background noise. But was there any way to understand how to get from Gauss's theoretical guess to the way the prime number dice had really landed? Marcus du Sautoy works a lot with metaphors, which is frowned upon by real mathematicians, but which help to keep the layman in line. He is an extraordinarily charismatic figure whose fiery style is far from the image of the staid, awkward mathematician. 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 Music of the Primes - University College Oxford

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.I really like the quote from Weber "When the globe is covered with a set of railroads and telegraph wires, this net will render services comparable to those of the nervous system in the human body, partly as a means of transport, partly as a means for the propagation of ideas and sensations with the speed of lightning. What we are not taught is that primes represent the most tantalizing mystery in the pursuit of human knowledge. O un matematico indiano cresciuto nel totale isolamento dalla comunità scientifica riesce a percorrere a suo modo un lungo cammino nella storia matematica, mentre un incontro quasi fortuito all’ora del tè getta luce sulla connessione tra i numeri e la fisica quantistica. Connes’s audacious belief that his new geometry could unmask not only the world of quantum physics but explain the Riemann Hypothesis – the greatest mystery about numbers – was met with surprise and even shock.