Marcus Du Sautoy

P.S.: The Music of the Primes (Paperback)

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Inthe tradition of Fermat's Enigma and Pi, Marcus du Sautoy tells the illuminating, authoritative, and engagingstory of Bernhard Reimann and the ongoing quest tocapture the holy grail of mathematics--the formula to predict prime numbers.Oliver Sacks, author of The Man Who Mistook His Wife for a Hat, calls TheMusic of the Primes "an amazing book. . . . I could not put it down once Ihad started." Simon Winchester, author of The Professor and the Madman, writes, "this fascinating account, decoding the inscrutable language of themathematical priesthood, is written like the purest poetry. Marcus du Sautoy's enthusiasm shines through every line of this hymnto the joy of high intelligence, illuminating as it does so even the darkestcorners of his most arcane universe."


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Marcus Du Sautoy
The Music of the Primes
Publication Date
August, 2012
Assembled Product Dimensions (L x W x H)
9.00 x 6.00 x 1.50 Inches

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Indeholder 1. Who Wan...

Indeholder "1. Who Wants To Be a Millionaire?", "2. The Atoms of Arithmetic", "3. Riemann's Imaginary Mathematical Looking-Glass"; "4. The Riemann Hypothesis: From Random Primes to Orderly Zeros", "5. The Mathematical Relay Race: Realising Riemann's Revolution", "6. Ramanujan, the Mathematical Mystic", "7. Mathematical Exodus: From Göttingen to Princeton", "8. Machines of the Mind", "9. The Computer Age: From the Mind to the Desktop", "10. Cracking Numbers and Codes", "11. From Orderly Zeros to Quantum Chaos", "12. The Missing Piece of the Jigsaw". Desuden Acknowledgements, Further Reading, Illustration and Text Credits, Index. Kapitel 1 indeholder de basale ting om primtal. Kapitel 2 har en sjov konjekture: 2^n mod n = 2 hviss n er primtal. Det passer ikke, for 341 = 11 * 31. Er der uendeligt mange mersenne primtal? Tjah. Fermat, Mersenne, Euler, Gauss. Euler 2,3,5,11,17,41. Gauss n/log(n) / pi(n) går mod 1 for n gående mod uendelig. men han kan ikke bevise det. Legendre's tilsvarende formel. Kapitel 3. Riemann Kapitel 4. Riemann finder en analytisk fortsættelse af zetafunktionen på de komplekse tal. Riemann's refinement til pi(x) approximationen mangler lige bidragene fra nulpunkterne. Fourier var med Napoleon på hans togt til Ægypten og kom flere år senere tilbage og var besat af varme. Deraf fourierrækker og differentialligninger for varmeudbredelse. Kapitel 5. Hilbert, Minkowski og Landau i Göttingen. Hadamard's bevis for Gauss' formodning. Harald Bohr. Hardy - Littlewood axiomer for samarbejde. Kapitel 6. Ramanujan dukker op og Hardy - Littlewood bliver helt elektriske, omend de ikke tager sig helt godt af gæsten. Side 143 har en eksakt, men mærkelig formel for partiionstallene, 1,2,3,5,7,11,15,22,30... Ramanujan har et fif til at angribe Goldbach-formodningen. De første 38 nuller. Kapitel 7. Riemann-Siegel formel finder de næste 1041 nuller. Kapitel 8. Turing og Gödel. Cohen løser Hilberts 1. problem Kontinuumshypotesen og viser at nej, det er ikke beviseligt ud fra axiomerne. Julia Robinson og Yuri Matijasevich viser at hver Turing beregnelig sekvens svarer til en ligning, dvs primtallene svarer også til en ligning - det er her den der ubrugelige ligning med 26 variable kommer fra. Kapitel 9. Lehmer-Lucas test for Mersenne primtal. Firfarve teorem, Zagier og de første 300 millioner nuller. Kapitel 10. RSA kryptografi og lidt historie om elliptiske kurver. Kapitel 11: Class number theorem følger både hvis Riemannhypotesen gælder og hvis den ikke gælder. Kapitel 12: Opremsning af nyere forsøg fra nye matematikere på at tackle problemet. Glimrende bog, som dog fuser lidt ud fordi Riemann hypotesen stadig ikke er bevist.

Average Rating:(4.0)out of 5 stars

Subtitled: why an uns...

Subtitled: "why an unsolved problem in mathematics matters", this book offers an inspiring tour of the dizzying mindscapes of higher mathematics. Particularly fascinating is du Sautoy's account of the huge impact of eggheads in their ivory towers on the big bucks world of e-commerce. The unifying thread of this narrative is prime number theory, notably the century-old quest for the crucial proof of Riemann's Hypothesis. The Hypothesis itself is unfortunately so arcane that du Sautoy struggles to make it accessible to the layman. But he still captures the passion and the excitement of the search, the relevance of mathematics to the everyday world. Along the way we can savour many anecdotes and biographical sketches of the celebrities of this strange world. The story of the self-taught Indian genius, Ramanujan, is enthralling. Imagine: Ramanujan is sharing a London taxi with a Cambridge professor when the latter remarks that the taxi registration - 1729 - is not a very interesting number. On the contrary, Ramanujan replies, it is the smallest number expressible as the sum of two cubes in two different ways: 1729 = 13 cubed + 12 cubed = 10 cubed + 9 cubed. Obvious, really, when you think about it. Then there is the Riemann himself. Working quietly at the university of Göttingen in 1866, he suddenly finds himself in the middle of a battle between Hanoverian and Prussian troops. He abruptly makes his escape to Italy. Meanwhile, professorial colleagues rush to his lodgings to rescue his papers. There they find Riemann's housekeeper, with her German sense of order, busily consigning the great man's untidy papers to the fire. Much is saved, but a century later the mathematically world still wonders what treasures were lost. By the way, Riemann's Hypothesis remains at large, with a million dollar prize waiting for the solver.

Average Rating:(3.0)out of 5 stars

Marcus du Sautoys boo...

Marcus du Sautoy's book jumps too quickly from topic to topic and is often way too shallow, especially in the more mathematical parts. He also constantly uses vague metaphors, usually without even mentioning the proper term. Especially the constant mentioning of 'clocks' and 'hours' when talking about modular arithmetic annoyed me to no end. Likewise, many theorems are mentioned without ever explaining what they are. Some kind of footnotes or endnotes would have been perfect here for those with a background in mathematics, or even for interested readers who don't. Regardless, the biographical sections are often very interesting, and the book contained quite a few mathematical tidbits I didn't know about. Also enjoyed the parts about the connection to quantum physics, which really surprised me.

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