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Name:Mathematical Mountaintops~tqw~ darksiderg

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Mathematical Mountaintops
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General Information
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Type.................: Ebook
Part Size............: 8,571,269 bytes




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Posted by............: ~tqw~

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Release Notes
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In Mathematical Mountaintops, John Casti brilliantly recreates the solutions to
the five greatest mathematical problems of all time: The Four-Color Map Problem,
Fermat's Last Theorem, The Continuum Hypothesis, Kepler's Conjecture, and
Hilbert's Tenth Problem.

Casti recounts these mathematical quests with great verve. In retelling the
story of Hilbert's Tenth Problem, for instance, he sweeps from Britain to New
York to Leningrad and introduces us to such luminaries as Alan Turing, before
turning to the young Soviet researcher who credited his breakthrough to a 700-
year-old Italian problem about rabbits. He describes how Fermat's Last Theorem
tantalized generations of scientists, who tried for three centuries to answer
it, and relates how the final solution was greeted with the unprecedented front
-page headlines, prize money, and international celebration--before a flaw (soon
resolved) turned up. Casti's account of the struggle to solve Kepler's
Conjecture wittily reveals how the "proof of the obvious" sometimes eludes us
for centuries. And his discussion of The Continuum Hypothesis movingly portrays
the tragic figure of Georg Cantor, the troubled genius who created the first
truly original mathematics since the Greeks, yet died insane in an institution.
Casti closes with a preview of the "Magnificent Seven"--the greatest unsolved
mathematical mysteries, each of which carries a million-dollar bounty from the
Clay Mathematics Institute--including the Poincare Conjecture, the Yang-Mills
Existence and Mass Gap (why physicists can't isolate quarks), and the Reimann
Hypothesis ("the granddaddy of all mathematical mysteries").

Mathematical Mountaintops is a brilliant account of mathematicians in action--
seeking hidden patterns and structures, forging elegant chains of reasoning--as
they struggle with problems that challenged the greatest minds for decades, if
not centuries.

Table of Contents

Prologue: The Art of the Problem 1
1 Hilbert's Tenth Problem 11
2 The Four-Color Problem 43
3 The Continuum Hypothesis 77
4 The Kepler Conjecture 109
5 Fermat's Last Theorem 137
Epilogue: The Magnificent Seven 163
Suggested Readings 169
Index 178

Product Details

* ISBN: 0195141717
* ISBN-13: 9780195141719
* Format: Hardcover, 196pp
* Publisher: Oxford University Press
* Pub. Date: October 2001

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