Visions of infinity : the great mathematical problems
 Responsibility
 Ian Stewart.
 Language
 English.
 Imprint
 New York, NY : Basic Books, c2013.
 Physical description
 x, 340 p. : ill. ; 24 cm
Access
Creators/Contributors
 Author/Creator
 Stewart, Ian, 1945
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [305]306) and index.
 Contents

 Great problems
 Prime territory : Goldbach Conjecture
 The puzzle of pi : squaring the circle
 Mapmaking mysteries : Four Color theorem
 Sphereful symmetry : Kepler Conjecture
 New solutions for old : Mordell Conjecture
 Inadequate margins : Fermat's Last Theorem
 Orbital chaos : Threebody problem
 Patterns in prime : Riemann Hypothesis
 What shape is a sphere? : Poincaré Conjecture
 They can't all be easy : P/NP problem
 Fluid thinking : NavierStokes Equation
 Quantum conundrum : Mass Gap Hypothesis
 Diophantine dreams : BirchSwinnertonDyer Conjecture
 Complex cycles : Hodge Conjecture
 Where next?
 Twelve for the future.
 Publisher's Summary
 It is one of the wonders of mathematics that, for every problem mathematicians solve, another awaits to perplex and galvanize them. Some of these problems are new, while others have puzzled and bewitched thinkers across the ages. Such challenges offer a tantalizing glimpse of the field's unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility. In Visions of Infinity, celebrated mathematician Ian Stewart provides a fascinating overview of the most formidable problems mathematicians have vanquished, and those that vex them still. He explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. The threecentury effort to prove Fermat's last theoremfirst posited in 1630, and finally solved by Andrew Wiles in 1995led to the creation of algebraic number theory and complex analysis. The Poincare conjecture, which was cracked in 2002 by the eccentric genius Grigori Perelman, has become fundamental to mathematicians' understanding of threedimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which Stewart refers to as the "Holy Grail of pure mathematics, " and the P/NP problem, which straddles mathematics and computer science, could easily remain unproved for another hundred years. An approachable and illuminating history of mathematics as told through fourteen of its greatest problems, Visions of Infinity reveals how mathematicians the world over are rising to the challenges set by their predecessorsand how the enigmas of the past inevitably surrender to the powerful techniques of the present.
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Contributor biographical information
Publisher description
Subjects
 Subject
 Mathematics.
 Number theory.
Bibliographic information
 Publication date
 2013
 ISBN
 9780465022403 (hardcover)
 0465022405 (hardcover)
 9780465065998 (ebook)
 0465065996 (ebook)