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The Resource Visions of infinity : the great mathematical problems, Ian Stewart

Visions of infinity : the great mathematical problems, Ian Stewart

Creator
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 this book the author, a mathematician, provides an 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 three-century effort to prove Fermat's last theorem, first posited in 1630, and finally solved by Andrew Wiles in 1995, led 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 three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which the author 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, this book reveals how mathematicians the world over are rising to the challenges set by their predecessors, and how the enigmas of the past inevitably surrender to the powerful techniques of the present. -- From publisher's website
  • A history of mathematics as told through foureen of its greatest problems explains why mathematical problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole
Language
eng
Work
Publication
Extent
x, 340 p.
Contents
  • Great problems
  • Prime territory : Goldbach conjecture
  • The puzzle of pi : squaring the circle
  • Mapmaking mysteries : four colour theorem
  • Sphereful symmetry : Kepler conjecture
  • New solutions for old : Mordell conjecture
  • Inadequate margins : Fermat's last theorem
  • Orbital chaos : three-body problem
  • Patterns in primes : Riemann hypothesis
  • What shape is a sphere? : Poincaré conjecture
  • They can't all be easy : P/NP problem
  • Fluid thinking : Navier-Stokes equation
  • Quantum conundrum : mass gap hypothesis
  • Diophantine dreams : Birch-Swinnerton-Dyer conjecture
  • Complex cycles : Hodge conjecture
  • Where next?
  • Twelve for the future
Isbn
9780465022403
Instance
Label
Visions of infinity : the great mathematical problems
Title
Visions of infinity
Title remainder
the great mathematical problems
Statement of responsibility
Ian Stewart
Creator
Subject
Language
eng
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 this book the author, a mathematician, provides an 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 three-century effort to prove Fermat's last theorem, first posited in 1630, and finally solved by Andrew Wiles in 1995, led 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 three-dimensional shapes. But while mathematicians have made enormous advances in recent years, some problems continue to baffle us. Indeed, the Riemann hypothesis, which the author 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, this book reveals how mathematicians the world over are rising to the challenges set by their predecessors, and how the enigmas of the past inevitably surrender to the powerful techniques of the present. -- From publisher's website
  • A history of mathematics as told through foureen of its greatest problems explains why mathematical problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole
Cataloging source
BTCTA
http://library.link/vocab/creatorDate
1945-
http://library.link/vocab/creatorName
Stewart, Ian
Illustrations
illustrations
Index
index present
LC call number
QA93
LC item number
.S745 2013
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Mathematics
  • Number theory
  • Mathematisches Problem
  • Mathematik
  • Zahlentheorie
  • Mathematics
  • Number theory
Label
Visions of infinity : the great mathematical problems, Ian Stewart
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [305]-324) and index
Contents
Great problems -- Prime territory : Goldbach conjecture -- The puzzle of pi : squaring the circle -- Mapmaking mysteries : four colour theorem -- Sphereful symmetry : Kepler conjecture -- New solutions for old : Mordell conjecture -- Inadequate margins : Fermat's last theorem -- Orbital chaos : three-body problem -- Patterns in primes : Riemann hypothesis -- What shape is a sphere? : Poincaré conjecture -- They can't all be easy : P/NP problem -- Fluid thinking : Navier-Stokes equation -- Quantum conundrum : mass gap hypothesis -- Diophantine dreams : Birch-Swinnerton-Dyer conjecture -- Complex cycles : Hodge conjecture -- Where next? -- Twelve for the future
Control code
808413612
Dimensions
25 cm
Extent
x, 340 p.
Isbn
9780465022403
Lccn
2012924095
Other physical details
ill.
System control number
(OCoLC)808413612
Label
Visions of infinity : the great mathematical problems, Ian Stewart
Publication
Bibliography note
Includes bibliographical references (p. [305]-324) and index
Contents
Great problems -- Prime territory : Goldbach conjecture -- The puzzle of pi : squaring the circle -- Mapmaking mysteries : four colour theorem -- Sphereful symmetry : Kepler conjecture -- New solutions for old : Mordell conjecture -- Inadequate margins : Fermat's last theorem -- Orbital chaos : three-body problem -- Patterns in primes : Riemann hypothesis -- What shape is a sphere? : Poincaré conjecture -- They can't all be easy : P/NP problem -- Fluid thinking : Navier-Stokes equation -- Quantum conundrum : mass gap hypothesis -- Diophantine dreams : Birch-Swinnerton-Dyer conjecture -- Complex cycles : Hodge conjecture -- Where next? -- Twelve for the future
Control code
808413612
Dimensions
25 cm
Extent
x, 340 p.
Isbn
9780465022403
Lccn
2012924095
Other physical details
ill.
System control number
(OCoLC)808413612

Subject

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