Waubonsee Community College

Visions of infinity, the great mathematical problems, Ian Stewart

eng

Includes bibliographical references and index

illustrations

index present

non fiction

Visions of infinity

bibliography

808413612

Ian Stewart

the great mathematical problems

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 websiteA 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

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