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Visions of Infinity: The Great Mathematical Problemsby Ian Stewart
Synopses & Reviews
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 fields 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 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 Poincaré 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 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 predecessors — and how the enigmas of the past inevitably surrender to the powerful techniques of the present.
"Popular mathematics writer and researcher Stewart (The Mathematics of Life) delivers an entertaining history of mathematics and a fresh look at some of the most challenging problems and puzzles in the history of the field. The usual suspects are all present and accounted for, including the infamous algebraic muddle of Fermat's Last Theorem, the quintessential prime number puzzler of the Goldbach Conjecture, the cartographical conundrum of the Four-Colour Theorem, and the topological intricacies of the Poincaré Conjecture, as well as some fascinatingly cryptic modern ones. An emeritus professor of mathematics at the University of Warwick, Stewart proceeds chronologically, offering historical insights as he discusses the multiple disciplines touched on by each problem and the decades or centuries during which obsessive mathematicians have searched for their solutions. Stewart's loquacious yet lucid style makes the most complex mathematics accessible, even when discussing esoteric concepts like homology (used to measure and categorize topological surfaces) or the quantum physics behind the still-unsolved Mass Gap Hypothesis. Capping the discussion is a quick chapter detailing some of the problems that may give mathematicians fits and nightmares into the next century, including quaintly named perfect cuboids, Langton's Ant, and mysterious constructs called Thrackles. Once again, Stewart delivers an intriguing book that rewards random reading as much as dedicated study. Agent: George Lucas, Inkwell Management." Publishers Weekly Copyright PWxyz, LLC. All rights reserved.
Stewart's imaginative, often-witty anecdotes, analogies and diagrams succeed in illuminating some very difficult ideas. It will enchant math enthusiasts as well as general readers who pay close attention.” Kirkus
Entertaining and accessible....Ian Stewart belongs to a very small, very exclusive club of popular science and mathematics writers who are worth reading today.” New York Journal of Books
Few of us share Stewart's mathematical skills. But we relish the intellectual stimulation of joining him in exploring mathematical problems that have pushed even genius to the limit....Stewart repeatedly shows how a trivial mathematical curiosity can open up vital new conceptual insights....A bracing mental workout for armchair mathematicians.” Booklist, starred review
For every problem mathematicians solve, another waits to perplex and galvanize them. Such challenges offer a tantalizing glimpse of the fields unlimited potential, and keep mathematicians looking toward the horizons of intellectual possibility. In Visions of Infinity, celebrated mathematician Ian Stewart explains why these problems exist, what drives mathematicians to solve them, and why their efforts matter in the context of science as a whole. Stewart describes solved problems — like Fermat's Last Theorem, proved three centuries after it was posited, and the Poincaré Conjecture, cracked by eccentric genius Grigori Perelman — as well as those like the P/NP problem, which 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 have risen to meet the challenges set by their predecessors — and how the enigmas of the past inevitably surrender to the powerful techniques of the present.
About the Author
Ian Stewart is Emeritus Professor of Mathematics and active researcher at the University of Warwick. The author of many books on mathematics, he lives in Coventry, England.
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