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Visions of Infinity: The Great Mathematical Problems [NOOK Book]

Overview


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 ...
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Visions of Infinity: The Great Mathematical Problems

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Overview


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 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.
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Editorial Reviews

From Barnes & Noble

For centuries, mathematicians have anguished over problems that most of us know only at best as names: Fermat's Last Theorem; Goldbach's Conjecture; Four-Color Theorem. What these conundrums mean and why they cause such bafflement are the subjects of this expansive new book by mathematician/author Ian Stewart (In Pursuit of the Unknown; The Mathematics of Life). As in previous books, Stewart makes no presumption that readers possess advanced mathematical skills. Indeed, his presentations of the theories and their history somehow manage to possess both accessibility and allure. An eye-opening introduction to a language all too few of us know.

Publishers Weekly
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. (Mar.)
From the Publisher
Science News
“As a guide to the inner workings of the mathematical jungle, Stewart provides an engaging and informative experience. If you wish to intelligently discuss the Riemann hypothesis, P/NP problems or the Hodge conjecture, you ought to read this book first.”

Choice
“A designated math popularizer, Stewart writes books that are always enlightening and enjoyable.... Again, Stewart provides another interesting read for anyone intrigued by mathematics.”

Dallas Morning News
“Anyone who has always loved math for its own sake or for the way it provides new perspectives on important real-world phenomena will find hours of brain-teasing and mind-challenging delight in the British professor’s survey of recently answered or still open mathematical questions.... Individual readers will dig deeply into certain chapters and skim others according to personal preference, but every one of them will be captivated by the technical achievements, loose ends and human insights that Stewart shares on his grand mathematical tour.”

New York Journal of Books
“Entertaining and accessible.... Ian Stewart belongs to a very small, very exclusive club of popular science and mathematics writers who are worth reading today.”

Publishers Weekly
“An entertaining history of mathematics and a fresh look at some of the most challenging problems and puzzles in the history of the field…. Stewart’s loquacious yet lucid style makes the most complex mathematics accessible, even when discussing esoteric concepts…. Once again, Stewart delivers an intriguing book that rewards random reading as much as dedicated study.”

Booklist, starred review
“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.”

Kirkus
“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 Reviews
An aggressively unsimplified account of 14 great problems, emphasizing how mathematicians approached but did not always solve them. Fermat's Last Theorem, 350 years old and solved by Andrew Wiles in 1995, produced headlines because laymen were amazed that mathematicians could make new discoveries. In fact, mathematics is as creative as physics, writes prolific popularizer Stewart (Mathematics Emeritus/Univ. of Warwick; The Mathematics of Life, 2011): "Mathematics is newer, and more diverse, than most of us imagine." Goldbach's Conjecture--that every even number can be written as the sum of two prime numbers (250 years old, probably true but not proven)--provides the background for a chapter on the unruly field of prime numbers: those divisible only by one and itself (3, 5, 7, 11, 13…). Squaring the Circle--constructing a square with an area identical to a given circle (2,500 years old; proven impossible)--introduces pi. Schoolchildren learn that pi is the ratio of the circumference of a circle to its diameter, but it's a deeply important number that turns up everywhere in mathematics. Most readers know that Newton's laws precisely predict motions of two bodies, but few know that they flop with three. The Three-body Problem (330 years old, unsolved) continues to worry astronomers since it hints that gravitational forces among three or more bodies may be unstable, so the planets may eventually fly off. Stewart's imaginative, often-witty anecdotes, analogies and diagrams succeed in illuminating many but not all of some very difficult ideas. It will enchant math enthusiasts as well as general readers who pay close attention.
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Product Details

  • ISBN-13: 9780465065998
  • Publisher: Basic Books
  • Publication date: 3/5/2013
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 356
  • Sales rank: 657,799
  • File size: 6 MB

Meet the Author


Ian Stewart is Emeritus Professor of Mathematics and active researcher at the University of Warwick. He is also a regular research visitor at the University of Houston, the Institute of Mathematics and Its Applications in Minneapolis, and the Santa Fe Institute. His writing has appeared in New Scientist, Discover, Scientific American, and many newspapers in the U.K. and U.S. He lives in Coventry, England.
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Sort by: Showing 1 Customer Reviews
  • Posted June 20, 2013

    Good overview

    Ian Stewart makes math accessible to the non-mathematician. Recommended for anyone who thinks math is not evolving and discovering new results.

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