Acclaimed writer and mathematician Ian Stewart investigates history's most important and elusive math problems
For every problem mathematicians solve, another awaits to perplex and galvanize them. 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, 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 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 mathematics 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.
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 Poincar 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.