Visions of Infinity: The Great Mathematical Problems

Front Cover
Basic Books, Mar 5, 2013 - Mathematics - 340 pages
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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LibraryThing Review

User Review  - K.G.Budge - LibraryThing

Yet another book on the great problems in mathematics that have attracted great prize money. Yet not just another such book; Stewart has a gift for explaining the problems and their solutions at a ... Read full review

LibraryThing Review

User Review  - amarcobio - LibraryThing

I really feel that my opinion of Ian Stewart has evolved. I found the first books I read not particularly good, while the recent one more interesting. In any case I frequently browse my local book ... Read full review


Prime territory I Goldbach Conjecture
The puzzle of pi I Squaring the Circle
Mapmaking mysteries I Four Colour Theorem
Sphereful symmetry I Kepler Conjecture
New solutions for old I Mordell Conjecture
Inadequate margins I Fermats Last Theorem
Orbital chaos I ThreeBody Problem
Patterns in primes I Riemann Hypothesis
They cant all be easy I PNP Problem
Quantum conundrum I Mass Gap Hypothesis
Diophantine dreams I BirchSWinnertonDyer Conjecture
Complex cycles I Hodge Conjecture
Where next?

What shape is a sphere? I Poincaré Conjecture

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About the author (2013)

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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