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 Fermats last theoremfirst posited in 1630, and finally solved by Andrew Wiles in 1995led 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 predecessorsand 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. 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.
Table of Contents
1. Great problems
2. Prime territory
3. The puzzle of pi
4. Mapmaking mysteries
5. Sphereful symmetry
6. New solutions for old
7. Inadequate margins
8. Orbital chaos
9. Patterns in primes
10. What shape is a sphere?
11. They cant all be easy
12. Fluid thinking
13. Quantum conundrum
14. Diophantine creams
15. Complex cycles
16. Where next?
17. Twelve for the future