From Here to Infinity

Rating:
Summary: A great 'survey of the ideas of cutting edge math' book!
Review: Ian Stewarts book is a survey of the developments in mathematics over the last couple of years, allowing the reader to come to grips with cutting edge mathematics without the need to equip him or her -self with the technical apparatus normally required to cross this intellectual terrain. He does this by transmitting concepts intuitively and concisely, and keeping the text warm, lively and accessible. The book will appeal to the interested layperson, to someone who is interested in what mathematics is really about at the higher levels, and to undergraduate mathematics or science/engineering students who are wondering a bit about the horizons of the mathematics that they are interested in.

Rating:
Summary: A detailed book designed to inspire.
Review: In another of his books designed to make mathematics popular, Ian Stewart takes us through some of the latest advances in mathematics. He gives a history of some of the world's finest mathematicians and trickiest problems before showing how they can (or can't) be solved. This book is not confined to theory though; the author applies the concepts he has described to such topics as computer public/private key encryption (as used in PGP) and the lottery to show how apparently abstract theory has a valid use, even if that use is discovered many years after the original theory.

The book goes into detail about each of the author's chosen topics. Whilst this detail is sometimes too complex for the layman to understand, it is useful for future reference and can provide ideas for some interesting computer programming exercises. The material is presented in such a manner that skipping some of the more technical maths doesn't interrupt the flow of the information.

The book represents great value for money. There is a lot of content here, and each chapter is relatively self-contained so that the work does not need to be read in order but can be dipped into. Good use is made of cross-referencing between the chapters though, which really helps to bind the book together.

The author makes further research beyond the scope of the book easily possible by giving names of mathematicians and scientists responsible for discoveries, along with a list of suggested material for further reading at the back of the book. There is also an index, which is useful for a volume of this size.

As well as being interesting from a mathematical point of view, the book is genuinely entertaining, which keeps the pages turning. The book is also inspiring, which is handy if you're a disillusioned student facing endless revision and maths exams. By showing where mathematics came from and where it is going, the author injects interest into what is often thought of as a stale subject.

From Here to Infinity can be highly recommended t! o many readers, all of whom will find and take away something different, something unique to themselves. For the mathematically bored will come enthusiasm. For the casual mathematician and armchair computer programmer will come some interesting ideas for a rainy day, and for those with more mathematical knowledge will come a wealth of new areas to explore and sources to refer to. This book thoroughly deserves all five stars.

Rating:
Summary: Thrilling view of Cutting Edge mathematics
Review: This is Stewart's finest popularisation. My favourite of all time (I have three well-thumbed copies in two different editions).

Why is this book so special? Well, firstly it benefits from Stewart's accomplished story telling and crystal clear mathematical explanations. Secondly, because it looks at the *unsolved* problems at the cutting edge of mathematics, whereas all his other texts cover either recreational math, or well-known fully-solved theories.

Each chapter studies a different problem, starting with the roots of the history of the topic; covering successes and embarrassing failures in the development of the subject; introducing personalities and concluding with a state-of-the art review, where he conveys the surprise and excitement of new discovery. Thrillingingly Stewart reports strange, glamorous and unexpected results from all areas of pure mathematics, and leaves us with an aching sense of mystery for those matters that still elude our grasp.

A total turn-on for the mathematically sensitive, this would be a special gift for an aspiring mathematician or a layman who has made good progress with the standard math popularisations.