The book shows what the power of mathematics is, how it changes, and how it expands to new areas. Unlike books that aim to popularize math, the book does not pontificate a mystic view of the meaning of mathematics; rather, it gives a sober perspective of what has happened in mathematics and what can be expected of the field.

The book requires somewhat serious mathematical thinking.

A great strength of the book is the diverse mathematical concepts that it presents: homology groups, group theory, Turing machines, undecidability, Monte Carlo method. In a compact book, you learn a little about some important ideas in advanced mathematics.

Important!! This book is not written to popularize its subject matter, so it is different and definitely less entertaining than most popular science books.

With new mathematics growing wild in the trees in the new century, one should review those things that have given modern mathematics direction and flavor. This classic little book sits along side of Sawyer's " Prelude to Mathematics" as the go to books for basic understanding. To these books I have added an unlikely candidate " Elliptical Curves" by McKean and Moll. If one has these three books, he will have a crack in the dam of mathematics...

Kac and Ulam were both strong mathematicians; this encyclopedia article which they coauthored provides a nice counterweight to the answers-without-questions view of math which can result from a little indifferent coursework.

Easy and lively reading, written for everyone.

This is an unusual book on the discipline of mathematics. Don't look here for the usual fluffy collages of fractals, chaos theory and hagiographies.

What this book offers is a collection of essays on the state and nature of mathematics by three top mathematicians. They're honestly worried about the schism between math and science, interested in the effect the computer could have on math, critical about the mathematical establishment. They're completely honest, and their criticisms are incisive and well reasoned. This book is food for thought, and not only about math.

The authors differ in their writing styles. While all three have good essays, Rota is a fantastic writer, and his mixture of serious thought, pith and gossip is completely refreshing. You should also read (before this book) Rota's "Indiscrete Thoughts".