Aha! Insight

This book does a wonderful job of encouraging problem solving and critical thinking techniques. What I like most about it, though, is how it is able to present all of its problems at a high level, in an entertaining context, so as not to discourage those who might be scared or frustrated by math and other such topics.Each problem, for the most part, has cute comics to illustrate it, as well as a plain-english explanation of how to approach finding a solution and the solution itself. Many of the problems are restricted forms of actual unsolved, or at least highly-researched, mathematical/computer science problems; the book does a excellent job of keeping that aspect separate from the problem and solution itself (how the problem is studied in the "real world" is usually mentioned in the text as an, "Oh, by the way, did you know that...")In addition to the author's wonderful presentation, I think the subject matter is what emphasizes this book's importance. Problem solving, critical thinking, and finding elegant simple solutions seems to me to be underemphasized in quite a few disciplines, and this book can offer good practice in all those important areas. Even if you don't ever deal with problems which require critical thinking, the book is still an interesting read because it makes you say, "Why didn't I think of that?" -- and then by half way through the book, you DO start to think of "that."The only negative thing I would say is that a few of the problems in the book are presented without solutions, which can frustrate some people (namely, myself :) ) Also, a few problems are underspecified, yielding to answers which depend on the interpretation -- then again, that's part of what problem solving is about, I guess.

This book gave me a lot to think about when I was young, and of all the books with math and logic puzzles I enjoyed, this was one of the best. Gardner has a way of turning problems into challenges, making the solving of them fun, and he also provides interesting explanations of problems with simplicity and clarity. For children, this book is an opportunity to explore math as something other than repetitive calculations or irrelevant word problems from bad textbooks. Adults too can use this book to hone their problem solving skills. The difficulty of aha! insights is the lack of technique in coming to such an insight. It's a spontaneous reaction, something sudden and unexpected when you discover a simple solution. These problems do not teach you how to have these insights, but allows for practice in order that they may become more frequent. But the point is: it's recreational math... Enjoy it for the sake of enjoyment.

I consider Martin Gardner to be the best there ever was in writing about mathematics. His essays are always entertaining and contain enough content to suggest other applications of the main point of his thesis. This book contains a series of short puzzles, most of which have quick solutions based on an "alternate" form of reasoning. That form is described as an "Aha" moment, where looking at the problem a different way leads to a simple solution to what appears to be a hard problem. I first read this book when it was first published over twenty years ago and recently read it again. It has stood the test of time quite well and I consider it to be the best of the collections of material by Gardner. I have three children under the age of ten and they are occasionally subjected to a puzzle in this book. It is always interesting to see how well they do. Quite frankly, there are occasions when they get the aha! answer faster than I did. Recent research indicates that the risk of developing Alzheimer's disease can be reduced by constantly stressing your mental abilities. Martin Gardner has received many accolades in his life, We can now add that his books can help prevent serious mental diseases. Go ahead and clap, he has earned the applause.

Any of Martin Gardner's book is very good and this and the other Aha (paradox) book are the two pearls in recreational mathematics. Many of the topics he tackles have a deep bearing in serious mathematics. These two Aha books can be the starting point for mathematical thinking.

This book is about tough problems with easy answers -- easy, that is, once seen in the right way. Illustrated with cartoons and full of humor, it is readily enjoyable by many people who wouldn't normally touch a book on recreational mathematics. We have given at least a dozen copies as gifts.