Mathematics and Plausible Reasoning, Volume 1: Induction and Analogy in Mathematics

Though a math book, this is one of the best explanation of scientific reasoning ever written. I am amazed at the shoddy reasoning that now passes as 'scientific'. I assume that science majors are no longer expected to study more than basic calculus and probability unless they are physics majors. This is unfortunate. This book and its second volume would go a long way in clearing up sloppy thinking. Anyone interested in clear thinking, regardless of their interests and background, could do worse than study these books.

If you have ever watched a star trek movie and seen Spock in action,then this is the book for you. Its all about logicical thinking when approaching problems in math.Excellent!

The book delves deeply into logic and mathematical reasoning with quite a bit of intermediate math. While most of the chapters and concepts are mathematical Polya has skillfully made the reading easy and the concepts more universal. The book is really about thinking and looking at ideas with a clear light. Above all it's just good reading. Don't let the math scare you - there's lots of good stuff here.

This book shows you how simple concepts when applied properly can lead to ingenious solutions. For example, the author's proof of the Pythagorean Theorem will leave you shocked by its amazing elegance. And, there are several of these throughout the book.Read this book. It's money more than well spent.

One of the most beautiful books on scientific discovery. Read this book and then keep it at bedside for sheer amusement. Analogies are frequently the key to a discovery, but it is rare that this essential step receives credit. Here there is a collection of them: some of the most beautiful. Perhaps the most famous is Bernoulli's solution of the brachistochrone problem, based on an analogy with the path of light in the atmosphere. But there are many others, with comments and analysis by Polya, who spent a life thinking at these things. It's a pity he didn't include Riemann's "proof" of the theorem of conformal representation, based on an analogy with the physics of electrical currents on a surface. The reader can find it beautifully described in Richard Courant's "Dirichlet Principle".