How to Solve It! A book review

"Schule des Denkens"  means school of thought. The title of the original manuscript reveals the motivation for this book: to teach better. George Polya wrote it as a guide on how to lecture mathematics. But only the publicized edition, after Polya's migration to the United States, tells in plain English why its relevant for a broader audience: How to Solve It. I am not a teacher, the didactic musings of a lecturer would produce nothing more than a spark of curiosity in me. But "How to Solve It" describes a general procedure for problem solving. This freaks me out! Polya hides this endeavor in favor of the didactic justification, and only later in this book he will reveal that it is about a Modern Heuristic, to "understand the process of solving problems, especially the mental operations typically useful in this process" [p. 129]. The book is divided into four parts, I will discuss them briefly:

Part I: In the Classroom

This 32 pages are all you need to grasp his algorithm of problem solving. Good ideas are simple and the procedure proposed is not counterintuitive. You could easily come a similiar conclusion by your own:

What is the first step of problem solving? 

(1) Understanding the problem. 

What is the next step? 

(2) Devise a plan. 

Then?

(3) Execute the plan. 

And finally

(4) Look back

Mightily impressed? Then you are a lobotomized PowerPoint disciple! But follow Polya in a Socratic dialog with the classroom and look into the train of thoughts of an educated problem solver. There are many subtilities to discover.

By reading this chapter, more than once I had moments of Heureka!, when Polya guides you to ask the so called right questions and instructs you how to take a different point of view of the problem.

Part II: How to Solve it - a Dialog

The second part compresses the problem solving procedure, the ars inveniendi, in a summary of two pages. I did not gain from this, but it might be helpful as a short rehearsal when time passes by.

Part III: Dictionary of Heuristic

This is a 200 pages collection of heuristics to use as a pattern language for problem solving. The autor advices to take your time read this piece by piece when you are struggling with problems. Which I do.

Part IV: Problems, Hints, Solutions

These 8 pages are filled with exercises and smart hints how to approach the individual problems.

Conclusions

Polya opens your mind for solutions. I will tackle future hard problems only with Polya's algorithm and benefit from the careful order he imposes to the confused mind.

Albeit written for teaching mathematics, I suspect that Polyas work is useful not only for quantitativ problem solving, but for qualitative problems too. Here, I have no proof and only the application of it will tell. 

The book is easy to read, and you might master the first fundamental part "In the Classroom" in 3-5 hours. It is also a really cheap book, 13-something Euros, and if you are a problem solver you will need and enjoy it.