G. Polya's How to Solve It

[Originally published at the now defunct group blog explananda.com]

G. Polya. How to Solve It: A New Aspect of Mathematical Method

This is a book about heuristic, the study “of the methods and rules of discovery and invention,” in which most (but not all) of the examples are drawn from mathematics. Polya is interested in the question of how we go about solving puzzles in general, and, having acquired a facility with problem-solving, how we then go on to teach others the same skill. There’s no straightforward algorithm for problem-solving, but there are general patterns. As Polya never tires of reminding us, we typically need to ask ourselves: What is the unknown? What are the data? Do we know a related problem? Can we use this problem in the solution of our current problem? And so on. These might sound obvious, but there’s a value in having them stated clearly, and significant value in some of Polya’s imaginary discussions with students who are walked through the solutions to puzzles by a teacher making intelligent use of Socratic questioning.

Since it’s about thinking in general, and not just mathematics, I think this book might be read with profit by most people. I imagine it would be especially useful for mathematics teachers, especially because the author clearly has a keen sense of pedagogy. Unfortunately, many of the mathematical examples were a bit over my head, since I’m awfully rusty these days. And the book is marred, in my opinion, by an unconscionable amount of repetition. Still, on the whole a decent book.