How to solve it; a new aspect of mathematical method (original: 1945; edição: 1957)

I'm conflicted about this book. There is a lot of good advice around the art of problem solving, but my god is there a lot of shit too. The layout is mostly a big alphabetical glossary of _math things_ --- everything from leading questions to notions of symmetry to anecdotes about absentminded professors --- and the layout doesn't particularly help. It's not organized by topic or ordered by first things first, it's just plopped down alphabetically. As such, it's hard to get into the flow.

This book however is lacking primarily in that it deals with how to solve "well-posed questions," which is to say, toy problems. There is very little about conducting your own open-ended research, and about how to turn wisps of ideas into well-posed ones. ( )

How to Solve It is decent, but overrated – the first 10% are pretty good, and then there are a few nuggets of really good advice interspersed with the neverending examples of the principles introduced in the first part. ( )

I came across this book as a result of my entry into Mathematics. If you have read enough Philosophy and question your own assumptions, ideas, you'll find the ideas in this book are repetitive. I would recommend this book to someone who wants to know basic problem-solving skills.

Deus Vult,
Gottfried

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[5 out of 5] My only regret is that I must return this book to the library. This is one of those rare books I recommend to pretty much anyone who has to deal with problem solving.

Not just mathematical problems, though. Polya writes an excellent case for the way we all should approach problems. It's not a formula, rather a scaffolding for thought, strategies for learning and teaching, reflections on successful solving and common pitfalls. If you want to think like a scientist, this is an excellent start, whether you have a science degree/background or not ( )

This book teaches a mathematical method that breaks a problem down into its components. It asks pointed questions and restates problems to increase understanding. I suppose this book is intended for math teachers or teachers in general, but it was still pretty interesting to read. ( )