How to Solve it

There's a lot of useful value here - even though the writing style and target audience is a bit too narrow:

- has some assumption of a teacher/student context
- assumes a more mathematical context
- generally assumes an academic context is most parts

But it's a good articulation of how to solve problems.

Wherever I first read this in college it freaking blew my mind. I read it a few times. Had a profound impact on my life etc etc. I hadn't really thought about heuristics one might use for divining proofs. I used to try to just think as hard as I could and maybe I'd figure out the answer. But this guy has a whole methodology for it and it makes sense. I printed out the summary and put it on my wall behind my desk so that it would watch over me and the wisdom would flow out.

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.