“How not to solve it”: I really wanted to like Polya’s classic how-to-math book, but like @DRMacIver I got little/nothing out of it.
Why hasn’t anyone written anything better? (Is there something better I don’t know about?)https://twitter.com/DRMacIver/status/1063841518656602118 …
I thought it was okay - glad I read it. Better books: Lakatos's "Proofs and Refutations". There was a book of (I think) Putnam problems-and-solutions that I found very helpful to work through, and a few similar. I really think mathematical problem-solving is best learnt by doing
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It's much like writing in that way. You can read 20+ books on writing, and if you're not writing seriously, they won't help. If you are writing seriously, the good ones will help a tiny bit each. But (like writing) it adds up...
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Ah, this is the book I liked: https://www.amazon.com/Problem-Solving-Through-Problems-Problem-Mathematics/dp/0387961712/ref=sr_1_1?ie=UTF8&qid=1542476113&sr=8-1&keywords=problem+solving+through+problems … Spent a few hundred hours with it. Basic problem-solving is only a small part of mathematics, of course, but it's so essential, and I found working through this book immensely helpful.
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I think it's best learnt by doing with occasional supervision from someone who is able to help you over the cognitive leaps that you fail to make on your own, and that was where I was hoping a book could help people.
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Sure. Or as part of a group that is serious about learning to problem solve. I was helped a lot by a friend who'd done Math Olympiad stuff - actually, he suggested the book to me, and provided encouragement.
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Engel’s Problem Solving Strategies is also very good, in the same vein of Olympiad preparation
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