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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Alan Schoenfeld's Mathematical Problem Solving is an interesting book, esp. Ch. 4 - Control. Link: http://math-dept.talif.sch.ir/pdf/manaba/%5BAlan_Schoenfeld%5D_Mathematical_Problem_Solving.pdf …
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I would be interested in a different book: "How to formulate it?" How to find/formulate mathematical problems worth solving, create new concepts etc.
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I suspect the goal here is very close to self-contradictory; distilling general strategies for doing mathematical research is essentially the same thing as doing mathematical research, so not really a *shortcut* to the latter.
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Polyá completely glosses over the question of motivation. Sure, with ‚well-behaved‘ students you might be able to have such Socratic dialogues bc they bring along the motivation. But it still leaves out the majority
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Polya wrote two more books on problem solving, each in two volumes: "Mathematics and plausible reasoning" and "Mathematical discovery". I think they are much better than "How to solve it", which is a short summary of his work on the subject, and treats only elementary examples
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I read Polya plus a lot of back-of-the-envelope problem solving books out there, and they all suffer from the self-contradictory goal
@St_Rev mentioned. Some are maybe good for a narrower and less impressive goal of polishing the skills of already-experienced practitioners. -
Polya took heuristics from Pappus, who (paraphrased) said they're useful for people who've already finished Euclid's Elements and want to learn how to solve problems, but that the techniques are "useful for this alone." If we take Pappus at his word, we're expecting too much.
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