Does he? Then my sympathies to his readers.
I largely agree with your original comment - I only ever skimmed Polya, because it didn't seem all that good.
Incidentally, Polya & Szego seemed quite good, though a bit far from my interests.
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I wonder whether we're talking about the same Polya book. I mean "How to solve it", which really does seem to be designed to help people to learn strategies for proving things. Some people even allege to get that from it, though I think mostly what they learn is permission to try
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Yes, we're talking about the same book. I subscribe to the belief that you only learn such strategies by a _lot_ of failure in trying to apply them, and varying them.
They're like other self-help: "reading" a self-help book well typically requires a few hundred hours.
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Both Wickelgren and Larson also discuss strategy, but with far more emphasis than Polya on actually doing the damned things... and that they often don't work.
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I didn't spend a huge amount of time with this one - it was just a bit too far from my interests. But it seemed like the kind of thing that'd be good to spend time with, if that was your interest.
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Funny, I agree with this too, and your comment about permission-giving: twitter.com/DRMacIver/stat
Polya may well be a good example of a book that wants to be an essay. Or even a Twitter thread.
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Replying to @pozorvlak and @LydiaMonnington
Hmm I had forgotten how good the four principles were. I should circulate this more.
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The key thing, IMO - since I'm ranting (apologies :-) - is that so many people good at executing procedures have been told they're "good at mathematics". Then they get given a problem for which there is no procedure. Rather, they need to _invent an approach to solution_.
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Not having any experience doing so, they panic & don't know what to do. They have little or no experience with making partial progress, or trying to learn tidbits from failures. Yet this is most of what mathematics is.
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So many people give up, saying "I'm not good at proof". When really it has nothing to do with not being good at proof, but at not being good at dealing with being stuck and uncertain, and learning from ideas that don't immediately succeed.
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This was definitely my experience as a freshman. I wish someone had told me as much—but don't know if that would have worked. Much of my career has been a process of trying to internalize this tweet again and again, more and more deeply, each time I hit some new apparent limit!
I switched to CS in large part because I had been the “good at math/physics” person who only knew how to solve known problems, and when I got stuck, I became convinced I was actually bad at math/physics. 😔 On the plus side, CS was far more interesting than I feared
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