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Meaningness's profile
David Chapman
David Chapman
David Chapman
@Meaningness

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David Chapman

@Meaningness

Better ways of thinking, feeling, and acting—around problems of meaning and meaninglessness; self and society; ethics, purpose, and value.

meaningness.com/about-my-sites
Joined September 2010

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    David Chapman‏ @Meaningness 17 Nov 2018
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    David Chapman Retweeted David R. MacIver

    “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 …

    David Chapman added,

    David R. MacIver @DRMacIver
    "How to Solve It" - Polya. I already knew I didn't like this book but kept it around hoping the heuristics might be better than the main pedagogy. They aren't.
    Show this thread
    9:29 AM - 17 Nov 2018
    • 2 Retweets
    • 9 Likes
    • admzmf ʞןɐʍɯopuɐɹ sanjaya Shital Shah Alphydan Matjaž Leonardis Cole Hudson Shubhendu Trivedi kmartino
    9 replies 2 retweets 9 likes
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      2. michael_nielsen‏ @michael_nielsen 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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

        3 replies 3 retweets 16 likes
      3. michael_nielsen‏ @michael_nielsen 17 Nov 2018
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        Replying to @michael_nielsen @Meaningness @DRMacIver

        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...

        1 reply 1 retweet 6 likes
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      1. NADPH‏ @f0late 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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 …

        0 replies 4 retweets 12 likes
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      2. Szymon Majewski‏ @brewingsense 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        I would be interested in a different book: "How to formulate it?" How to find/formulate mathematical problems worth solving, create new concepts etc.

        2 replies 1 retweet 8 likes
      3. 5 more replies
      1. St. Rev  ☯️ 🏴 😻‏ @St_Rev 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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.

        0 replies 2 retweets 8 likes
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      1. Ben Hambrecht‏ @BenHambrecht 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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

        0 replies 0 retweets 1 like
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      1. Jarosław Rzeszótko‏ @jaroslawrz 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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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      2. Bob Peterson‏ @rwpeterson 17 Nov 2018
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        Replying to @Meaningness @DRMacIver

        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.

        1 reply 0 retweets 0 likes
      3. Bob Peterson‏ @rwpeterson 17 Nov 2018
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        Replying to @rwpeterson @Meaningness

        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.

        0 replies 0 retweets 1 like
      4. End of conversation

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