[HN Gopher] G. Polya, How to Solve It
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G. Polya, How to Solve It
Author : GamerUncle
Score : 56 points
Date : 2023-08-22 19:09 UTC (3 hours ago)
(HTM) web link (www.math.utah.edu)
(TXT) w3m dump (www.math.utah.edu)
| furyofantares wrote:
| I remember this book as being written for teachers and was about
| about prompting students as you help them solve problems.
|
| I read it as a student, and felt it was somewhat formative even
| though I don't think I ever explicitly applied anything it said.
| OldGuyInTheClub wrote:
| It's easy when you have John von Neumann as a student.
| bee_rider wrote:
| > What is the unknown? What are the data? What is the condition?
|
| ...
|
| > Did you use all the data? Did you use the whole condition? Have
| you taken into account all essential notions involved in the
| problem?
|
| What sort of problems are they solving, that they can somehow
| identify the relevant data to the point that they know once
| they've chomped their way through the data, the problem is done?
| It seems oddly constructed (I can only imagine that I know I've
| only been given relevant data if I'm working a textbook problem
| or playing a video game; somebody has set the problem up for me,
| but clearly this was written by somebody prestigious, so that
| isn't it).
| bonoboTP wrote:
| It's about advanced school exercises or math contest questions
| that are designed by someone, not real-world/research problems,
| where you don't even know how to best frame the issue or
| whether it's even solvable or the appropriate thing to tackle
| at the time.
| bee_rider wrote:
| Oh! That's a huge difference, haha.
| jxramos wrote:
| > Did you use all the data...
|
| It's a good articulation that informs one while working on
| complex stuff. Here's a recent example of this where the above
| advice came to mind while reading over this advice the other
| day (I believe someone linked it on HN)
|
| > A good way to stress-test this sort of false argument is to
| try to run the same argument without the initial assumption
| that X is false. If one can easily modify the argument to again
| lead to a contradiction, it shows the problem wasn't with X -
| it was with the argument.
| https://terrytao.wordpress.com/career-advice/be-sceptical-
| of....
| UltimateEdge wrote:
| I think the author is talking about maths problems, or proofs
| of theorems/propositions.
|
| A problem might give you one or more mathematical objects, and
| ask you to show that some further condition holds true. To get
| started, you might consider how the given properties of those
| objects will help you to achieve your goal (and typically you
| would need to use every given property).
| ergocoder wrote:
| I read it and it doesn't help much.
|
| What helps with solving problems like math and algorithmic
| problems is to go through a lot of problems to see different
| patterns and strategies of solving problems. I'm talking about
| going through thousands of problems. That is very effective.
| mathisfun123 wrote:
| > I'm talking about going through thousands of problems.
|
| you don't need thousands of problems. you don't even need
| hundreds, unless, no offense, your medium-term memory is very
| poor.
|
| personal anecdote 1: in between undergrad and grad school i
| decided i was gonna try this "solve all of the problems"
| approach, as opposed to my usual "sit there and ponder
| approach", in order to prepare for eventual quals in grad
| school. i started with calculus, using apostol's calculus
| (famous for its rigor and difficulty right?). some sections
| have double digits (maybe even 100? i don't remember) problems
| and invariably (no pun intended) by the time i got about a
| quarter of the way through they got trivially easy. i did
| finish and do all the problems in both volumes. i didn't feel i
| learned any of it better than the first time i took calc
| (wherein i didn't solve many at all beyond assignments). i did
| not keep on with this kind of slavish dedication and just
| skimmed the rest of the books. i didn't end up doing a phd in
| math but i did take math and cs theory classes and i did well.
|
| personal anecdote 2: after my MS i did hundreds of leetcode
| problems. it was roughly the same phenomenon: in every category
| it only took about a dozen to be able to solve the remainder
| trivially (yes even hard DP problems).
|
| and i'm willing to bet (if you're on this board) your memory is
| better than mine (i smoked incredible amounts of pot in high
| school...).
| rahimnathwani wrote:
| This is consistent with a sentence on page 1 of the book:
|
| 'The student should acquire as much experience of independent
| work as possible.'
| jvanderbot wrote:
| Not only that, my take on this book is it's meant to help you
| classify those patterns and better recall them by going
| through consistent triage and process.
| RcouF1uZ4gsC wrote:
| Or you can just be like von Neumann
|
| From:
| https://www.tennessean.com/story/opinion/columnists/teachabl...
|
| >George Polya, one of his university teachers, said, "I came to a
| certain theorem, and I said it is not proved and it may be
| difficult. Von Neumann didn't say anything but after five minutes
| he raised his hand. When I called on him, he went to the
| blackboard and proceeded to write down the proof. After that I
| was afraid of von Neumann."
| sverona wrote:
| _Mathematics and Plausible Reasoning_ , in two volumes also by
| Polya, is the closest thing I've ever found to an explanation of
| how a working mathematician goes about her business. It has
| exercises, too. Great fun when I was in undergrad.
| 3abiton wrote:
| Any recommendations of similar books?
| i_am_a_peasant wrote:
| How to Prove it is pretty nice
| dingosity wrote:
| Weird. I was just talking about this book to my offspring. You're
| reading my mind, @GamerUncle.
| modeless wrote:
| It's prompt engineering for humans.
| js2 wrote:
| Ah yes, just four steps:
|
| 1. Understand the problem.
|
| 2. Devise a plan.
|
| 3. Carry out the plan.
|
| 4. Look back.
|
| ---
|
| Compare with the Fenyman Algorithm:
|
| 1. Write down the problem.
|
| 2. Think real hard.
|
| 3. Write down the solution.
|
| https://wiki.c2.com/?FeynmanAlgorithm
|
| (The discussion on FeynmanAlgorithm links back to Polya's book
| since not everyone is Feynman.)
| jiggawatts wrote:
| Reminds me of the official Microsoft guidance for big projects
| like migrating Exchange to the cloud, merging an Active
| Directory, or whatever.
|
| They're all verbatim the same, except for the product name.
|
| 1. Gather requirements.
|
| 2. Devise plan.
|
| 3. Run a proof of concept
|
| 4. Run production migration
|
| ...etc.
|
| It's about as helpful as someone telling you to "do your job".
| bonoboTP wrote:
| Or his steps to do science:
|
| 1. Guess 2. Compute consequences 3. Compare with experiment -
| if they disagree, the guess was wrong.
|
| https://www.youtube.com/watch?v=OL6-x0modwY
| morkalork wrote:
| >Write down the problem
|
| Sometimes this step is enough to get you 80% of the way to
| solving a problem.
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