[HN Gopher] G. Polya, How to Solve It ___________________________________________________________________ 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. ___________________________________________________________________ (page generated 2023-08-22 23:00 UTC)