How To Solve Any Problem

how to solve any problem that's right this book will actually teach you how to solve any problem how to solve it a system of thinking which can help you solve any problem and I believe this is an older addition I think this might be signed this is written by George Pia so George Paia was a super famous mathematician he has very clever solutions to problems he was very smart very brilliant mathematician very very famous Super Famous and it is signed by George Pia really cool right so I'm a collector of math books this is uh a version of the book I have I'll leave a link in the description to this book in case you want to check it out how to solve it a new aspect of mathematical method by George Paia Princeton University Princeton University press cool right and so here he talks about it how to solve it first you have to understand the problem that's right so think about it so no matter what you're trying to do your first step is to understand the problem if you are doing a mathematics problem let's just take mathematics right because George Pao was a mathematician that is a huge deal I remember spending one time maybe like four hours on maybe okay maybe not four hours maybe two hours on the simple statement fix snot and S and I didn't know what that meant I was like what does that mean and I was on some IRC Channel talking to this guy and I I won't mention his name I remember who he was great guy really good at mathematics he would help me all the time and he knew how to write proofs and stuff so he you know so that really really helped me and two hours right so just to understand the problem that is a big step second find the connection between the data and the unknown you may be obliged to consider auxiliary problems if an immediate connection cannot be found you should a eventually a plan of the solution right so this is good for mathematics it's a little bit harder in the real world let me explain why so in mathematics the way you're trained when you learn mathematics is you have a lot of areas of math like linear algebra for example or abstract algebra everything builds it's very very linear you have some places where you can Branch off but like before you learn XYZ you have to know about ABC a lot of times and there's a lot of that so it's pretty deep some of the proofs have some tricky things in them um it's a lot of work right so you get used to building on things in the real life you're not trained like you are in mathematics right in the real world if if you have a problem in life maybe it's with a significant other maybe it's a job May a problem at work you have a problem with your teacher um problems with friends any type of problem you have right if you can actually break it down into auxiliary problems then you know you that can really help sometimes if you really think it out but it's harder to plan the solution because human beings are not like mathematics right they their reactions aren't the same so if your plan depends on the reaction of other people or things like that it becomes more complicated right in math everything is is black and white so it's a little bit easier step three carry out your plan yeah so a lot of people are planners and they're not doers this is a real thing and this is something that I uh I I I know I'm aware of this and I think you should be too whenever you're doing self-study for example if you're trying to learn mathematics and you have a bunch of books one common issue that people have is that they have a plan for study but they don't take action and the reason people don't take action is because they can't make a decision so if you have 30 books which one do you pick to study with well you just grab one and start studying just just pick one and just do it right after this video just do a math problem and what's going to happen is once you do one problem it's going to clear your head you're going to feel like wow I have some clarity here I've used my mind you know it's it's really good for you I think that that is a good one fourth examine the solution obtained right mathematics this is very very important especially the further you go I first actually you know I didn't learn this until I was I mean I'm sure my teachers said it but it didn't really stick to me until I was in graduate school for mathematics you know examine the solution obtained and the same thing with other problems right like you know was the outcome um you know what you wanted um but yeah this is mainly meant for mathematics but you could you could apply this to things in life it's a little bit harder though right because um a lot of things in life depend on people and people's reactions aren't perfect in mathematics you know something is true or false you know you you can you have statements and so you can work through them let's see what this says here understanding the problem so here it says what is the unknown right what is the unknown what are the data what is the condition is it possible to satisfy the condition is the condition sufficient to determine the unknown so just a lot of questions there devising a plan have you seen it before do you know a related problem look at the unknown yeah here is a problem related to yours and solv before could you use it so it's really going deep here right and that's really good these are things that come up in mathematics and that's why Paia does this right so it's just really brilliant carrying out the plan looking back can you check the result can you check the argument just this is a very very original book especially for its time right this was published wow signed by the legendary Paia this was published in 1948 1948 well here it's actually 1945 so this must not be this is the fifth printing so this is no this is not the first I probably couldn't afford the first that's probably what it was um you know books are expensive I have a lot of books people say well you have you spend a lot of money on books I do but I've been collecting books for you know like 15 years so I have a lot of books yeah what's this say look at the preface here see what this says a great discovery solves a great problem but there is a grain of Discovery in the solution of any problem your problem may be modest but if it challenges your curiosity and brings into play your inventive faculties and if you solve it by your own means you may experience the tension and enjoy the Triumph of Discovery that's that's right I because your problem may be modest he's he's being humble here because Paia was a freaking genius right I mean the man was a genius that's what I don't think people realize you should read about him on Wikipedia it's very I'll try to remember to leave a link in the description uh to his Wikipedia page in case you don't want like just go to the description you can click it and uh you can read about Paia because the dude was amazing yeah just really really good mathematician right and then here we have um contents you can look at the contents so helping the student questions recommendations mental operations generality comments it's it's a book so it's not not just we spent a lot of time there at the beginning but it's not just that but I mean that's pretty much the idea um it gives you examples and stuff it's a really pretty interesting book you know people always say problem solving is really important you know critical thinking all those things this is a book on problem solving right that's what this is and it's not a math book but at the same time it is you know it's written by a mathematician a very famous genius mathematician I mean this was written by a genius right so I think that's uh and I mean he was a genius for writing this book this is a great book and again for the time no one else was really writing books like this I mean I can think of other unique books from from this era before um there's like a calculus Made Easy by Sylvanas Thompson that's another like you know wow what is that book you know that's another like Game Changer um pretty pretty incredible move but yeah great book um I think it's great if you found any value in this content feel free to hit subscribe if you want to if not that's okay too I have courses they're on my website math sourcerer docomo vids.com uh check them out I have calculus differential equations algebra all that stuff trig but yeah great book I recommend it and um yeah hope it's been helpful keep learning math

Channel: The Math Sorcerer

Views: 138,649

Keywords: solve, any, problem, math, polya

Id: T9SONj3fHz0

Length: 8min 29sec (509 seconds)

Published: Thu May 16 2024