4 Steps To Solve Any Problem 

Back in '72 I had a chance to talk to Prof. Polya. I told him that I'd read his books (mostly), and it seemed to me that his advice boiled down to 2 things: When faced with a difficult problem 1) do PART of it & try again, or 2) do a SIMILAR problem & try again. As a really low level grad student, kinda challenging a world famous mathematician and teacher, I was expecting to get brusquely Blown Away. Instead, he smiled & replied, "Young man, I am 85 years old and I'm still learning how to do those 2 things." What a man. I've never forgotten, so I guess I really WAS Blown Away.

1. Understand the problem. 2. Connect what you know with the unknown. 3. Carry out a plan. 4. Examine obtained solutions.

As a programmer, How to Solve It actually helped me pass quite a few of those technical assessments. It's definitely a good read!

My father [I miss him badly - He was a math teacher and a great admirer of Pólya] once told me that math is basically applied good sense.

‘This is not a text book, you can actually read it and learn from it.” Lol. That was awesome 👏

Polya is a Hungarian surname and the L is silent. The correct pronunciation is just simply Poya. Thanks for sharing your experience with this wonderful book from this great scientist.

I have never read the book of prof. Polya. But when my students asked me to give a talk on how to solve a problem, I tried to deduce a method from my experiences. It turns out that my method is the same as that given by prof. Polya. Each time I face a problem, I divide the problem into sub-problems (a sub-problem can be divided into sub-sub-problems, and so on) and solve them. Each sub-problems must be tested. Eventually, I connect all the sub-problems to solve the problem.

I can't say how much I appreciate this reference. I work in a HS as an in-house math tutor, and after reading just a bit in, already am thinking about what I can do better, different, to help my students. Also going to buy your Calculus Udemy courses. I've helped students right through calculus, but never sat and watched a teacher teach the classes. The sample lessons tell me that it's a great step to take.

I started using this book in 1962 when I was taking geometry and 10th grade and have used it since. Actually the copy I have right now is the fifth one I owned. I loaned out the first four and never got them back so now I just tell people to get it from Amazon. It really does help, but it should be reserved for difficult problems. Essentially, the method enables a person to solve a problem that’s more difficult than they could solve otherwise. While the book focuses on geometric problems, it can be used to solve almost any problem with a slight generalization of the terms.

The Greeks used mathematics as the source for solving all their problems and this occupied my mind for some time until I realised (discovered) that it was more a way of thinking that resonated with each number. Another person who "discovered" this approach IMO was Edward de Bono who had a classical education and I think this helped him in coming up with his thinking skills courses the component pieces which when all put together can assist in solving any problem in life. Stanford seems to be a place where much of this "type of thinking" was exposed to the world albeit the student has to fathom out the structure it is ubiquitous.

RU-vid is showing out with their recommendations. My analytical brain really loves this advice. I took from this video that in order to be great at problem solving you have to create better systems of solving them. By following these tips I'm sure my brain will create new neural networks and eventually become a pro at problem solving. Thank you so much. I'm adding this to my Amazon wishlist

Hi Math Sorcerer! Love the content as always and I've been really enjoy these book reviews lately!

I've had this on my reading list for too. This convinced me that now is the time to read it. Thanks!

Since the late 80's, pilots have been taught a concept called aeronautical decision-making (ADM) to reduce accidents caused by pilot error. At its core is a decision loop called the DECIDE model, which stands for: Detect the problem, Estimate the need to react, Choose a desirable outcome, Identify solutions, Do the necessary action, and Evaluate the effect of the action. The chapter about ADM used to be the last chapter in the FAA Pilot's Handbook of Aeronautical Knowledge, but they promoted it to chapter 2 in the most recent edition.

I discovered "How to Solve IT" In the Whole Earth Catalog" in 1973 or74. It should be a cornerstone in any serious library.

Thank you ! I'm so enthousiased by your presentation of this book 🤗 I will get this masterpiece as soon as I can

The steps are pretty clear... The issue with problem solving is seeing relationships between things that are seemingly unrelated , and predicting or anticipating the unknown. Unfortunately not all people are capable of doing this

... A must read book for any math learner. Thx 4 posting it.

Thank you for the tip! Just ordered the book from the library, and look forward to read it!

Bought this book preparing for a chem undergrad last year. My gap year is coming to a close and I’ve come to notice myself gravitating towards mathematics videos more than any of the other sciences. Copies like “How to Solve It” and RU-vidrs like MathSorcerer and 3Blue1Brown have got me considering majoring in mathematics.

I read this great book in high school in nowhere Alaska whenI thought I was Mr Cool in math. I got the second highest score in the state on the little Math association high school test, even tho I skipped my Junior year. 800s of course. So off I went to Yale, just full of myself. I bragged to my Friend Richard Mann about my results on the MAA test. He asked my score then howled with laughter, telling me that my score would only have been sixth in his Long Island high school. I bragged to my two years younger classmate Cherlin about reading the Polya book. He said he knew about it and that he had spent time in the summer working with “George.” I got called up to the math Major league but I certainly couldn’t hit major league pitching. This is a really cool book.

I failed maths exam by 1 mark and giving an improvement exam and here I'm. I made up my mind to learn problem solving and learning maths from scratch as I will be pursuing CS in first year. Your videos are really helpful. Thanks:)

Each and every video of the Math Sorcerer is so informative and inspiring!!! Thank you 😊

The Auxiliary problem (7:10) is a good technique. It's like how I once read in a book about Zen, digging out a thorn with another thorn.

I realize that this is a book on how to solve arithmetic but I can't help but notice how useful this information is in the real world of practical problem solving

I thoroughly enjoyed the follow up book, Mathematics and Plausible Reasoning. Amazing read!

I need to read more math books

Costs less than a taco and feeds you for a lifetime. Thanks for sharing. Your enthusiasm for this book is great. Makes me wanna dig up another great book about the principles of typography. Not the most exciting topic but there's something about the writers passion for it that makes it special.

I studied under Paul Halmos as a senior and graduate student at UC Santa Barbara from 1976-1979. Amazing teacher!

Thank you for the helpful review. ‘How to Solve it’ by George Pólya is also available as an ebook via Perlego, an online, academic, library.

Still available as an ebook! This got me really into Calc and linear algebra. Vellaman's "How to Prove it" is another must have. Wait...signed?! 🤩

Thanks for this video. I was fascinated and ordered the book. Just received it, but the modern paperback isn't quite the same as the great layout of the plan on the inside covers in your older, hardback version. Still looking forward to reading it though. Will definitely be looking out for a second hand copy now.

I actually have that book, I purchased it as it is recommended in the prologue of the 7th edition Precalculus by James Stewart, Redlin, and Watson. Admittedly I haven't been able to read through it so this video is a well received overview of the book. Too many books, so little time!

Thanks sir, for your constructive advice.

This s a great book. I read mine multiple times, and took time to memorize the summary pages. Also you should review his other great books: Mathematics and Plausible Reasoning. There's 2 volumes. It's a book on how to conjecture. Back to How to Solve It. The greatness of this book to me is in the prose and how he times the prompting of your mind to open and grope for dimensions you were not aware of and not so much the content of what he says in particular. I think his book is tailored to technical problems expressed mathematically. But, outside of that, its effectiveness diminishes. I've had more success and much less stress to think about problems like a biologist studies organisms in the lab and in their habitats. I get more mileage reading popular books on ecology, like "Why Big Fierce Animals Are Rare" The best way I've found so far to solve problems, it to solve lots of problems *on your own*, struggle with the problem, solve it on your own. Then go back and see what the solution is or see part of the solution, and solve the problem in another way. Anyways, thanks for the trip down memory lane.

God dam I never imagined maths could be so good after watching this video I will now read this book I totally appreciate your work

I love when your videos about books pop up early! You can still find them cheap!

Reminds me of an Art Critique : Describe, Analyze, Interpret, and Judge (reflect, assess) ---- I am a HUGE fan of Mr. John Forbes Nash - I'm sure he was quite aware of this book. 😊

Your library just gets better day by day man

Thank you for sharing !! I will obtain this book and read it 👍👍👍👍👍👍👍

This is awesome! I found it in PDF. It's going on the short list. Thanks!

Sir, thank you for making us aware of Professor George Polya and his work.

i subscribed at the one minute and fifty seven seconds mark. A superb reviewer with an easy to listen to voice!!! Top Marks. :)

Thank you very much for nice book recommendation. Very usefull when programming.

Such a wonderful book. The first time I read it, it seemed to drop straight into my subconscious, and I could barely remember anything in it, but I suddenly got better at solving maths problems. Then I read it again. Unfortunately, I couldn't find a buyable copy and was using my university library's copy. I really should get another copy, and yes, it is applicable to a lot more than just mathematics. BTW, I have a copy of Einstein's "The Meaning of Relativity". A little paperback that you can fit in your back pocket, and I did. The intro by AE is amazing, showing his mind pondering why classical physics is not enough, using simple thought experiments that show that even special relativity is not complete, and then jumping into tensors.

The is awesome stuff. Very cool book. When I was preparing for my Professional Engineering Exam, I had a University Professor that repeatedly reminded me of the basic steps to take in the exam, no matter what the problem or discipline. This approach served me well during the challenging exam, especially considering there is not much time available for each problem. Thankfully I passed. 1. Carefully read and understand the problem. 2. List and define the knowns and unknowns. 3. Draw a free-body diagram. 4. Write down the fundamental equations and list units to be used. 5. List all assumptions. 6. Simplify the problem by cancelling out unnecessary and irrelevant terms. 7. Rearrange equations as necessary for the unknowns. 8. Plug in the numbers and solve. 9. Justify the solution. Is the answer reasonable from an engineering perspective?

Can’t wait to get my hands on this book. I spent 30 years solving complex problems using the 8D problem solving methods. (8 Disciplines). I expect to find that the 8D approach was derived from the methods taught in this book.

Amazing! Thank you very much! Old books are really magical!

Today You became one of my math role model.

Thank you! I love books and your wonderful videos

I just started to read it, I will write another review after I finished it. Thank you for the suggestion.

Thanks for introducing this book. Bought one!

Just found a copy on amazon (Princeton version) and I am genuinely looking forward to using this daily. I am going to school to become a programmer and I've been dying to find out why I have been experiencing such hardship and I know it's because I tend to tackle big chunks and then I get frustrated. Thanks for the video!

Oh man , so cool you got a original print/version🤘be very kind to it😁 Polya kicks ass🤜!

I went a step further and reduced it to 2 steps. Step 1, define problem. Step 2, solve problem. Thank you!

This book sounds awesome and informative. I have to say that you have promoted/recommended this book very well and I can't wait to read it. Thanks for the content.

Based on observations of book, with its 4 steps, it appears all 4 steps consist of several queries, ultimately indicting additional sub-steps, which may or may not produce more unknows, or "problems." Ones rendition of solving any problem: Step 1: there is no problem, there is no spoon. What one individual sees as a problem, another sees an opportunity, a challenge or puzzle. I was going to complete the viewing of clip, however, the passion of the moment compelled an immediate interjection of doublepence. Thanks for sharinggg

I am now reading the book you recommended sir. It's really a very good book.

its a real beauty this little book, and its back in print as a paperback

As a grad student, that is really helpful, thanks sorcerer!

Yes, your hope is correct. The video was helpful, a lot, indeed.

Informative. Thank you.🙏

As an engineer and an entrepreneur this is a gem of a book!

Oh this is awesome, I gotta buy this! Thank you!

Love your content man! I just subscribed

Thanks for information

As a result of this video I bought the book and have just begun reading it.

This book is a bridge that helps a person gain confidence by asking questions. It ought to be mandatory reading for school leavers on which ever path they find themselves on.

Thanks; lovely video.

A similar book that I have is The 5 Elements of Effective Thinking. Also written by a mathematician. Highly recommended.

this is truly amazing

I noticed the video and am glad I did because this kind of book is a great book of interest after learning about it because there are people such as myself who read most of everything to learn with math or reading most of the words On a page to begin the thought process with count numbers and the how to think while trying to solve math problems and the many kinds of solutions to the various counting methods Only get me excited to want to purchase this book just from all you presented in it and I just wanted to take a moment to say thank you for presenting a book that seems as if it's great in many ways for good reads and learning purposes that I have now decided from the information in the book It is a must-buy and so excited to have it on my next book order of books that I have ordered on regular books that have excellent meaning to teach the mind for better growth to become better at reading while counting which is not an always easy task for me but some people are natural to doing both at the same time, reading and counting at the same time I mean to that just said and I do believe this book is gonna teach me knew things and how to think better at trying to both reading snd counting at the same time which will provide a bitterness of learning in both areas of studies that I often struggle to do both at the same I am trying to say thank you for making this video and introducing a book that I know I can learn from Again, I am a struggling student in many different subjects, and happy that I have a new book to purchase that I know is going provide me with some how-to methods for learning while trying to count and read at the same time something I struggle to do I just hope it won't be difficult to find or order wish me to look in locating it at book stores, I shall search as many if needed because I want this book Again this great book I must get and it's because you previewed it in this video for an audience to learn about it! Thank you so very much for making this video about a great book and I agree with every word you said about it seems as its a nook to not want to put down and keep reading Just watching it I just want it now and gonna search engine it at the book stores on my next book order Thank you so very much for you noticing such a great book which makes your value of thinking just as great if not greater and not comparing minds just saying it takes a great mind to recognize great words to teach others what great words of how to think to look like, on the page and in the video who presents such a great book of value for me and I know so many other Can't stop thank-you you enough because it's what I need and never knew someone wrote a book that explains it like that and it's my style of thinking to read and figure the numbers with words but which words to ask? And the book has it and the way you showed it was just as grand! Thank you so much again and again I need this book and thanks to you I have a book I can't wait to get my hand on to read cover to cover, and I am so excited about this book I had a great day because of this video, and trying not to be redundant but AGAIN thank you so very much for the book presentation, I need it with my books for learning better... 😊

Yes! A great book. I recommend it highly.

I was so dumb when I was young that I did not even know that I could plan things out. I came from a rural environment, I had a learning disability with memory. I never learned algebra, geometry, trig, chemistry, etc. I am technically illiterate in those subjects. I only graduated from high school because I think they just passed me out of kindness. I did know that I wanted to permanently get out of that little town as soon as I turned 18 and I did. I had no plan. I actually did the old “if you don’t know where you want to go then any road will take you there” trick. I did not know how to solve problems using organized steps. But I do now and I am still going to read that book in case their are some techniques I am missing. Thank you for bringing that book to our attention!.

I have this book...love it! Given the paucity of critical thinking these days....more important than ever👍

I am getting this book from thr library. Thanks for thr recommendation

Hello! Thank you for sharing! ;)

Went to Amazon India, it said I had bought this book on 30 Aug 2016... :) never even openned it.. I was thinking it is purely mathematics... But I can see that it is way more than that.. almost like a thinking process! My interest is rekindled! Thanks a lot!!!!

Beautiful edition

Lovely. I want that book now.

I love these book reviews

I’m a former Elementary-level teacher returning to school soon, it’s amusing hearing this because it’s very similar or exactly similar to what we taught students.

thank you!

Thanks!

Awesome!!!

AYYY YOU FINALLY REVIEWED IT!!!

Great vid yet again

Thanks for sharing

Wow! This is the kind of book, that makes you think differently.

Thank you for the random book recommendation

It is an authentic treasure

A part of me wished schools would teach students some of these methods in tandem with the other things they learned. On the rare occasion when some problem-solving steps are actually taught, they're always an afterthought, since students aren't tested on them, nor are they given the opportunity to apply these steps. Children won't listen to dry lectures - they're boring, but if you teach them problem solving steps when they're asking you how to solve a problem, they will often see the immediate benefits and pay attention right then and there.

I have found that the TIME and MONEY spent in reading a book is well worth those costs IF i have learned at least one thing from the book. This book looks like one that can teach us many lessons.

LOVE THIS ❤️

Thank you very much!

Seems like a good companion book to The Art of Making Sense by Lionel Ruby.

OMG!!! I have two separate editions of George Polya's HOW TO SOLVE IT!!!

Good review, thanks. Now, I just have to find a copy!

Thank you for this Book)

I've had two books by Polya in my collection for years, and I finally read How to Solve It because of your review. I found it to be as interesting and useful as you say--thanks for the review. The other Polya book is Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. Would you consider reviewing Mathematical Discovery?