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How to Solve It: A New Aspect of Mathematical Method

4.16  ·  Rating details ·  4,144 ratings  ·  229 reviews
A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be reasoned out--from building a bridge to winning a game of anagrams. Generatio ...more
Paperback, 288 pages
Published September 25th 2015 by Princeton University Press (first published November 30th 1944)
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Tamoghna Biswas Like, if you are asking his motive, it might be that Polya wanted the new generation of mathematicians to know how to correctly approach a problem,and…moreLike, if you are asking his motive, it might be that Polya wanted the new generation of mathematicians to know how to correctly approach a problem,and for the teachers to learn to do their jobs in a more sophisticated way. And for all, of course, excel in the art of problem solving.(less)

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Ivan Vuković
Dec 27, 2012 rated it it was amazing
This book contains no magic, no tricks. It's not one of those "esoteric knowledge revealed" books nor a book which promises you'll get an Abel prize or a Fields Medal someday.

What this books is, is a systematic and incredibly instructive overview of guidelines in mathematical problem solving, which are, as the author put it - "natural, simple, obvious, and proceed from plain common sense."

If you've ever put yourself against a serious problem which you really, really, really wanted to have solved
Tamoghna Biswas
Jun 10, 2020 rated it really liked it  ·  review of another edition
Shelves: mathematics
"When Caesar's given your opponent the thumbs-down, it's easy to forget you still have to administer the coupe-de-grâce."
-Ian Stewart

Majority of the people who are aware of the Mathematics Events around the world have heard of George Polya even if they are not that much into mathematics themselves, for his name is on a par with legends like Gauss and Leibnitz now. Okay so we are all more or less familiar with his genius, but how many with his meant-to-be-simple-yet-intuitive works?

As a matter o
Nov 24, 2010 rated it really liked it
George Polya's classic How to Solve It is a seminal work in mathematics education. Written in 1945 and referenced in almost every math education text related to problem solving I've ever read, this book is a short exploration of the general heuristic for solving mathematical problems. While the writing is a bit clunky (Polya was a mathematician and English was not his first language), the ideas are so deeply useful that they continue to have relevance not just for solving mathematical problems, ...more
Mirek Kukla
Jan 18, 2011 rated it liked it
Shelves: math-logic
Polya tries to explain how to become a better 'problem solver', and how to guide others to better solve problems themselves. The core of the content is terrific, and gets you thinking about 'how to best think'.

Unfortunately, almost everything gets repeated numerous times, and as a whole the books ends up being thoroughly redundant. You don't really need to read beyond the first 36 pages (the rest of the book consists of a 'problem solving dictionary', and here's where the redundancy begins).

Oct 26, 2008 rated it it was amazing  ·  review of another edition
Recommends it for: Anyone who has to analyze situations not seen before
Shelves: math-stats
This is a book I wish I had read at the beginning of grad school. How to Solve It is not as much about methods of solving mathematical problems as it is about various approaches to solving problems in general. The method he uses to teach problem solving is to apply the approaches to problems of geometry. This is actually in line with the ancient greek (Aristotle) opinion that the young should learn geometry first, then when they have learned logic and how to prove things with physical reality, t ...more
Jul 12, 2007 rated it it was ok  ·  review of another edition
This is one of those mathematical "classics" that those of us with a training in math are supposed to love. Fact of the matter is that it is poorly written and pedestrian in nature. If you are seeking insight into how mathematicians think and approach problem-solving, give this one a miss. You'd be far better off to read Hardy's "A Mathematician's Apology" (dated, but still charming), or Ian Stewart's recent "Letters to a Mathematician" (charming and not dated at all). ...more
Omar Halabieh
Jul 25, 2011 rated it it was amazing
I recently finished reading How To Solve It - A New Aspect Of Mathematical Method - by George Polya.

Below are key excerpts from this book that I found particularly insightful:

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.
Jun 11, 2015 rated it really liked it  ·  review of another edition
This is an important book. Possibly historical in its utility and impact. I'm proud to have this on my shelf and will likely reference it every so often for the rest of my life. ...more
Sumit Ghosh
Dec 08, 2017 rated it it was amazing
Pólya is the teacher I never had.
Now you might get scared with the word "Mathematical" in the title - don't be. It is a general guide to how to solve a problem. Starting from establishing the question, gathering the known and to find the unknown. The method you are using to find the minimum distance between two points can also be used to find the most convenient road to your nearest grocery store. This book shows you -"How to Solve it".
Alex Ott
Apr 06, 2011 rated it really liked it
Shelves: own-pbook, math
The whole content of this book is presented in first two pages at start of it. All other text is explanation of these 2 pages, illustrated with examples, etc. I think, that it could be very useful for teachers...
andrew y
May 24, 2017 rated it liked it
you know if you should read this and a review on this site will be meaningless
Héctor Iván Patricio Moreno
One of the most useful books I've read in my life.

It's an authentic treasure to everyone interested in problem-solving (and every one of us has enough problems to be interested in with problem-solving).

I think this should be one of the obligatory lectures for high-school or college education because it states clearly the steps one intuitively follows when trying to solve a problem mathematical or not.

The key takeaways for me are:

1. If you conceive a plan to solve the problem you're almost done.
Sandy Maguire
I'm conflicted about this book. There is a lot of good advice around the art of problem solving, but my god is there a lot of shit too. The layout is mostly a big alphabetical glossary of _math things_ --- everything from leading questions to notions of symmetry to anecdotes about absentminded professors --- and the layout doesn't particularly help. It's not organized by topic or ordered by first things first, it's just plopped down alphabetically. As such, it's hard to get into the flow.

This bo
Jul 01, 2014 rated it did not like it
This book was used as a reference in several of the other books I have read, and I understood it to be more of a general methodology of problem solving when I decided to read it. It is written in a somewhat awkward style, to an audience that is difficult to discern, and with enough repetition that I had to skip pages at a time to get to the next topic. This was frustrating as I really wanted to like this book. When Polya does focus on the generalized concepts of problem solving, he has wonderful ...more
Stefan Kanev
Nov 23, 2013 rated it it was amazing
This is a great book.

It teaches solving mathematical problems. It is mostly focused on high-school problems, but it is applicable to most types of mathematical problems out there. The author has developed a nice heuristic framework for tackling problems and has done a wonderful job of explaining it. It's not just the methods – exposition is also a great takeaway from this read.

On the downside, the book was written in 1945 and sometime it shows. It's more cute than a nuisance, though :)
Adam Peterson
Jun 11, 2019 rated it really liked it
It's not that you won't stumble upon some of Polya's methods on your own. This book saves you the time and gives you a foundational rubric for many types of problems. It's worth reading no matter your background. ...more
Shadrack Lilan
Aug 10, 2020 rated it it was amazing
Shelves: favorites
Hands down one of the best books I have ever read (and a couple of years late too), and I plan to reread this every so often.

I stumbled on this book after watching Rich Hickey’s talk titled “Hammock driven development”, and if you know Rich Hickey then you know there is some weight behind the recommendation. I saw the book getting recommended again in other popular software talks and conferences and I decided to treat myself to the book. 100% worth it.

Although the direct audience is math/logic/s
Feb 10, 2018 rated it it was amazing
This is such a great book. Polya lays out the different approaches you can take to solve a problem. He primarily uses Euclidean geometry to explain the possible ways to approach different problems.

This is especially great when you have to analyze a problem that you haven't seen before - where and how to begin? He goes through the problem-solving process in detail, beginning with the detailed analysis of the question and then the systematic synthesis of the answer.

This book really changed how I
Pablo Prieri
Apr 07, 2019 rated it really liked it
The book, written in 1950, still applies today and attempts to find a method to discover the solution to any mathematical problem we may encounter in our life. Although sometimes repetitive, the author is very pedagogical and presents various examples to illustrate his method. Despite the fact the examples are mainly on the Math field, he manages to translate them into other domains (like engineering, physics, psychology, etc.). A book nice to have in our library :)
Apr 13, 2017 rated it really liked it  ·  review of another edition
The first small part of the book is instructive and useful, but the second larger part "Dictionary of Heuristics" is somewhat repetitive, you have to sift through it to find nuggets of new wisdom :) ...more
Teo 2050


Polya G (1945) How to Solve It - A New Aspect of Mathematical Method

From the Preface to the First Printing (1944)

From the Preface to the Seventh Printing (1954)

Preface to the Second Edition (1956)

“How to Solve It” list
• Understanding the problem
• Devising a plan
• Carrying out the plan
• Looking back

Foreword (by John H. Conway)


Part I: In the Classroom

• 01. Helping the student
• 02. Questions, recommendations, mental operations
• 03. Generality
• 04. Com
May 09, 2014 rated it really liked it  ·  review of another edition
Here's how you solve it:

You have to understand the problem.
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? Or is it insufficient? Or redundant? Or contradictory?
Draw a figure. Introduce suitable notation.
Separate the various parts of the condition. Can you write them down?
Find the connection between the data and the unknown.
You may be obliged to consi
Jul 23, 2015 rated it really liked it
Shelves: owned-books, math
On the surface How to Solve It by George Pólya is a short little book about strategies of solving mathematical problems. Deep down, however, it is not a book about mathematics, but it's a book devoted to heuristic - the study of methods and rules of discovery and invention.

The book is divided into four parts "In The Classroom" - tips for the educator on guiding a student, "How To Solve It" - presenting the main questions you should ask yourself while solving problems, "Short Dictionary of Heuris
Greg Talbot
Oct 08, 2013 rated it it was amazing
Elegance in solving problems is not strictly a mathematical skill set. Polya wisely formats word problems, critical thinking problems, and yes mathematical problems that occasionally are intimidating.

But one of the big takeaways is that problems are only as hard as they are unresolved. Not only does Polya give excellent ideas for solving problems: creating auxiliary problems, using heuristics, working backwards.

Each example that Polya gives takes concentration and critical analysis. But when yo
Michael Scott
Dec 28, 2017 rated it liked it
Shelves: design, math, teaching
+ Good ideas on how to teach average math students a process for solving problems in mathematics. Overall, useful concept, but limited and ill-aged approach.
+/- (Heuristic) Process based on four stages: 1. Understanding the problem. 2. Use related work = Finding related (solved) problems and decide on a plan to solve the current problem based prior solutions and/or their principles. 3. Solve = Show the plan works. 4. Check carefully the result and ask related questions about it. Process in
This review has been hidden because it contains spoilers. To view it, click here.
Oct 14, 2008 rated it really liked it
This is a cool book. It's a comparatively rare thing for a first-class mathematician to write really seriously and thoughtfully about math education; at least it's not something I've come across too much. And it's been about a year and a half since I read anything about math education I didn't feel like I already knew. (Props to the _Young Mathematicians at Work_ series by Fosnot and Dolk, which was the last thing I read like that...)

The thing that makes this book unusual is that it's about the
Aug 09, 2007 rated it it was amazing  ·  review of another edition
Recommends it for: everyone
Shelves: owned
I don't remember when I first encountered this book -- I think it was early in my time at Cornell. It's had a great deal of influence on how I approach math. It's one of the best math books I've ever read, and quite possibly the best book on mathematical problem solving ever written.

There are two copies of it floating around my lab at Berkeley, evidence, i think, that I'm not the only one who appreciates it.

Polya was a first rate mathematician, and his book is devoted to explaining simply and u
Thai Son
Oct 30, 2013 rated it liked it
Hailed as the classic guide to problem solving, this book did quite a good job at categorizing the ways of looking at a problem, and some general methods of solving and treating them. However, I think I read this at the wrong time - it could have fascinated me much more had I read it in the early 2000s (then again, there was not any translation to Vietnamese back then, and I suspect my mediocre English back then would not let me finish it).

Still, the way I went at the book is that I skimmed thro
Jan 19, 2017 rated it it was amazing
I picked this up by happenstance in a college bookstore over the summer. I'm always looking for educational texts on analytical methods, so this one caught my eye. What an amazing find! Pólya presents the reader with a list of steps to use when analyzing a problem and breaks each one down comprehensively. The entire book references back upon itself repeatedly, so you can always circle back to important, related points.

The writing style is quirky, yet approachable, and very direct. The author's r
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Goodreads Librari...: Could you please fix the page number of this book? 7 27 Feb 20, 2018 07:30AM  

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“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.” 10 likes
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