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How to Solve It: A New Aspect of Mathematical Method

4.16  ·  Rating details ·  3,736 ratings  ·  196 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. ...more
Paperback, 288 pages
Published October 27th 2014 by Princeton University Press (first published November 30th 1944)
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Ivan Vuković
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
Nov 24, 2010 rated it really liked it  ·  review of another edition
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  ·  review of another edition
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).

Omar Halabieh
Jul 25, 2011 rated it it was amazing  ·  review of another edition
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.
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).
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, ...more
Jun 11, 2015 rated it really liked it
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.
Sumit Ghosh
Dec 08, 2017 rated it it was amazing  ·  review of another edition
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".
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.
Stefan Kanev
Nov 23, 2013 rated it it was amazing  ·  review of another edition
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 :)
Alex Ott
Apr 06, 2011 rated it really liked it  ·  review of another edition
Shelves: math, own-pbook
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
you know if you should read this and a review on this site will be meaningless
Feb 10, 2018 rated it it was amazing  ·  review of another edition
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  ·  review of another edition
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
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 :)
Adam Peterson
Jun 11, 2019 rated it really liked it  ·  review of another edition
How to Solve It is basically a +1 intelligence potion bottled in a math text. I read this book one rainy day and it boosted my ability to creatively problem solve thereafter. It's not that you won't stumble upon Polya's methods on your own, but rather 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.
Greg Talbot
Oct 08, 2013 rated it it was amazing  ·  review of another edition
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
This review has been hidden because it contains spoilers. To view it, click here.
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
Jan 19, 2017 rated it it was amazing  ·  review of another edition
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
Thai Son
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
Jul 01, 2014 rated it did not like it  ·  review of another edition
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
Mar 23, 2011 rated it it was amazing  ·  review of another edition
This book may not necessarily make you a better problem solver—that comes only from practice—but it is a useful first step in examining the types of creativity that go into problem-solving. Thus it's almost more a philosophical or psychological work than a how-to guide. The examples are all at middle-school or high-school level; the real point of the book is the enumeration of problem-solving strategies. It may even help you get unstuck when you're overlooking some trick you've used in the past.
Jan 17, 2017 rated it it was amazing  ·  review of another edition
This book is not only for math teachers, but anyone who has problems to solve. It gives very simple and precise suggestion to solve a problem; such as 'understand the problem'. It is obvious but often people forget those principals when they face a hard problem, particularly long time.
Reading this book is fun and will be useful once I hit a tough problem to solve.
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. Common sense
•05. Teacher and
Michael Scott
+ 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
Q. D.
Apr 13, 2019 rated it it was amazing  ·  review of another edition
America in the 1950's:

"... mathematics has the dubious honor of being the least popular subject in the curriculum ..."
-- Educational Testing Service, Princeton, N.J., cf. Time, June 18, 1956

You might say this book is a set of heuristics helping students properly court math. He believes we should inspire our students to love it. Passion. He says that those who are interested will pursue the solutions. They may sometimes go to bed after an exhausting attempt, spend time with her in his dreams, and
Jan Spörer
I didn't read the whole book as it is probably more suited for math teachers and not so much for people that just want to improve their mathematical reasoning skills.

Here are my key take-aways from the book:

-First ask if you understand the unknown and ask futher general questions about the data and the conditions. (p. 2)
-Common sense and generality are characteristics of helpful suggestions and questions that one can give to a student. Hints should be on such a level that they could have come
Ahmawan Johnson
Sep 23, 2018 rated it liked it  ·  review of another edition
Shelves: math
For the most part, I enjoyed the book. I liked the way it was written. However, some of the math examples were completely above my level of comprehension, and I had to bribe myself to read through those droll parts to understand what the author was trying to illustrate rather than just skipping. I had to read the book twice, because I kept "checking out" after those droll parts, but the second time I read it, the concepts it was trying to teach really started clicking.

This book helped open my
Nigrum Corde
Feb 03, 2018 rated it it was amazing  ·  review of another edition
The book is written in an ‘easy to read’ manner, I had thought when I read the introduction that it is made for mathematical teachers only, but when I read further, i understood that it’s made for anyone who can ‘think’ and want to ‘solve’ any sort of problem, this book can be read by people in the mathematics field or anyone who just reads book to kill the time. This book, needless to say teaches how to solve any sort of problems, not only pure mathematical but also physical, crossword puzzles ...more
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Goodreads Librari...: Could you please fix the page number of this book? 7 25 Feb 20, 2018 07:30AM  

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