Customer Reviews

How to Solve It: A New Aspect of Mathematical Method

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Are you like a dog with a bone when you're working on a brain teaser? After pages of scribbles, do you get a big grin on your face when you turn to the answers and say: "I'm right!" Then this book is for you.

And if you're not yet a die-hard problem-solver? You should step right up, too. You may get hooked.

G. Polya's book is based on the fact that, if we study how someone does something successfully, we can learn to do it successfully as well. How To Solve It is an application of 'heuristics' to solving problems.

There are certain mental operations useful in solving problems, any sorts of problems. Polya (who was an eminent mathematician and former Professor of Mathematics at Stanford University) describes and illustrates the most usual and useful of these operations, in a way that is irresistible and eye-opening.

These useful mental operations are organized according to when they come into play during the four steps to solving a problem. 1. You have to understand the problem. (Not as easy as it sounds.) 2. Find the connection between the data given and the unknown. Conceive the idea of a plan for the solution. 3. Carry out the plan. 4. Examine the solution obtained.

If you take some time and try to solve the problems selected to illustrate each mental operation, you will be well-rewarded. You will likely discover something surprising about your own problem-solving methods, and improve them in the process. You will definitely discover many new ideas and techniques to add to your arsenal.

For example, a first impulse when confronted with a problem is often to try to 'swallow it whole' -- to try to meet all of the conditions of the problem at once. G. Polya suggests keeping only part of the condition, and dropping the other part. This can lead you straight to a solution you might otherwise have completely missed.

His techniques help you to stand back and get to the heart of the problem, rather than getting lost in it.

Something else I liked very much about his book is his encouragement to guess, or to reason 'plausibly.' While the final proof must be strictly logical, "Anything is right that leads to the right idea." Problem-solving has every right to be fun, as well as purposeful.

Polya struck gold with this book! "How To Solve It" contains a simple, 5 step method for solving problems that's applicable in multitudes of disciplines. While the emphasis of this book is on story problems; Polya's method for problem solving is useful in areas such as computer programming, automotive troubleshooting, electronics repair, heating and cooling services, research writing, and much more.

I am constanly recommending this book to anyone in college. You can read the method and all the examples, or just read the method and a few examples. This book is easy to read, extremely relevant to today's promising careers, and can be understood in only 4 hours.


Marty A. Nickison II, BSCS Net+
author: Beyond the Books (Lulu)

A really helpful book that goes way beyond math. In our hurry to get through algebra we almost completely sidestep problem solving in teaching. It's true that we have `story problems' but they're usually just applications that restate the chapter's contents. That's why so many people get to a class like physical chem in college and flounder: they've never really been taught how to solve a problem only to regurgitate what's been read. This book by Polya fills in that gap.

More than that, though, this book is useful for life in general. Much of life is a leap from one decision to another and this book will help in looking at all problems and decision from new angles. (See Polya's book "Plausible Thinking" for lots more detail on this subject.)

Like in his other books the author has a knack for making the difficult seem a whole lot easier but parts can still be heavy going. Well worth the trudge, though.

This is a wonderful book. On a first reading it may seem a little confusing because the heuristics are organized alphabetically, rather than pedantically. This is not hard to overcome because Polya helpfully boldfaces related heuristics and by following the suggested threads you can get a fairly smooth read on the first reading. The way I dealt with it was I put sticky notes on the topics as I read them, so I could skim the ones I had already looked when threads hit a topic repeatedly.

I read this book many years ago, but it is still by my work station. I consult it when I get stuck on a problem, the heuristics do work.

For a first reading, the flipping around is annoying, but for reference purposes, the alphabetical order of the heuristics is quite convenience. I suspect that the first reading will not be your last, so the author's tradeoff was the right one.

I know the original version seemed like it would be great for someone that study math or physics and was heavily involved with proofs. However after reading the whole book and with some time I was able to really apply it to how I solve engineering problems. I will be honest it took some trial and error but within a year I was able to completely changed the way I solved problems (i.e. it needed an overhaul). The area I use it the most is thermal fluid systems and have had many complements on the way I articulated or solved problems, and I'm not a genius. The book is helpful and for the price you could take away a couple of items with out a hit in the pocket and just be that much better at figuring out problems.

As a professional LSAT tutor/blogger in NYC, I found this book to offer simple advice on problem solving and logical thinking. It's useful because it gives you a framework to identify and analyze the relationship between evidence and conclusion.

The book gives you some questions to ask yourself about any Logic Game or Logical Reasoning stimulus.

When to read it: Before you begin studying or when you need a break.

Good content, but reading it in the Kindle app for iPad is almost impossible. Holding the iPad in portrait orientation produces text in landscape layout; holding it in landscape orientation produces a portrait text layout.

As I have no issue with dozens of other Kindle edition books read on my iPad, I attribute this to the book being ~66 years old and so probably scanned into Kindle.

Very poorly done IMHO.

I agree totally with other reviewers that the title is far too narrow. This book is useful to anyone who ever has to solve any problem--does that exclude anyone? My fridge broke while I was mid-read and I decided to try out some of Polya's main strategies. Amazingly applicable. (And the fridge works great now.)

One word of caution, after a brief structured section, the remainder of the book is arranged by alphabetical topics. After skimming the first few, I assumed that they were just obvious definitions and "notes" about the "body" of the book. That was a big mistake. Much as I hate alphabetical arrangement (particularly with seemingly randomly generated titles), the alphabetical section is where the best stuff is. And the "title" of the section is no help in finding the good ones. The best way for me to think about it was to just imagine it as a blog: some days he wrote a little nothing, other days he wrote something awesome. The crossreferences within the blog entries are helpful for finding the best entries.

I first read this book some 35 yrs ago and the knowledge I acquired by studying it remained in my memory ever since, not because I have a great memory but because I have used this knowledge and heuristics again and again, first in the high school, then at the University, and later on in my career as a professional engineer. From D student in elementary school Math I first became A student in High School, then Math champion of the high school, then Math champion of the district and even went on to state championships competing with the best. I am not saying that only this book helped me in this transformation, but this book alone empowered me to be able to study other math books and solve all sorts of problems in math, and even science and engineering.
I highly recommend this book to any elementary, middle, high school, and even University student. The wisdom you will gain from this book will remain with you forever.

After more than 50 years, Polya's advice on tackling problems is still worth reading. But be warned, this is not the latest, brightest, trendiest, best-selling "problem solving book" out there that target MBAs or a kind of personal self-development book. Its author had contributed to important fields of mathematics and he had been through many problems, many difficulties, many students and many different questions by those students.

If you're a young but eager student who faces problems in math (or in natural sciences), a person trying to solve some puzzles or practical problems, or a researcher about to start a long and unguaranteed journey in order to solve a big problem then you owe yourself to have this classic on your bookshelf, or better on your table.

I'd like to quote some important passages from the book but last time I checked my notes they are about as long as the book. So maybe it is better to let Polya do the talking...