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# How to Solve It: A New Aspect of Mathematical Method

George Polya was a Hungarian mathematician. He wrote this, perhaps the most famous book of mathematics ever written, second only to Euclid's "Elements." "Solving problems," wrote Polya, "is a practical art, like swimming, or skiing, or playing the piano: You can learn it only by imitation and practice. This book cannot offer you a magic key that opens all the doors and sol
...more

Paperback, 280 pages

Published
June 1st 2009
by Ishi Press
(first published November 30th 1944)

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## Community Reviews

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Jan 03, 2013
Ivan Vukovic
rated it
5 of 5 stars
·
review of another edition

Shelves:
mathematics,
informal-but-technical

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 ...more

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 ...more

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 :)

Still, the way I went at the book is that I skimmed thro ...more

This book takes a simple, interesting approach and though it's written in the 40s, many benefits remain to-be-had from popularity outside its field. For me, beginning this book, I recalled how as an undergrad tutor for ESL students, our cla ...more

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 ...more

Oct 26, 2008
Louis
rated it
5 of 5 stars
·
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
Aug 09, 2007
Ari
rated it
5 of 5 stars
·
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 ...more

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 ...more

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).

The ...more

...moreFirst.

You have tounderstandthe problem.

UNDERSTANDING THE PROBLEMWhat 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?Second.

Find the connection between the data and the unknown.

You may be obliged to cons

The thing that makes this book unusual is that it's about the ...more

Nov 01, 2014
Mitchell
rated it
4 of 5 stars
·
review of another edition

Recommends it for:
math students and teachers

This was a pretty good book. I think I should read it a second time to get more out of it. The structured approach to problem-solving it presents seems like it would be helpful in math classes.

- Know the purpose in each step of your problem-solving

- If you can't solve a problem, solve a different problem that is similar enough to help you

- Account for all the data

- Can you check the result?

- Can you derive it differently?

I also really enjoyed the section on proverbs (p. 221):

Who understands ill, answer ill.

A fool looks to the beginning, a wise man reg ...more

I'm giving this three stars ...more

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