How to Solve It

How to Solve It

George Pólya's 1945 book "How to Solve It" is a small volume describing methods of problem solving.cite book
first = George
last = Pólya
author-link = George Pólya
title = How to Solve It
year = 1945
pages =
place =
publisher = Princeton University Press
url =
doi =
id =
isbn = 0-691-08097-6]

Overview

This book was published at Princeton University. It suggests the following steps when solving a mathematical problem:
# First, you have to "understand the problem".
# After understanding, then "make a plan".
# "Carry out the plan".
# "Look back" on your work. How could it be better?

If this technique fails, Pólya advises: "If you can't solve a problem, then there is an easier problem you can solve: find it." [ [http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Polya.html Quotations by Polya ] ] Or: "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"

His book contains a dictionary-style set of heuristics, many of which have to do with generating a more accessible problem. For example:

The technique "have I used everything" is perhaps most applicable to formal educational examinations (e.g., "n" men digging "m" ditches) problems.

The book has achieved "classic" status because of its considerable influence (see the next section).

Other books on problem solving are often related to more creative and less concrete techniques. See lateral thinking, mind mapping and brainstorming.

Other Methods

There are other methods of problem solving:

Influence

* It has been translated into several languages and has sold over a million copies, and has been continuously in print since its first publication.
* Marvin Minsky said in his influential paper "Steps Toward Artificial Intelligence" that "everyone should know the work of George Pólya [87] on how to solve problems." [Citation
last = Minsky
first = Marvin
author-link = Marvin Minsky
title = Steps Toward Artificial Intelligence
journal =
volume =
issue =
pages =
date =
year =
url = http://web.media.mit.edu/~minsky/papers/steps.html
doi =
id = .]
* Pólya's book has had a large influence on mathematics textbooks as evidenced by the bibliographies for mathematics education. [cite journal
last = Schoenfeld
first = Alan H.
coauthors = D. Grouws (Ed.)
title = Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics
journal = Handbook for Research on Mathematics Teaching and Learning
publisher= MacMillan
location= New York
pages = pp. 334–370
date =
year = 1992
url = http://gse.berkeley.edu/faculty/ahschoenfeld/Schoenfeld_MathThinking.pdf
doi =
id = .]
* Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book.

Notes

See also

* Heuristic
* "How to Solve It By Computer"

External links

* [http://www.math.utah.edu/~alfeld/math/polya.html More information on Pólya can be found here.]
* [http://freefeel.org/wiki/SummaryHowToSolveIt#s-1 An uneven summary of the whole book.]


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