George Pólya

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George Pólya (December 13, 1887 – September 7, 1985, in Hungarian Pólya György) was a Hungarian mathematician.

He was born George Pollák in Budapest, Hungary to Jewish converts to Catholicism, and died in Palo Alto, USA.

He worked on a great variety of mathematical topics, including series, number theory, combinatorics, and probability.

In his later days, he spent considerable effort on trying to characterize the general methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote three books on the subject: How to Solve It, Mathematics and Plausible Reasoning Volume I: Induction and Analogy in Mathematics, and Mathematics and Plausible Reasoning Volume II: Patterns of Plausible Reasoning.

In How to Solve It, Pólya provides general heuristics for solving problems of all kinds, not simply mathematical ones. The book includes advice for teaching students mathematics and a mini-encyclopedia of heuristic terms. It was translated into several languages and has sold over a million copies. Russian physicist Zhores I. Alfyorov, (Nobel laureate in 2000) praised it, saying he was very pleased with Pólya's famous book.

In 1976 The Mathematical Association of America established the George Pólya award for "for articles of expository excellence published in the College Mathematics Journal."

In Mathematics and Plausible Reasoning Volume I, Pólya discusses inductive reasoning in mathematics, by which he means reasoning from particular cases to the general rule. (He also includes a chapter on the technique called mathematical induction, but that technique is not his main theme.) In Mathematics and Plausible Reasoning Volume II, he discusses more general forms of inductive logic that can be used to roughly determine to what degree a conjecture (in particular, a mathematical conjecture) is plausible. Volume II gives equal expression to his interests in mathematics, natural science, cognitive psychology, and most of all, community of interest. Its breadth makes it highly readable for those who share his interests and his perspective upon them. Pólya could (can) teach at once as an individual, and as a role model. His 3-book series regarding Plausible Reasoning seeks to reach an audience far beyond his formal peers of the time.

Some quotes:

How I need a drink, alcoholic of course, after the heavy chapters involving quantum mechanics (This is a mnemonic for the first fifteen digits of π; the lengths of the words are the digits).
If you can't solve a problem, then there is an easier problem you can solve: find it.
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.
Wishful thinking is imagining good things you don't have...[It] may be bad as too much salt is bad in the soup and even a little garlic is bad in the chocolate pudding. I mean, wishful thinking may be bad if there is too much of it or in the wrong place, but it is good in itself and may be a great help in life and in problem solving.

[edit] Bibliography

Pólya, George (1990). How to Solve It. Penguin Books. ISBN 0140124993. includes foreword by Ian Stewart
Pólya, George (1954). Mathematics and plausible reasoning.
Pólya, George (1962). Mathematical discovery.