Early in his career, Pólya wrote with Gábor Szegő two influential problem books Problems and Theorems in Analysis. Later in his career, he spent considerable effort to identify systematic methods of problem-solving to further discovery and invention in mathematics for students, teachers, and researchers. He wrote five books on the subject: How to Solve It, Mathematics and Plausible Reasoning, and Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. In How to Solve It, Pólya provides general heuristics for solving a gamut of problems, including both mathematical and non-mathematical problems. The book includes advice for teaching students of 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 praised it, noting that he was a fan. The Australian-American mathematician Terence Tao used the book to prepare for the International Mathematical Olympiad. The book is still used in mathematical education. Douglas Lenat's Automated Mathematician and Euriskoartificial intelligence programs were inspired by Pólya's work. In addition to his works directly addressing problem solving, Pólya wrote another short book called Mathematical Methods in Science, based on a 1963 work supported by the National Science Foundation, edited by Leon Bowden, and published by the Mathematical Association of America in 1977. As Pólya notes in the preface, Bowden carefully followed a tape recording of a course Pólya gave several times at Stanford in order to put the book together. Pólya notes in the preface "that the following pages will be useful, yet they should not be regarded as a finished expression."
Legacy
There are three prizes named after Pólya, causing occasional confusion of one for another. In 1969 the Society for Industrial and Applied Mathematics established the George Pólya Prize, given alternately in two categories for "a notable application of combinatorial theory" and for "a notable contribution in another area of interest to George Pólya." In 1976 the Mathematical Association of America established the George Pólya Award "for articles of expository excellence" published in the College Mathematics Journal. In 1987 the London Mathematical Society established the Pólya Prize for "outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom." A mathematics center has been named in Pólya's honor at the University of Idaho in Moscow, Idaho. The mathematics center focuses mainly on tutoring students in the subjects of algebra and calculus. Stanford University has a Polya Hall named in his honor. It was built while he was still teaching and he complained to his students that it made people think he was dead.
Selected publications
Books
Aufgaben und Lehrsätze aus der Analysis, 1st edn. 1925.. Springer, Berlin 1975.