George Pólya
Encyclopedia
George Pólya was a Hungarian mathematician
. He was a professor of mathematics from 1914 to 1940 at ETH Zürich
and from 1940 to 1953 at Stanford University
. He made fundamental contributions to combinatorics
, number theory
, numerical analysis
and probability theory
. He is also noted for his work in heuristics and mathematics education.
, Austria-Hungary
to originally Ashkenazi Jewish parents Anna Deutsch and Jakab Pólya who converted to Roman Catholicism in 1886. He was a professor of mathematics from 1914 to 1940 at ETH Zürich
in Switzerland and from 1940 to 1953 at Stanford University
carrying on as Stanford Professor Emeritus the rest of his life and career. He worked on a great variety of mathematical topics, including series
, number theory
, mathematical analysis
, geometry
, algebra
, combinatorics
, and probability
.
, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving; 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 only mathematical ones. 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
, (Nobel laureate
in 2000) praised it, saying he was very pleased with Pólya's famous book. The book is still referred to in mathematical education. Douglas Lenat
's Automated Mathematician
and Eurisko
artificial 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 (MAA) in 1977. As Pólya notes in the preface, Professor Bowden carefully followed a tape recording of a course Pólya gave several times at Stanford in order to pull a book together. Pólya notes in the preface "that the following pages will be useful, yet they should not be regarded as a finished expression."
He died in Palo Alto, California, USA
.
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 his honor at the University of Idaho in Moscow, Idaho. The mathematics center focuses mainly on tutoring students in the subjects of algebra and calculus.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
. He was a professor of mathematics from 1914 to 1940 at ETH Zürich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
and from 1940 to 1953 at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
. He made fundamental contributions to combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and probability theory
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
. He is also noted for his work in heuristics and mathematics education.
Life and works
He was born as Pólya György in BudapestBudapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
, Austria-Hungary
Austria-Hungary
Austria-Hungary , more formally known as the Kingdoms and Lands Represented in the Imperial Council and the Lands of the Holy Hungarian Crown of Saint Stephen, was a constitutional monarchic union between the crowns of the Austrian Empire and the Kingdom of Hungary in...
to originally Ashkenazi Jewish parents Anna Deutsch and Jakab Pólya who converted to Roman Catholicism in 1886. He was a professor of mathematics from 1914 to 1940 at ETH Zürich
ETH Zurich
The Swiss Federal Institute of Technology Zurich or ETH Zürich is an engineering, science, technology, mathematics and management university in the City of Zurich, Switzerland....
in Switzerland and from 1940 to 1953 at Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
carrying on as Stanford Professor Emeritus the rest of his life and career. He worked on a great variety of mathematical topics, including series
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
, number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, mathematical analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...
, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
, combinatorics
Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...
, and probability
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
.
Heuristics
In his later days, he spent considerable effort on trying to characterize the methods that people use to solve problems, and to describe how problem-solving should be taught and learned. He wrote four books on the subject: How to Solve ItHow to Solve It
How to Solve It is a small volume by mathematician George Pólya describing methods of problem solving.- Four principles :How to Solve It suggests the following steps when solving a mathematical problem:...
, Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving; 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
How to Solve It
How to Solve It is a small volume by mathematician George Pólya describing methods of problem solving.- Four principles :How to Solve It suggests the following steps when solving a mathematical problem:...
, Pólya provides general heuristics for solving problems of all kinds, not only mathematical ones. 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
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
Zhores I. Alfyorov
Zhores Ivanovich Alferov
Zhores Ivanovich Alferov is a Soviet and Russian physicist and academic who contributed significantly to the creation of modern heterostructure physics and electronics. He is an inventor of the heterotransistor and the winner of 2000 Nobel Prize in Physics. He is also a Russian politician and has...
, (Nobel laureate
Nobel Prize in Physics
The Nobel Prize in Physics is awarded once a year by the Royal Swedish Academy of Sciences. It is one of the five Nobel Prizes established by the will of Alfred Nobel in 1895 and awarded since 1901; the others are the Nobel Prize in Chemistry, Nobel Prize in Literature, Nobel Peace Prize, and...
in 2000) praised it, saying he was very pleased with Pólya's famous book. The book is still referred to in mathematical education. Douglas Lenat
Douglas Lenat
Douglas B. Lenat is the CEO of Cycorp, Inc. of Austin, Texas, and has been a prominent researcher in artificial intelligence, especially machine learning , knowledge representation, blackboard systems, and "ontological engineering"...
's Automated Mathematician
Automated Mathematician
The Automated Mathematician is one of the earliest successful discovery systems. It was created by Doug Lenat in Lisp, and in 1977 led to Lenat being awarded the IJCAI Computers and Thought Award....
and Eurisko
Eurisko
Eurisko is a program written by Douglas Lenat in RLL-1, a representation language itself written in the Lisp programming language. A sequel to Automated Mathematician, it consists of heuristics, i.e. rules of thumb, including heuristics describing how to use and change its own heuristics...
artificial 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 (MAA) in 1977. As Pólya notes in the preface, Professor Bowden carefully followed a tape recording of a course Pólya gave several times at Stanford in order to pull a book together. Pólya notes in the preface "that the following pages will be useful, yet they should not be regarded as a finished expression."
He died in Palo Alto, California, USA
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
.
Legacy
In 1969 the Society for Industrial and Applied MathematicsSociety for Industrial and Applied Mathematics
The Society for Industrial and Applied Mathematics was founded by a small group of mathematicians from academia and industry who met in Philadelphia in 1951 to start an organization whose members would meet periodically to exchange ideas about the uses of mathematics in industry. This meeting led...
established the George Pólya Prize
Pólya Prize (SIAM)
The Pólya Prize is a prize in mathematics, awarded by the Society for Industrial and Applied Mathematics. First given in 1969, the prize is named after Hungarian mathematician George Pólya...
, 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
Mathematical Association of America
The Mathematical Association of America is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists;...
established the George Pólya Award "for articles of expository excellence" published in the College Mathematics Journal
College Mathematics Journal
The College Mathematics Journal, published by the Mathematical Association of America, is an expository journal aimed at teachers of college mathematics, particular those teaching the first two years. It is a continuation of Two-Year College Mathematics Journal. It covers all aspects of mathematics...
. In 1987 the London Mathematical Society
London Mathematical Society
-See also:* American Mathematical Society* Edinburgh Mathematical Society* European Mathematical Society* List of Mathematical Societies* Council for the Mathematical Sciences* BCS-FACS Specialist Group-External links:* * *...
established the Pólya Prize
Pólya Prize (LMS)
The Pólya Prize is a prize in mathematics, awarded by the London Mathematical Society. Second only to the triennial De Morgan Medal in prestige among the society's awards, it is awarded in the years that are not divisible by three – those in which the De Morgan Medal is not awarded...
for "outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom."
A mathematics center has been named in his honor at the University of Idaho in Moscow, Idaho. The mathematics center focuses mainly on tutoring students in the subjects of algebra and calculus.
See also
- Multivariate Pólya distributionMultivariate Polya distributionThe multivariate Pólya distribution, named after George Pólya, also called the Dirichlet compound multinomial distribution, is a compound probability distribution, where a probability vector p is drawn from a Dirichlet distribution with parameter vector \alpha, and a set of discrete samples is...
- Pólya conjecturePólya conjectureIn number theory, the Pólya conjecture stated that 'most' of the natural numbers less than any given number have an odd number of prime factors. The conjecture was posited by the Hungarian mathematician George Pólya in 1919, and proved false in 1958...
- Pólya enumeration theoremPólya enumeration theoremThe Pólya enumeration theorem , also known as the Redfield–Pólya Theorem, is a theorem in combinatorics that both follows and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set. The theorem was first published by John Howard Redfield in 1927...
- Landau–Kolmogorov inequality
- Pólya–Vinogradov inequality
- Pólya inequality