George Pólya

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George Pólya, ca.1973

George (György) Pólya (born December 13, 1887 in Budapest , Austria-Hungary , † September 7, 1985 in Palo Alto ) was a mathematician of Hungarian origin. His areas of work were in particular probability theory , analysis , combinatorics and number theory .

He was citizens of Hungary, Switzerland (Zurich) from 1918 and the USA from 1947.


Pólya's parents were the lawyer Jakab Pollák and Anna Deutsch. They had converted from Jewish to Catholic in 1886, and Pólya was baptized a Catholic. After the Austro-Hungarian Compromise of 1867 Magyarized Jakab 1882 his Slavic surname Pollák into the Hungarian sounding Pólya. His father had his own law firm, but with which he failed, was employed by an insurance company and then pursued an academic career (he was interested in economics and statistics). He managed to become a private lecturer before he died in 1897.

Pólya had two brothers, Jenő Pólya (* 1876), who was also very interested in mathematics, but studied medicine and became a surgeon, and László (* 1891), who died in World War I and was considered the most gifted child in the family, and two Sisters, Ilona (* 1877) and Flóra (* 1879). The sisters worked for an insurance company to support the family.


At Dániel Berzsenyi Gymnasium he learned Latin, Greek and German. In 1905 Pólya began studying law in Budapest, financially supported by his brother Jenö, who was a surgeon. However, he dropped out of law studies after one semester in order to study languages ​​and literature afterwards, which were his favorite subjects at school alongside biology. After graduating, which allowed him to teach Latin and Hungarian at Hungarian high schools, he turned to philosophy and soon afterwards to physics , among others with Loránd Eötvös , as well as mathematics , in which Leopold Fejér was one of his teachers. This was followed by study stays in Vienna (1910/11), where he heard from Wilhelm Wirtinger and Franz Mertens and also attended physics lectures, and Göttingen (1912/13), at that time a center of mathematics with many famous mathematicians. He received his doctorate in mathematics in Budapest with a dissertation in geometric probability theory. In 1913 he had to leave Göttingen because he got into an argument on a train ride with a student whose father was an influential privy councilor at the university. In early 1914 he made a brief visit to Paris, including with Émile Picard and Jacques Hadamard . In mediation Adolf Hurwitz 'who exercised a profound influence on Polya, he became in 1914 a lecturer at the ETH Zurich , where he was titular professor in 1920 and in 1928 full professor of higher mathematics. During the First World War, he was not drafted because of an injury that he sustained as a student at a soccer game. He later refused to obey a draft order in Hungary, which is why he was unable to enter his home country for a long time after the First World War and did not visit it again until 1967.

In 1918 he married the Swiss Stella Vera Weber, daughter of a physics professor at the University of Neuchatel. In 1924 he was on a Rockefeller Fellowship in Oxford and Cambridge with Godfrey Harold Hardy and John Edensor Littlewood , which resulted in their book on inequalities. In 1933 he was on another Rockefeller scholarship in Princeton and in Stanford (at the invitation of Hans Blichfeldt ). In 1940 he moved to the USA, where he spent two years at Brown University , briefly taught at Smith College, and from 1942 taught at Stanford University in Palo Alto. In 1953 he officially retired, but remained active and still gave a course in combinatorics in 1978.


His focus was probability theory and analysis (series, complex analysis, harmonic analysis, potential theory, boundary value problems of partial differential equations), but also geometry, number theory, mathematical physics and combinatorics. His book Mathematical Problems with Gábor Szegő Exercises and Theorems from Analysis , first published by Springer in 1925, is considered a classic and established its reputation. The problems are classified there according to solution methods instead of topics. Since he came to mathematics relatively late, he was particularly interested in the question of how mathematical results and theorems are discovered. In the second half of his work, he concentrated in particular on conveying and characterizing problem-solving strategies. In addition, Pólya published a number of works that have now become part of the standard mathematical literature. Especially his series is known here by solving mathematical problems (how to solve it), which first appeared in 1945 by Princeton University Press, translated into 17 languages was (the manuscript was originally in German) and sold over one million copies. His counting theory of trees from 1937 ( Pólya's counting theorem ) was used in chemistry .

In 1920 he coined the term Central Limit Value Theorem . In 1921 he proved the famous Pólya theorem about random walks , according to which a point A in a D-dimensional integer lattice can only be reached in D = 1.2 with probability 1 from a random walk starting from the origin, in more dimensions only with probability less than 1. In 1918 he characterized characteristic functions (Fourier transforms of probability measures) in Pólya's theorem in probability theory, and in 1923 he showed that they clearly define probability measures.

In 1924 he treated the two-dimensional case of crystallographic space groups independently of Paul Niggli .

Honors and memberships

An honorary scholarship from the Mathematical Association of America (MAA) is named after him (Pólya Lecturer). In 1950 he was invited speaker at the International Congress of Mathematicians (ICM) in Cambridge (Massachusetts) (On plausible reasoning).

The ETH Zurich awarded him an honorary doctorate in 1947. In 1974 Pólya was elected to the American Academy of Arts and Sciences , in 1976 to the National Academy of Sciences . He was a corresponding member of the Académie des Sciences , honorary member of the London Mathematical Society and the Hungarian Academy of Sciences.

In 2002 the asteroid (29646) Polya was named after him.

Works (selection)

  1. Rows . 1975, ISBN 3-540-04874-X .
  2. Function theory, zeros, polynomials, determinants, number theory . 1975, ISBN 3-540-05456-1 .
  • Math and plausible reasoning . Birkhäuser, Basel 1988,
  1. Induction and Analogy in Mathematics , 3rd edition, ISBN 3-7643-1986-0 (Science and Culture; 14).
  2. Types and structures of plausible inference , 2nd edition, ISBN 3-7643-0715-3 (Science and Culture; 15).
  • - English edition: Mathematics and Plausible Reasoning , Princeton University Press 1954, 2 volumes (Volume 1: Induction and Analogy in Mathematics , Volume 2: Patterns of Plausible Inference )
  • School of thought. About solving math problems (“How to solve it”). 4th edition Francke Verlag, Tübingen 1995, ISBN 3-7720-0608-6 (Dalp collection).
  • - English edition: How to solve it , Princeton University Press 2004 (with foreword by John Horton Conway , expanded edition)
  • About solving math problems . 2nd edition Birkhäuser, Basel 1983, ISBN 3-7643-0298-4 (Science and Culture; 21).
  • - English edition: Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving , 2 volumes, Wiley 1962 (edition in one volume 1981)
  • Collected Papers , 4 volumes, MIT Press 1974 (editor Ralph P. Boas). Volume 1: Singularities of Analytic Functions, Volume 2: Location of Zeros, Volume 3: Analysis, Volume 4: Probability, Combinatorics
  • with Godfrey Harold Hardy : John Edensor Littlewood Inequalities , Cambridge University Press 1934
  • Mathematical methods in Science , School Mathematics Study Group 1963, MAA, Washington DC 1977 (Editor Leon Bowden)
  • with Gordon Latta: Complex Variables , Wiley 1974
  • with Robert E. Tarjan , Donald R. Woods : Notes on introductory combinatorics , Birkhäuser 1983
  • with Jeremy Kilpatrick: The Stanford mathematics problem book: with hints and solutions , New York: Teachers College Press 1974
  • with others: Applied combinatorical mathematics , Wiley 1964 (editor Edwin F. Beckenbach )
  • Isoperimetric inequalities in mathematical physics , Princeton, Annals of Mathematical Studies 27, 1951
  • About a task regarding the random walk in the road network, Mathematische Annalen, Volume 84, 1921, pp. 149-160, SUB Göttingen

See also


  • Ralph P. Boas : George Polya , Biographical Memoirs National Academy of Sciences 1990, pdf .
  • Ingram Olkin, Friedrich Pukelsheim:  Pólya, George. In: New German Biography (NDB). Volume 20, Duncker & Humblot, Berlin 2001, ISBN 3-428-00201-6 , p. 610 f. ( Digitized version ).
  • Donald J. Albers, Gerald L. Alexanderson: Mathematical People - Profiles and Interviews , Birkhäuser 1985.
  • Gerald L. Alexanderson: The Polya Picture Album: Encounters of a Mathematician , Birkhäuser 1987.
  • Gerald L. Alexanderson LH Lange Obituary: George Polya , Bulletin London Mathematical Society 19, 1987, 559-608.
  • Gerald L. Alexanderson: The random walks of George Polya , Mathematical Association of America (MAA), Washington DC 2000 (with contributions from Ralph P. Boas and others).
  • Harold Taylor, Loretta Taylor: George Polya: Master of Discovery 1887-1985 , Palo Alto: Dale Seymour Pub., 1993.

Web links

Individual evidence

  1. Polya, combinatorial number determination of groups, graphs and chemical compounds, Acta Mathematica, Volume 68, 1937, pp. 145–245
  2. ^ Nicolaas Govert de Bruijn , Polyas Counting Theory - Patterns for Graphs and Chemical Compounds. In: Konrad Jacobs (Ed.): Selecta Mathematics III., Springer 1971
  3. Pólya: About the central limit theorem of probability theory and the moment problem, Mathematische Zeitschrift, 8, 1920, pp. 171–181
  4. Polya: About a task regarding the random walk in the road network, Mathematische Annalen, Volume 84, 1921, pp. 149-160
  5. Alexanderson, The Random Walks of George Polya, MAA p. 193. There reference is made to a hidden mention in Polya, About the zeros of certain functions, Mathematische Zeitschrift, Volume 2, 1918, pp. 352-383. The result is cited in Polyas essay by Math. Z., Volume 18, 1923, pp. 96-108
  6. Polya, Derivation of the Gaussian Error Law from a Functional Equation, Math. Zeitschrift, Volume 18, 1923, pp. 96-108
  7. Georg Pólya: About the analogy of the crystal symmetry in the plane. In: Journal of Crystallography and Mineralogy. Volume 60, 1924, pp. 278-283