George Pólya
George Pólya | |
|---|---|
ETH Zürich Stanford University | |
| Doctoral advisor | Lipót Fejér |
| Doctoral students | Albert Edrei Hans Einstein Fritz Gassmann Albert Pfluger Walter Saxer James J. Stoker Alice Roth |
George Pólya (heuristics and mathematics education.[2] He has been described as one of The Martians,[3] an informal category which included one of his most famous students at ETH Zurich, John von Neumann.
Life and works
Pólya was born in
ETH Zürich in Switzerland and from 1940 to 1953 at Stanford University. He remained a Professor Emeritus at Stanford for the rest of his career, working on a range of mathematical topics, including series, number theory, mathematical analysis, geometry, algebra, combinatorics, and probability.[7] He was invited to speak at the ICM at Bologna in 1928,[8]
at Oslo in 1936 and at Cambridge, Massachusetts, in 1950.
On September 7, 1985, Pólya died in
Palo Alto, California, United States[9]
due to complications of a stroke he suffered during that summer.
Heuristics
Early in his career, Pólya wrote with
Mathematics and Plausible Reasoning
(Volume I: Induction and Analogy in Mathematics, and Volume II: Patterns of Plausible Inference), and Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving (volumes 1 and 2).
In 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, 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
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."[11]
In 1976 the
College Mathematics Journal.[12] In 1987 the London Mathematical Society (LMS) established the Pólya Prize for "outstanding creativity in, imaginative exposition of, or distinguished contribution to, mathematics within the United Kingdom."[13] In 1991, the MAA established the George Pólya Lectureship series.[14]
Stanford University has a Polya Hall named in his honor.[15]
Selected publications
Books
- Aufgaben und Lehrsätze aus der Analysis, 1st edn. 1925.[16] ("Problems and theorems in analysis“). Springer, Berlin 1975 (with Gábor Szegő).
- Reihen. 1975, 4th edn., ISBN 3-540-04874-X.
- Funktionentheorie, Nullstellen, Polynome, Determinanten, Zahlentheorie. 1975, 4th edn., ISBN 3-540-05456-1.
- Mathematik und plausibles Schliessen. Birkhäuser, Basel 1988,
- Induktion und Analogie in der Mathematik, 3rd edn., ISBN 3-7643-1986-0(Wissenschaft und Kultur; 14).
- Typen und Strukturen plausibler Folgerung, 2nd edn., ISBN 3-7643-0715-3(Wissenschaft und Kultur; 15).
- – English translation: Mathematics and Plausible Reasoning, Princeton University Press 1954, 2 volumes (Vol. 1: Induction and Analogy in Mathematics, Vol. 2: Patterns of Plausible Inference)
- Schule des Denkens. Vom Lösen mathematischer Probleme ("How to solve it"). 4th edn. Francke Verlag, Tübingen 1995, ISBN 3-7720-0608-6(Sammlung Dalp).
- – English translation: How to Solve It, Princeton University Press 2004 (with foreword by John Horton Conway and added exercises)
- Vom Lösen mathematischer Aufgaben. 2nd edn. Birkhäuser, Basel 1983, ISBN 3-7643-0298-4(Wissenschaft und Kultur; 21).
- – English translation: Mathematical Discovery: On Understanding, Learning and Teaching Problem Solving, 2 volumes, Wiley 1962 (published in one vol. 1981)
- Collected Papers, 4 volumes, MIT Press 1974 (ed. Ralph P. Boas). Vol. 1: Singularities of Analytic Functions, Vol. 2: Location of Zeros, Vol. 3: Analysis, Vol. 4: Probability, Combinatorics
- with R. C. Read: Combinatorial enumeration of groups, graphs, and chemical compounds, Springer Verlag 1987 (English translation of Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen, Acta Mathematica, vol. 68, 1937, pp. 145–254)
- with Godfrey Harold Hardy: John Edensor LittlewoodInequalities, Cambridge University Press 1934
- Mathematical Methods in Science, MAA, Washington D. C. 1977 (ed. 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 several co-authors: Applied combinatorial mathematics, Wiley 1964 (ed. Edwin F. Beckenbach)
- with Gábor Szegő: Isoperimetric inequalities in mathematical physics, Princeton, Annals of Mathematical Studies 27, 1951
Articles
- Pólya, G. (1922). "On the mean-value theorem corresponding to a given linear homogeneous differential equation". Trans. Amer. Math. Soc. 24 (4): 312–324. MR 1501228.
- Polya, G. (1941). "On Functions Whose Derivatives Do Not Vanish in a Given Interval". Proc Natl Acad Sci U S A. 27 (4): 216–218. PMID 16578010.
- Polya, G. (1941). "Sur l'existence de fonctions entières satisfaisant à certaines conditions linéaires". Trans. Amer. Math. Soc. 50 (1): 129–139. MR 0004304.
- with PMID 16588467.
- Pólya, George (1942). "On converse gap theorems". Trans. Amer. Math. Soc. 52 (1): 65–71. MR 0006577.
- with MR 0007169.
- "On the zeros of a derivative of a function and its analytic character" (PDF). Bull. Amer. Math. Soc. 49, Part 1 (3): 178–191. 1943. MR 0007781.
- Polya, G. (1947). "A Minimum Problem About the Motion of a Solid Through a Fluid". Proc Natl Acad Sci U S A. 33 (7): 218–221. PMID 16588747.
- Polya, G. (1950). "Remark on Weyl's Note "Inequalities Between the Two Kinds of Eigenvalues of a Linear Transformation". Proc Natl Acad Sci U S A. 36 (1): 49–51. PMID 16588947.
See also
- Integer-valued polynomial
- Laguerre–Pólya class
- Landau–Kolmogorov inequality
- Multivariate Pólya distribution
- Pólya's characterization theorem
- Pólya class
- Pólya conjecture
- Polya distribution
- Pólya enumeration theorem
- Pólya–Vinogradov inequality
- Pólya inequality
- Pólya urn model
- Pólya's theorem
- Pólya's proof that there is no "horse of a different color"
- Wallpaper group
- The Martians (scientists)
References
- ^ George Polya in the Swiss historic lexicon.
- ISBN 9780883855287.
- ^ Marx, György (March 1997). "A marslakók legendája". Retrieved September 11, 2022.
- ^ "Polya biography". Archived from the original on March 2, 2012. Retrieved July 4, 2009.
- ISBN 978-0-86651-611-2.
Plancherel was a military man, a colonel in the Swiss army, and a devout Catholic; Pólya did not like military ceremonies or activities, and he was an agnostic who objected to hierarchical religions.
- ^ "George Pólya". Mathematics Genealogy Project. Retrieved January 10, 2023.
- ISBN 0-06-501069-8.
- ^ Pólya, G. "Ueber eine Eigenschaft des Gaussschen Fehlergesetzes". In: Atti del Congresso Internazionale dei Matematici: Bologna del 3 al 10 de settembre di 1928. Vol. 6. pp. 63–64.
- ^ Dembart, Lee (September 8, 1985). "George Polya, 97, Dean of Mathematicians, Dies". Los Angeles Times. Retrieved January 20, 2022.
- JSTOR 2690409.
- ^ Society for Industrial and Applied Mathematics George Pólya Prize
- ^ Mathematical Association of America George Pólya Award
- ^ "London Mathematical Society Polya Prize". Archived from the original on May 10, 2010. Retrieved October 9, 2009.
- ^ "Pólya Lectures". Mathematical Association of America. Retrieved November 15, 2022.
- ^ "POLYA HALL, 14-160". Retrieved April 3, 2020.
- (PDF) from the original on April 2, 2015.
External links
Wikiquote has quotations related to George Pólya.
- The George Pólya Award
- O'Connor, John J.; Robertson, Edmund F., "George Pólya", MacTutor History of Mathematics Archive, University of St Andrews
- George Pólya at the Mathematics Genealogy Project
- George Pólya, Gábor Szegö, Problems and theorems in analysis (1998)
- PolyaPower—an introduction to Polya's Heuristics at the Wayback Machine (archived July 28, 2009)
- George Pólya on UIUC's WikEd
- Memorial Resolution
- George Pólya — Biographical Memoirs of the National Academy of Sciences
- "Polya Guessing" on Vimeo
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