Oskar Perron

Oskar Perron
Oskar Perron
	Perron in 1948; Photo courtesy MFO
Born	7 May 1880; Frankenthal
Died	22 February 1975 (aged 94); Munich
Nationality	German
Alma mater	University of Munich
Known for	Perron's paradox; Perron effect; Perron's formula; Perron integral; Perron method; Perron number; Perron tree; Perron's irreducibility criterion; Perron–Frobenius theorem; Moessner's theorem
	Scientific career
Fields	Mathematics
Institutions	University of Heidelberg; University of Munich
Doctoral advisor	Ferdinand von Lindemann
Doctoral students	Helmut Röhrl; Georgi Bradistilov

Oskar Perron (7 May 1880 – 22 February 1975) was a German mathematician.

He was a professor at the University of Heidelberg from 1914 to 1922 and at the University of Munich from 1922 to 1951. He made numerous contributions to differential equations and partial differential equations, including the Perron method to solve the Dirichlet problem for elliptic partial differential equations. He wrote an encyclopedic book on continued fractions Die Lehre von den Kettenbrüchen. He introduced Perron's paradox to illustrate the danger of assuming that the solution of an optimization problem exists:

Let N be the largest positive integer. If N > 1, then N² > N, contradicting the definition of N. Hence N = 1.

Works

Über die Drehung eines starren Körpers um seinen Schwerpunkt bei Wirkung äußerer Kräfte, Diss. München 1902
Grundlagen für eine Theorie der Jacobischen Kettenbruchalgorithmus, Habilitationsschrift Leipzig 1906
Die Lehre von den Kettenbrüchen, 2 vols., 1913, 3rd edn. Teubner Verlag 1954 (vol. 1 Elementare Kettenbrüche,^[1] vol. 2 analytische und funktionentheoretische Kettenbrüche^[2])
Irrationalzahlen, 1921,^[3] 2nd edn. 1939,^[4] 4th edn. de Gruyter, Berlin 1960
Algebra I, II, Sammlung Göschen 1927,^[5] 3rd edn, 1951
with Evelyn Frank: Frank, Evelyn; Perron, Oskar (1954). "Remark on a certain class of continued fractions". Proc. Amer. Math. Soc. 5 (2): 270–283. doi:10.1090/s0002-9939-1954-0061185-4. MR 0061185.
Nichteuklidische Elementargeometrie der Ebene, Teubner, Stuttgart 1962

Edmund Hlawka: Das Werk Perrons auf dem Gebiete der diophantischen Approximationen. Jahresbericht der DMV 80, 1978, S. 1–12
Josef Heinhold: Oskar Perron, Jahresbericht der DMV 90, 1988, S. 184–199 (in der DML Bielefeld: [1])
Freddy Litten: Oskar Perron – Ein Beispiel von Zivilcourage im Dritten Reich, Mitteilungen der DMV Heft 3, 1994, S. 11–12; erweitert in: Frankenthal einst und jetzt, 1995, S. 26–28 (auf der Homepage von Litten: [2])
Leon Bernstein: The modified algorithm of Jacobi-Perron. Memoirs of the AMS 67, Providence, 1966
Leon Bernstein: The Jacobi-Perron algorithm - its theory and application. Lecture Notes Math. 207, Springer-Verlag, 1971

^ Scott, W. T. (1955). "Review: Oskar Perron, Die Lehre von den Kettenbrüchen. Vol. I. Elementare Kettenbruche. 3rd ed.". Bull. Amer. Math. Soc. 61 (6): 594–595. doi:10.1090/S0002-9904-1955-10003-1.
^ Scott, W. T. (1958). "Review: Oskar Perron, Die Lehre von den Kettenbruchen. Vol. II. Analytische-funktionen-theoretische Kettenbruche. 3rd ed.". Bull. Amer. Math. Soc. 64 (5): 299–300. doi:10.1090/s0002-9904-1958-10240-2.
^ Kempner, A. J. (1923). "Review: Oskar Perron, Irrationalzahlen". Bull. Amer. Math. Soc. 29 (1): 34–36. doi:10.1090/s0002-9904-1923-03650-1.
^ Hazlett, Olive C. (1940). "Review: Oskar Perron, Irrationalzahlen, 2d revised edition" (PDF). Bull. Amer. Math. Soc. 46 (1): 15–16. doi:10.1090/s0002-9904-1940-07136-8.
^ Hazlett, O. C. (1928). "Review: Oskar Perron, Algebra". Bull. Amer. Math. Soc. 34 (1): 115–116. doi:10.1090/s0002-9904-1928-04528-7.

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