Detlef Laugwitz

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Detlef Laugwitz

Detlef Laugwitz (born May 11, 1932 in Breslau ; † April 17, 2000 ) was a German mathematician who dealt with differential geometry , the history of mathematics, didactics, functional analysis and non-standard analysis .

Live and act

After the expulsion of his family from Silesia to Saxony Detlef Laugwitz attended the high school for boys in Rinteln , where in 1949 he obtained a high school. In the same year he began studying mathematics, physics and philosophy at the University of Göttingen , where he received his doctorate in 1954 with a thesis on differential geometry. From 1955 to 1957 he was a research assistant at the Mathematical Institute at the University of Freiburg , and from 1956 onwards, as a DFG scholarship holder, also worked in Oberwolfach and at the University of Erlangen . In 1958 he became a private lecturer at the Technical University of Munich , where he had completed his habilitation. In the same year he went to the Technical University of Darmstadt , where he received a full professorship in 1962, which he held until his retirement . He conducted research at the Accademia Nazionale dei Lincei in Rome and was visiting professor at the California Institute of Technology (Caltech) in Pasadena , California during 1976/77 and 1984/85 .

Laugwitz dealt with differential geometry of infinite dimensional vector spaces (as in his dissertation) and Finsler - geometry . From 1958 he and Curt Schmieden developed his own approach to non-standard analysis via body extensions, independently of Abraham Robinson . They called this "infinitesimal mathematics" and Laugwitz traced the historical roots back to Leibniz . In 1996 he published the first and so far only biography of Bernhard Riemann - apart from Dedekind's Abriß in the collected works - which has since been regarded as a standard work. In the 1980s, he (and his student Detlef Spalt ) tried to show traces of the use of nonstandard analysis in the history of mathematics (forerunners in this were already another founder of nonstandard analysis Abraham Robinson and Imre Lakatos ), for example with Augustin-Louis Cauchy , which led to controversy Debates led. Laugwitz examined in detail which sentences classified as incorrect in the later nonstandard analysis (of which there are different versions) are valid and which are not. He found Cauchy's sum theorem salvable, but it was criticized that this did not correspond to Cauchy's way of thinking and the original attempt at proof.

In 1968, Laugwitz was the founder of the series Mathematics Yearbook Overviews at BI-Wissenschaftsverlag.

Fonts

  • with Herbert Meschkowski : Meyers Handbuch der Mathematik. Bibliographical Institute 1967, 1972.
  • School math from a higher point of view. BI Wissenschaftsverlag 1969.
  • Infinitesimal Calculus: Continuum and Numbers - An Introduction to Non-Standard Analysis. BI university paperback 1978.
  • Numbers and Continuum - An Introduction to Infinitesimal Mathematics. Scientific Book Society 1986.
  • Engineering math. BI university pocket book, 7 volumes, 1964–1967.
  • with Benno Fuchssteiner: functional analysis. BI Wissenschaftsverlag 1974.
  • Differential geometry. Teubner 1960, 2nd edition 1968, 3rd edition 1977.
  • Differential geometry in vector spaces with special consideration of the infinitely dimensional spaces. Vieweg 1965.
  • Bernhard Riemann 1826-1866. Birkhäuser 1996, 2008, ISBN 0-8176-4776-7 .
  • with Curt Schmieden: An extension of infinitesimal calculus. Mathematische Zeitschrift Vol. 69, 1958, pp. 1-39.
  • One way to nonstandard analysis. Annual report DMV 1973.

Individual evidence

  1. ↑ D. Laugwitz: Differentialgeometrie ohne Dimensionaxiom , Mathematische Zeitschrift Vol. 61, 1954, p. 100ff
  2. ^ University archive of the ALU Freiburg, Mathematical Institute 1945-1970, Freiburg 1997 [1]
  3. ↑ See, for example, Detlef Spalt, Collegium Logicum, Springer, Volume 1, 1995, p. 30. Spalt later joined the criticism and later advocated a different interpretation of Cauchy's proof.

Web links


personal data
SURNAME Laugwitz, Detlef
BRIEF DESCRIPTION German mathematician
DATE OF BIRTH May 11, 1932
PLACE OF BIRTH Wroclaw
DATE OF DEATH April 17, 2000