Detlef Laugwitz
Encyclopedia
Detlef Laugwitz was a German mathematician
, who worked in Differential geometry, History of mathematics
, Functional analysis
, and Non-standard analysis
.
, and philosophy
at the Georg-August-University at Göttingen
, where he received his doctorate in 1954. Until 1956 he worked in the Mathematical Research Institute of Oberwolfach
. In 1958 he became a lecturer at the Technical University of Munich
, where he obtained his Habilitation. In 1958 he moved to the Technical University of Darmstadt, where in 1962 he became a professor, and remained until his retirement. From 1976 to 1984 he was a visiting professor at Caltech
.
s through field extensions, independently of Abraham Robinson
. They described this as "infinitesimal mathematics" and leading back to the historical roots in Leibniz. In 1996 he published the standard biography of Bernhard Riemann
.
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....
, who worked in Differential geometry, History of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
, Functional analysis
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, and Non-standard analysis
Non-standard analysis
Non-standard analysis is a branch of mathematics that formulates analysis using a rigorous notion of an infinitesimal number.Non-standard analysis was introduced in the early 1960s by the mathematician Abraham Robinson. He wrote:...
.
Biography
Starting in 1949, Laugwitz studied mathematics, physicsPhysics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, and philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
at the Georg-August-University at Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
, where he received his doctorate in 1954. Until 1956 he worked in the Mathematical Research Institute of Oberwolfach
Mathematical Research Institute of Oberwolfach
The Mathematical Research Institute of Oberwolfach in Oberwolfach, Germany, was founded by mathematician Wilhelm Süss in 1944...
. In 1958 he became a lecturer at the Technical University of Munich
Technical University of Munich
The Technische Universität München is a research university with campuses in Munich, Garching, and Weihenstephan...
, where he obtained his Habilitation. In 1958 he moved to the Technical University of Darmstadt, where in 1962 he became a professor, and remained until his retirement. From 1976 to 1984 he was a visiting professor at Caltech
California Institute of Technology
The California Institute of Technology is a private research university located in Pasadena, California, United States. Caltech has six academic divisions with strong emphases on science and engineering...
.
Work
Laugwitz worked in differential geometry of infinite dimensional vector spaces (his dissertation) and in Finsler geometry. In 1958 he and Curt Schmieden developed their own approach to infinitesimalInfinitesimal
Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...
s through field extensions, independently of Abraham Robinson
Abraham Robinson
Abraham Robinson was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics....
. They described this as "infinitesimal mathematics" and leading back to the historical roots in Leibniz. In 1996 he published the standard biography of Bernhard Riemann
Bernhard Riemann
Georg Friedrich Bernhard Riemann was an influential German mathematician who made lasting contributions to analysis and differential geometry, some of them enabling the later development of general relativity....
.