Detlef Laugwitz (1932–2000) was a

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and historian, who worked in

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

history of mathematics The history of mathematics deals with the origin of discoveries in mathematics and the History of mathematical notation, mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples ...

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 (for example, Inner product space#Definition, inner product, Norm (mathematics ...

, and

non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definitio ...

Biography

He was born on 11 May 1932 in Breslau,

Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...

. Starting in 1949, he studied mathematics,

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

, and

philosophy Philosophy ('love of wisdom' in Ancient Greek) is a systematic study of general and fundamental questions concerning topics like existence, reason, knowledge, Value (ethics and social sciences), value, mind, and language. It is a rational an ...

at the Georg-August-University at

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

, where he received his doctorate in 1954. Until 1956 he worked in the

Mathematical Research Institute of Oberwolfach The Oberwolfach Research Institute for Mathematics () is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekly workshops on diverse topics where mathematicians and ...

. In 1958 he became a lecturer at the

Technical University of Munich The Technical University of Munich (TUM or TU Munich; ) is a public research university in Munich, Bavaria, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Established in 1868 by King Ludwig II ...

, where he obtained his Habilitation. In 1958 he moved to the

Technical University of Darmstadt Technical may refer to: * Technical (vehicle), an improvised fighting vehicle * Technical area, an area which a manager, other coaching personnel, and substitutes are allowed to occupy during a football match * Technical advisor, a person who ad ...

, where in 1962 he became a professor, and remained until his retirement. From 1976 to 1984 he was a visiting professor at

Caltech The California Institute of Technology (branded as Caltech) is a private university, private research university in Pasadena, California, United States. The university is responsible for many modern scientific advancements and is among a small g ...

Work

Laugwitz worked in differential geometry of infinite dimensional vector spaces (his dissertation) and in

Finsler geometry In mathematics, particularly differential geometry, a Finsler manifold is a differentiable manifold where a (possibly asymmetric) Minkowski norm is provided on each tangent space , that enables one to define the length of any smooth curve as ...

. In 1958 he and Curt Schmieden developed their own approach to

infinitesimal In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the " ...

s through field extensions, independently of

Abraham Robinson Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorp ...

. They described this as "infinitesimal mathematics" and leading back to the historical roots in

Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many ...

. In 1996 he published the standard biography of

Bernhard Riemann Georg Friedrich Bernhard Riemann (; ; 17September 182620July 1866) was a German mathematician who made profound contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the f ...

Publications

* (translated by Fritz Steinhardt); *. * (translated by Abe Shenitzer with the editorial assistance of Hardy Grant, Sarah Shenitzer, and the author Detlev Laugwitz)

References

{{DEFAULTSORT:Laugwitz, Detlef 20th-century German mathematicians German historians of mathematics Differential geometers Technical University of Munich alumni Academic staff of the Technical University of Munich 1932 births 2000 deaths 20th-century German historians Academic staff of Technische Universität Darmstadt