Detlef Laugwitz (1932–2000) was a

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

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, structure, space, models, and change. History On ...

and historian, who worked in

differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...

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

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 (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

, 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 epsilon–delta ...

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 is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...

. Starting in 1949, he studied mathematics,

physics Physics is the natural science that studies matter, its 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 which r ...

, and

philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...

at the Georg-August-University at

Göttingen Göttingen (, , ; nds, Chöttingen) 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. At the end of 2019, t ...

, where he received his doctorate in 1954.''Differential geometry without the axiom of dimension'', Mathematische Zeitschrift Bd.61, 1954, p. 100 Until 1956 he worked in the

Mathematical Research Institute of Oberwolfach The Oberwolfach Research Institute for Mathematics (german: Mathematisches Forschungsinstitut Oberwolfach) is a center for mathematical research in Oberwolfach, Germany. It was founded by mathematician Wilhelm Süss in 1944. It organizes weekl ...

. In 1958 he became a lecturer at the

Technical University of Munich The Technical University of Munich (TUM or TU Munich; german: Technische Universität München) is a public research university in Munich, Germany. It specializes in engineering, technology, medicine, and applied and natural sciences. Establis ...

, 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 analysis, a discipline for forecasting the future direction of prices through the study of past market data * Technical drawing, showing how something is co ...

, 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 or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

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 functional is provided on each tangent space , that enables one to define the length of any smooth c ...

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

infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referr ...

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 reincorpo ...

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

Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathema ...

. In 1996 he published the standard biography of

Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry. In the field of real analysis, he is mostly known for the first rig ...

Notes

Publications

* *. {{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