Ludwig Berwald

Ludwig Berwald (8 Dec 1883 – 20 Apr 1942) was a German mathematician best known for his contributions to differential geometry, especially Finsler geometry. He taught in Munich and Prague for 32 years, publishing 54 papers, before being deported by the German secret police to the Łódź Ghetto, where he and his wife Hedwig died within a year.^[1]

Biography

Ludwig was one of three children of Max Berwald, an East Prussian owner of a famous bookstore, and Friedericke Fischel. In 1900, the family moved to Munich, where Ludwig matriculated at Ludwig Maximilian University in 1902.^[1] There he studied mathematics under Aurel Voß, alongside notable mathematicians Hugo Dingler and Fritz Noether,^[2] and received his PhD in 1908 for his thesis entitled Über die Krümmungseigenschaften der Brennflächen eines geradlinigen Strahlsystems und der in ihm enthaltenen Regelflächen (On the properties of curvature on the internal surfaces of rectilinear systems, and surfaces contained thererin).^[3] Due to sanatorium treatment for pulmonary illness, he was unable to continue his work in Munich. Through friends, he eventually became a lecturer at the German University (now Charles University) back in Prague, achieving full professorship in 1924. There, he developed friendships and successful collaborations with fellow mathematicians Georg Pick, Paul Funk, and Élie Cartan, publishing some 54 articles^[1] which significantly advanced the field of Finsler geometry, pioneering important concepts which still bear his name such as Berwald curvature, Berwald spray,^[4] and the Berwald–Moór metric function.^[5] For extending the concept of Riemann curvature to Finsler spaces, Berwald has been credited as the founder of differential geometry of Finsler spaces.^[6] On 22 October 1941, the day after submitting his last article,^[7] the sickly 57 year old Berwald was deported to the Łódź Ghetto in Poland in the third transportation of Jews by the German secret police. The Berwalds were two of 55 people who lived in a room approximately 20 feet square with no beds. Hedwig, eight years older than her husband, died 27 March 1942; Ludwig followed 23 days later.^[7]

Selected works

• Berwald, L. "Untersuchung der Krümmung allgemeiner metrischer Räume auf Grund des in ihnen herrschenden Parallelismus," Mathematische Zeitschrift, 25 (1) (1926), pp. 40–73.
• "Über eine charakteristische Eigenschaft der allgemeinen Räume konstanter Krümmung mit geradlinigen Extremalen," Monatshefte für Mathematik und Physik, 36 (1929), pp. 315–30.
• Berwald, L. "On the Projective Geometry of Paths." Annals of Mathematics Second Series 37.4 (1936): 879–98. doi:10.2307/1968625

References