# Ludwig Berwald

### Born: 8 December 1883 in Prague, Bohemia (now Czech Republic)

Died: 20 April 1942 in Łódź, Poland

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**Ludwig Berwald**'s parents were Max Berwald and Friedericke Fischel. Max ran Andre's Bookshop, one of the most famous bookshops in Prague situated in the centre of the city in the Pulvertum area. Max and Friedericke had there children; Ludwig had one brother and one sister. The family were Jewish with Max coming from East Prussia and his wife being a native of Prague. They were German speaking.

Ludwig entered the Graben Gymnasium, previously called the Imperial Royal State High School of Prague, in 1893. He studied there for six years and his mathematics teacher, first Josef Guckla and later Prokop Knothe, taught the young boy well and gave him a love of the subject. Around 1900 Max Berwald sold his bookshop in Prague and moved with his family to Munich. There Ludwig continued his education at the Luitpold Gymnasium, completing his school education in 1902. He entered the Royal Ludwig-Maximilian University in Munich in the Fall of 1892, where he pursued his studies in mathematics and physics. Among his lecturers were Lindemann, Pringsheim, and Röntgen. In December of 1908, he was awarded his doctorate, after studying under professor Auriel Voss, with his dissertation

*Über die Krümmungseigenschaften der Brennflachen eines geradlinigen Strahlsystems und der in ihm enthaltenen Regelflächen*Ⓣ.

After the award of the doctorate, Berwald was appointed as assistant to Heinrich Burkhardt. This should have presented Berwald with the opportunity to work on his habilitation thesis so that he could become a privatdozent in Munich, but sadly he had rather severe health problems. For the next three years he spent most of the time in a sanatorium being treated for a lung problem. He did manage to do a little private tutoring but he was unable to undertake research for his habilitation. On 12 September 1915 Berwald married Hedwig Adler, the daughter of Friedericke and Emanuel Adler, who had also been born in Prague; she was eight years older than her husband. After that Berwald and his wife made many trips to Prague, and there he got to know two mathematics lecturers Gerhard Kowalewski and Georg Pick. With their support, Berwald became a lecturer at the German University in Prague. He was promoted to an extraordinary professorship on 24 March 1922, and became a full professor in 1924. After Pick retired in 1929, Berwald became Head of the Mathematics Department. Pinl [2] met Berwald for the first time in 1926. He writes that Berwald [1]:-

Berwald's scientific work was mainly in the area of differential geometry. He wrote 54 papers up to the time of his deportation. A portion of his work set up the basic theory of Finsler geometry and Spray geometry (i.e., differential geometry of path spaces). Many people working in Finsler geometry consider that Ludwig Berwald is the founder of Finsler geometry. Berwald and E Cartan developed a general theory of two-dimensional Finsler spaces. Berwald wrote a series of major papers... was primarily known as a typical scholar, pointedly reserved, choosing his words carefully and precisely, always serious and cautious, of somewhat sceptical outlook, but convincing and determined if need be. On close acquaintance one discovered behind the scientist a sensitive, artistic personality, exceptionally musical and, on rare occasions, even poetically inclined. Berwald was tall and slender in statue. Because of his nearsightedness he usually wore glasses. As a result of his early serious illness Berwald was very prone to colds. ... Berwald was an excellent pianist and also played chamber music with a certain well-ordered regularity that enabled him to study a broad range of musical literature together with his fellow musicians, among them Professor Pick who played the violin. ... One could make Berwald very happy if one turned the conversation to his Dalmatian trips - how he loved the hot sun of this stony country. How he loved to describe his travelling experiences and show his numerous pictures that he had collected.

*On Finsler and Cartan geometries*. Jesse Douglas, reviewing the third of these, writes:-

On 22 October 1941, Berwald's scientific work came to a close. The Berwalds were deported to the Ghetto in Łódź, Poland, by order of the German Secret Police as part of the third transportation of Jews [1]:-The principal problem(due to P Funk)solved in this paper is that of characterising in an invariant manner all two-dimensional Finsler spaces which can be mapped geodesically on a Euclidean plane("Finsler spaces with rectilinear extremals"). In the case where the Finsler space is Riemannian, this problem reduces to the classic one of Beltrami solved by surfaces of constant curvature.

Hedwig Berwald died on 27 March 1942; the cause of death was given as blocked arteries. Ludwig Berwald died a few weeks later on 20 April; the cause of death was given as intestinal catarrh and heart failure.The Berwalds were placed in an incomplete one storey schoolhouse ... There were no beds ... people simply lay down next to each other on the bare floor. ... Naturally, everybody slept in their day-time clothes. ... Fifty-five people slept in one room which was approximately twenty feet by twenty feet.

**Article by:** *J J O'Connor* and *E F Robertson*

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