This lecture is devoted to education of mathematics at the school which was the first technical school in Brno. The history of the German Technical University is the history of technical educational institution until 1945. In 1849 the school started as a Technical College, and during 1849-1873 it was transformed into Technical University of the second half of 19th century.
The students of the school came to Brno from many parts of the Austro-Hungarian Empire and later from many other countries. The aim of this lecture is to describe the staff at the Departments of Mathematics. There were many renowned mathematicians teaching at this school, especially up to 1918. These, in most cases young, mathematicians became professors of important universities in Austria and Germany. Some of them are e.g. Emanuel Czuber, Ernst Fischer, Johann Radon, Georg Hamel, Richard Mises, and Heinrich Tietze. Some well-known Czech, German, and Austrian mathematicians also tried to become professors at the German Technical University in Brno: for example, Matyas Lerch, Hans Hahn, Wilhelm Blaschke and Emil Artin.
The hundred years' history of this school still remains largely unexplored in the Czech Republic. The already existing works are mostly in German and their main concern is the foundation of the school. From later period, these works mention mainly organizational matters of the school. The most important resources are Geschichte der Deutschen Technischen Hochschule in Brünn by Professor Hellmer (1899) and Geschichte der Deutschen Technischen Hochschule in Brünn by Professor Haussner (1924). In both works, we can find the lists of professors, assistant professors, and assistants of mathematics.
The possibilities of compiling the development of the German Technical
University in Brno are very good. The complete archive of the school has
been preserved directly in Brno. It is stored in the Moravian Provincial
Archive in Brno. Among other documents the following have been preserved:
the protocols from the professors' meetings from the whole period of existence
of the school, the protocols of the competitions for professors' chairs,
the files of assistants and private associate professors, protocols about
substitution for the unoccupied places, personal files of the employees
since 1880, and many other items. In the Moravian Provincial Archive, there
is also complete correspondence between the school and the Moravian Governance,
and also part of the correspondence between the school and the Ministry
of Education. In the Library of the archive, almost all the study
programmes for the whole of the period of existence of the school are stored.
The main aim of this lecture is to approach the staff of the Departments of Mathematics at the German Technical University in Brno in the years 1849-1945. Mathematics forms a very important part of the education of future engineers, which was true in the past as well as it is now. We can remind the reader of Ecole Polytechnique, established in Paris in 1794, where mathematics represented about 16 % of teaching. The contents and forms of instruction of this subject developed not only in connection with the development of mathematics as a science, but also with regard to the needs of the specific branches.
The Department of Mathematics was one of the twelve departments, which were established at Technical College in 1849. The professor of mathematics taught Elementary Mathematics (10 hours per week) in the preliminary course and Higher Mathematics (5 hours per week) at the Technical Faculty.
The first professor of mathematics, Valentin Teirich, former professor of a grammar school in Vienna, was appointed by Emperor Franz Josef I. in March 1850. In 1854 he went to Vienna, where he was appointed the director of a secondary technical school. In the school year 1854-1855 mathematics was taught by Karl Prentner, an assistant of mathematics at Vienna Polytechnical Institute. Prentner was born in Bross (now in Rumania) in 1823. He studied at Vienna Technical Institute. He was appointed professor of mathematics in 1855, and worked in Brno until 1885, when he retired.
In 1873, the second Department of Mathematics was established at Technical University in Brno, and the Emperor appointed the first professor of this department, Franz Unferdinger (1833-1890), former associated professor at the Vienna Polytechnical Institute. Unferdinger remained in Brno for the rest of his life.
In 1886, Emanuel Czuber (1851-1925), came to Brno Technical University. He was the first important person at the Department of Mathematics. Czuber was born in Prague and studied at Prague Technical University where he habilitated for practical geometry in 1876, and worked as an assistant to Professor Koristka. He worked in Brno for only five years (Czuber was rector of the school in school year 1890-1891) and in 1891 went to Vienna Technical University. Czuber worked in the area of probability theory (he wrote a part of Encyklopaedie der mathematischen Wissenschaften), calculus of observations, and actuary mathematics. He initiated the education of actuary mathematics at Vienna Technical University in 1894. In 1909 his daughter Bertha married a brother of Franz Ferdinand, the successor to Austrian throne.
For only a few months, Oscar Peithner von Lichtenfels taught mathematics at Brno Technical University. Peithner studied at Vienna Technical University and Vienna University. He habilitated at both schools for mathematics. In May 1891 he went from Brno to Graz Technical University. Franz Hocevar (1853-1919) worked in Brno for four years, he came to Brno from Insbruck in 1891, and in 1895 he decided to leave Brno and go to Graz Technical University.
In 1891 Otto Biermann (1858-1908) was appointed to the free chair of professor of mathematics. He studied at Prague and Vienna Universities. He spent one year in Berlin under Weierstrass. Biermann habilitated in 1882 at Prague University. He taught at German secondary schools in Prague for a number of years (for a short time also in Klagenfurt, Austria). Biermann worked at Brno Technical University for the rest of his life. He worked in the area of mathematical analysis and mathematical physics.
In 1895 Emil Waelsch (1863-1927) came to Brno. He ifluenced mathematical education at the Brno German Technical University along thirty years. Waelsch attended German Technical University and German University in Prague. From 1884 to 1885 he studied under Felix Klein in Leipzig and from 1885 to 1886 under Paul Gordan and Max Noether in Erlangen where he received his doctorate in 1888. In the years 1892-1893 Waelsch studied under Sophus Lie in Leipzig. From 1886 to 1892 he was assistant of descriptive geometry at the Prague German Technical University. He habilitated there in 1890. In the school years 1893-1894 he became assistant to professor Fiedler at Zurich Technical University. In 1895 Waelsch became associated professor of mathematics at the German Technical University of Brno. In 1898 he was appointed full professor. In 1910 he was appointed professor of geometry and he remained in this position for the rest of his life.
In 1902 Ernst Fischer (1875-1954) came to Brno, and became an assistant to E. Waelsch. Fischer studied at Vienna University under Mertens from 1894. He spent 1899 in Berlin, then he studied in Zurich and Goettingen. In 1904 Fischer habilitated for mathematics at the Brno German Technical University. After Biermann's death he was appointed associated professor in 1910. One year later he was appointed full professor of mathematics at the University of Erlangen. He worked there until 1920, then he taught at Cologne. In 1938 he retired. In 1907 Fischer studied orthonormal sequences of functions and gave necessary and sufficient conditions for a sequence of constants to be the Fourier coefficients of a square integrable function. This led to the concept of a Hilbert space. The theorem, now called the Riesz-Fischer theorem (F. Riesz published a similar result in the same year), is one of the great achievements of the Lebesque theory of integration.
From 1910 E. Waelsch held the position of professor of geometry and Heinrich Tietze (1880-1964) was appointed professor of mathematics. Tietze was a student at Technical University in Vienna. He studied also at the universities of Vienna, Munich and Goettingen. In 1908 he habilitated at Vienna University. Tietze worked in Brno until 1919, and then he went to Erlangen where he was appointed professor at the university. From 1926 he taught at Munich University, where he remained for the rest of his life. Tietze worked in the area of topology and developed important work on subdivisions of cell complexes. His work led him to consider group presentations and he proposed his now famous Tietze transformations to change from one presentation to another without changing the group which is defined.
In 1912 Lothar Schrutka (1881-1945) was appointed associated professor of mathematics at the German Technical University in Brno. Schrutka studied under Mertens at Vienna University , in the years 1901-1902 at Goettingen University, and in 1905 in Berlin. He worked in Brno until 1925 when he was appointed professor at Vienna Technical University. He taught there until his tragical death.
From 1919 until 1923 the second professorship of mathematics was vacant. In 1923 Karl Mayr (1887-1940) came to Brno. He studied at Vienna University and from 1912 to 1913 he worked as an assistant at the Brno German Technical University. In 1920 he habilitated at Vienna Technical University. In 1924 Karl Mayr went to Graz Technical University where he remained for the rest of his life.
In 1925 Rudolf Weyrich (1894-1971) became associated professor. He studied at the universities in Rostock and Breslau (under Kneser). From 1923 he was assistant and lecturer at Marburg University. He worked in Brno until 1945 when the school was abolished. From 1948 to 1950 he was a lecturer at Braunschweig Technical University. In 1950 he went to Istanbul where he held full professorship at the university. He retired in Brauschweig in 1958.
In 1927 Lothar Koschmieder (1890-1974) became professor. He studied at the universities in Breslau, Freiburg and, Goettingen. He received his doctorate in Breslau in 1913. From 1913 until 1924 Koschmieder was an assistant to Adolf Kneser at Breslau University, and habilitated there in 1919. In 1924 Koschmieder was appointed associated professor at Breslau University. Before his arrival to Brno he substituted at Greifswald University. In Brno he was rector of the German Technical University in the years 1939-1940, and had a major role in the transformation of the school under the regency of the German Empire. At the beginning of 1940 he went to Graz Technical University. He worked there until 1946. Then he taught in Argentina (1948-49, University of Tucuman) and Iraq (1953-58, Bagdad). From 1958 to 1973 he taught at the University of Tuebingen.
The last professor of mathematics at the Brno German Technical University, Werner von Koppenfels (1904-1945), was appointed in 1941, during World War II. Koppenfels studied at the Technical Universities in Dresden and Stuttgart. From 1925 to 1928 he studied at Goettingen University where he was awarded his doctorate. From 1928 to 1937 Koppenfels was an assistant to Professor Prange at the Technical University in Hannover. He habilitated there in 1934. He came to Brno from Wuerzburg University where he was a lecturer for mathematics. Koppenfels died in Russian captivity.
Beside professors of mathematics, a lot of mathematicians worked at the German Technical University in Brno as assistants or lecturers. Most of them were secondary teachers, but there were some well-known people among them.
From 1853 to1959 Anton Winkler (1821-1892) was professor of practical geometry at Brno Technical College. In 1859 he went to Graz Technical University where he was appointed professor of mathematics. In 1863 he was appointed professor of mathematics at Vienna Technical University.
From 1896-1900 Karl Carda (1870-1943) was assistant of mathematics. In 1905 Carda was appointed associated professor at Vienna Technical University and in 1907 full professor at the German Technical University in Prague.
Two famous German mathematicians worked in Brno before World War I.
From 1905 to 1912 Georg Hamel (1877-1954) worked in Brno at the
German Technical University. Hamel studied in Aachen,
Berlin, and Goettingen. In 1901 he finished
his study under Hilbert in Goettingen. He spent one year as an assistant to F. Klein, and then he was an assistant of mechanics at the Technical University in Karlsruhe. In 1905 he was appointed full professor of mechanics at the Brno German Technical University. In 1912 he went to Aachen Technical University. From 1919 Hamel taught at Berlin Technical University and retired in 1949. Hamel's work is devoted to mechanics and mathematics. Hamel's base is one of the most important concepts of functional analysis.
In 1906 Richard von Mises (1883-1953) came to Brno as an assistant of mechanics and he habilitated for mechanics at the Brno German Technical University in 1908. Mises studied at Vienna Technical University and at Vienna University. In 1909 he went to Strassburg University and he taught there applied mathematics until 1918. From 1919 to 1920 he was a professor at Technical University in Dresden and from 1920 to 1933 at Berlin University. In 1933 he emigrated to Turkey where he was professor of Istanbul University. In 1939 he went to USA, and from 1939 to 1953 he worked at Harvard University. In 1913 Mises was the first to give university course on mechanics of powered flight. He contributed greatly to probability theory and statistics. He did scholarly work in philosophy and literature (he was a member of the Vienna Circle of Logical Positivists).
An important person is Johann Radon (1887-1956) who was an assistant to Professor Tietze in the years 1911-1912. Radon then returned to Vienna to Technical University. In 1919 Radon became associate professor at Hamburg University, and in 1922 he was appointed full professor in Greifswald. In 1925 he taught in Erlangen, then from 1928 until 1945 he worked at the University of Breslau. He was appointed to Vienna University in 1947 and he remained there for the rest of his life. Radon applied the calculus of variation to differential geometry which led to its applications in number theory. His best known results involve combining the integration theory of Lebesque and Stieltjes.
Some well-known Czech, German, and Austrian mathematicians also tried to become professors at the German Technical University in Brno. Below, you can see the list of the most outstanding applicants.The list is sorted chronologically. In brackets are given the universities where the applicants were appointed later.
Karl Bobek (U Prag), Gustav Kohn (U Wien), Georg Pick (U Prag), Matyá¹
Lerch (U Freiburg, TU Brno, U Brno), Wilhelm Wirtinger (U Wien), Ludwig
Schlessinger (U Giessen), Hans Hahn (U Greifswald, U Wien), Hermann Rothe
(TU Wien), Wilhelm Blaschke (U Hamburg), Robert Koenig (U Muenster, Jena,
Munich), Roland Weitzenboeck (U Amsterdam), Paul Funk (TU Prag, TU Wien),
Horst Sanden (TU Aachen), Georg Prange (TU Hannover), Maxmilian Krafft
(U Münster), Leopold Vietoris (U Insbruck), Emil Artin (U Hamburg, Princeton),
Helmuth Kneser (U Greifswald, Tübingen), Lothar Collatz (TU Berlin), Franz
Rellich (TU Dresden).