This year we hold two important anniversaries
of technical education in Brno - the 150th anniversary of the establishment
of Technical College (later German Technical University), and the 100th
anniversary of the establishment Czech Technical University (now Brno University
of Technology). The aim of this lecture is to approach the staff of the
departments of mathematics at the German Technical University in the years
1849-1945. The teaching of mathematics forms a very important part
of the education of the future engineers, which was true in the past as
well as it is now. We can remind the reader of École Polytechnique,
established in Paris in 1794, where mathematics represented about 16 %
of
teaching. The content and forms of instruction of this subject develop
not only in connection with the development of mathematics as a science,
but also with regard to the needs of the specific branches.
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 the Vienna Polytechnical Institute. Prentner was born in Bross (now in Rumania) in 1823. He studied at the 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 the Prague Technical University, where he habilitated for practical geometry in 1876 and worked as assistant to professor Kořistka. He worked in Brno for only five years (Czuber was rector of the school in school year 1890-1891) and in 1891 went to the 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 the Vienna Technical University in 1894. In 1909 his daughter Bertha got married brother of Franz Ferdinand, successor to Austrian throne.
For only a few months, Oscar Peithner von Lichtenfels
taught mathematics at Brno Technical University. Peithner studied at the
Vienna Technical University and Vienna University. He habilitated at both
schools for mathematics. In May
1891 he went from Brno to the Graz Technical University. Franz Hočevar
(1853-1919) worked in Brno four years, he came to Brno from Insbruck in
1891 and in 1895 he decided to leave Brno and go to the Graz Technical
University.
In 1891 Otto Biermann (1858-1908) was appointed
to the free chair of professor of mathematics. He studied at the 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 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 came to Brno mathematician, which influenced mathematical education at Brno German Technical University along thirty years. Emil Waelsch (1863-1927) 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 the Zurich Technical University. In 1895 Waelsch became associated professor for mathematics at the Technical University of Brno. In 1898 he was appointed full professor. In 1910 he was appointed professor for geometry and he remained in this position for the rest of his life.
In 1902 Ernst Fischer (1875-1954) came to Brno, and became assistant to E. Waelsch. Fischer studied at Vienna under Mertens from 1894. He spent 1899 in Berlin, then studied at Zurich and Goettingen. In 1904 Fischer habilitated for mathematics at the Brno 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. Heinrich Tietze (1880-1964) was appointed professor of mathematics. Tietze was a student at the Technical University in Vienna. He studied also at the universities of Vienna, Munich and Goettingen. In 1908 he habilitated at the Vienna University. Tietze worked in Brno until 1919, and then he went to Erlangen, where he was appointed full professor of mathematics at the university. From 1926 he taught at the university in Munich, 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 an 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 at the Vienna University under Mertens, in the years 1901-1902 at the Goettingen University and in 1905 in Berlin. He worked in Brno until 1925, when he was appointed to the 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 the Vienna University and from 1912 to 1913 he was assistant
at the Brno German Technical
University. In 1920 he habilitated at the Vienna Technical University.
In 1924 Karl Mayr went to the 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 Knesser). From 1923 he was assistant and lecturer at the Marburg
University. He worked in Brno
until 1945, when the school was abolished. Since 1948 to 1950
he was a lecturer at the Braunschweig Technical University. In 1950 he
went to Istanbul, where he was full professor at a university. In 1958
he retired in Brauschweig.
In 1927 Lothar Koschmieder (1890-1974) became full professor. He studied at the universities in Breslau, Freiburg and Goettingen. He received his doctorate in Breslau in 1913. Koschmieder was assistant from 1913 until 1924 to Adolf Knesser at Breslau University and habilitated there in 1919. In 1924 Koschmieder was appointed associated professor at the Breslau University. Before his arrival to Brno he substituted in the Greifswald University. In Brno he was rector of the German Technical University in the years 1939-1940 an he had a major role in transformation of the school under the regency of the German Empire. At the beginning of the year 1940 he went to the Graz Technical University. He worked there until 1946. Then he taught in Argentina (1948-49, University of Tucuman) and Iran (1953-58, Bagdad). From 1958-73 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 the World War II. Koppenfels studied at the Technical Universities in Dresden and Stuttgart. From 1925 to 1928 he studied at the Goettingen University, where he was awarded his doctorate. From 1928 to 1937 Koppenfels was assistant to professor Prange at the Technical University in Hannover. He habilitated there in 1934. He came to Brno from the Wuerzburg University, where he was a lecturer of mathematics. Koppenfels died in Russian captivity.
Beside professors of mathematics there worked at the German Technical University in Brno a lot of mathematicians as assistants or lecturer. Most of them were secondary teachers, these were some well-known people among them.
From 1853-59 Anton Winkler (1821-1892) was
professor of practical geometry in Brno Technical College. In 1859 he went
to Graz Technical University and he was appointed professor of mathematics.
In 1863 he was appointed professor
of mathematics at the Vienna Technical University.
From 1896-1900 Karl Carda (1870-1943) was assistant of mathematics. In 1905 Carda was appointed associated professor at the 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 assistant for mechanics at the Technical University in Karlsruhe. In 1905 he was appointed full professor for mechanics at the Brno German Technical University. In 1912 he went to the Aachen Technical University. From 1919 Hamel taught at the 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 the Vienna Technical
University and at the Vienna University. In 1909 he went to the Strassburg
University and he taught there applied mathematics until 1918. From 1919
to 1920 he was professor at the Technical University in Dresden and from
1920 to 1933 at the Berlin University. In 1933 he emigrated to Turkey,
where he was professor of the Istanbul University. In 1939 he went to USA
and from 1939 to 1953 he worked at the Harvard University. In 1913 Mises
was the first to give university course on mechanics of powered
flight. He contributed greatly to probability and statistics. He did
scholarly work in philosophy and literature (he was a member of the Vienna
Circle of Logical Positivists).
A 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 the Technical University. In 1919 Radon became
associated professor at Hamburg 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 the 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
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. We can see the list of the most outstanding applicants.The
list is sorted chronologicaly. In parentheses the schools are the universities,
where the applicants were appointed later.
Karl Bobek (U Prag), Gustav Kohn (U Wien), Georg Pick (U Prag), Matyáš
Lerch (U Freiburg, TH Brno, U Brno), Wilhelm Wirtinger (U Wien), Ludwig
Schlessinger (U Giessen), Hans Hahn (U Greifswald, U Wien), Hermann Rothe
(TH Wien), Wilhelm Blaschke (U Hamburg), Robert Koenig (U Muenster,
Jena, Munich), Roland Weitzenboeck (UAmsterdam), Paul Funk (TH Prag, TH
Wien), Horst Sanden (TH Aachen), Georg Prange (TH Hannover), Maxmilian
Krafft (U Muenster), Leopold Vietoris (U Insbruck), Emil Artin (U Hamburg,
Princeton), Helmuth Kneser (U Greifswald, Tuebingen), Lothar Collatz (TH
Berlin), Franz Rellich (TH Dresden).
