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).