The mathematics of the early Polytechnischen Schule (founded 1825) was aligned by the practical needs of the engineers and architects. Therefore Descriptive Geometry was of great importance. The first geometry teacher was Guido Schreiber, a former artillery officer of the “Großherzog von Baden”. His successor Christian Wiener distinguisly represented almost half a century the Geometry at Karlsruhe the University. Schreiber and Wiener became well known as authors of important educational books about Descriptive Geometry.

The first two distinguished teachers holding a mathematic chair were Jacob Lüroth (1868-1880) and Ernst Schröder, (1876-1902). Lüroths main field was geometry, including Differential Geometry and Analysis. Schröder was a pioneer in logics, showing in his book, "Der Operationskreis des Logikkalküls"; (Karlsruhe, 1877) an elegant and axiomatic illustration of Boole logic. However, Schröder became especially known for his bookset; "Algebra der Logik"; (Leipzig, 1890, 1891, 1895), which was, during his time, a standard work of the formal logic. However, at the beginning of the 20's this book was not longer updated.

Beside the chair for Geometry and the two chairs for mathematics there had been one chair of Mechanic and Synthetic Geometry (Theoretic mechanic from 1902 and Mechanic and Applied Mathematic from 1923). The first distinguished holder was Alfred Clebsch (from 1858 to 1863); he came from the Königsberger Schoole of Franz Neumann. He brought from Königsberg many new ideas, among other things the establishment of the mathematic colloquia. From his short but effective time in Karlsruhe appeared the book; "Theorie der Elastizität fester Körper"; (Leipzig, 1862). His successor was Wilhelm Schell, whom stayed over 40 years in Karlsruhe, wrote the first elaborated schoolbook of Mechanic in German language with the title; "Theorie der Bewegung und der Kräfte" (Leipzig, 1870).

During the XIX century the teaching was orientated to the needs of the technical academics (mainly Geometry). This changed by the turn of the century with Friedrich Schur, Adolf Krazer, Paul Stäckel, Rudolf Fueter and Karl Boehm, all of them pure mathematicians. Whose teaching and research field also could have fitted in a non-technical University. For about twenty years Karl Heun, a professor for Theoretic Mechanics, was the only representative at Karlsruhe University for the applied directions. He had a special ability to get younger talents from other Universities as assistants at his Institute. So were Georg Hamel, from 1902 to 1905 and Fritz Noether, the brother of Emmy Noether, from 1909 to 1917.

During the 30’s the presence of Gerhard Haenzel and Kurt von Sanden, both initially were engineers, changed again the research direction of the Department. Haenzel had been assistant professor at the TH Berlin while he became Doctor of Engineer. While teaching as a Professor for Geometry, in 1940 he also became a Doctor in Mathematics by Wilhem Süß at Freiburg University. In 1943 Haenzel received a call to work in Münster. He accepted the position, but he could not follow it since in 1944 he was driven to commit suicide due to denunciation.

By 1923 the chair of Theoretic Mechanics became renamed to "chair of Mechanics and Applied Mathematics"; and assigned to Kurt von Sanden. Von Sanden was deployed as engineer by the Friedrich - Krupp - Germania - dockyard at Kiel. Therefore give lectures on diesel engines regularly at the University. In 1927 he swapped to the chair of Krazer, which got the name "Lehrstuhl für Mathematik und Mathematische Technik". In1936 von Sanden then abandoned the University and went back to his old job at mechanic at dockyard as he was an important expert on submarine building. Theodor Pöschl was assigned in 1928 as chairman for Mechanics. Later, in 1937 he was retired for political reasons, but resumed after the 2nd World War as a chairman.