He read Galois theory, met the mathematician Emil Artin, and did research under the supervision of Leon Lichtenstein.

[2] He continued his studies at Leipzig for the following year, supported by fellowship from the Notgemeinschaft der Deutschen Wissenschaften, except for a research assistantship at the University of Königsberg in 1929.

In 1930 Kähler joined the Department of Mathematics at the University of Hamburg to work under the direction of Wilhelm Blaschke, writing a habilitation thesis entitled, "About the integrals of algebraic equations".

[5] He reported that his oath to Hitler (as a civil servant) was important to him, and remained an apologist for the Third Reich decades later, in a 1988 interview with Sanford Segal.

He accepted a professorship in 1948 at his alma mater the University of Leipzig, filling a post that had been left open by the death of Paul Koebe in 1945.

Kähler became increasingly unhappy with life in East Germany over the next decade, finally deciding to leave in 1958 to take up a lectureship at Technische Universität Berlin.