From 1928 to 1936, Schröter studied mathematics, physics, philosophy, and psychology at the Universities of Göttingen, Heidelberg and Frankfurt am Main. Due to family reasons he had to interrupt his studies several times. He then worked in the mathematical logic group at the University of Münster lead by Heinrich Scholz. From April 1, 1939, he was a research assistant at the Department of Philosophy at the University of Münster. On 20 December 1941, he took his examination for promotion of Dr. phil under the logician Heinrich Scholz studying mathematics, logic, and calculus with a thesis titled Ein allgemeiner Kalkülbegriff. On April 1, 1941, he took a leave of absence to join Pers Z S, the Foreign Office civilian cipher bureau, working as a mathematician. However, even during this time he continued to work on problems of basic mathematical research. On 19 March 1943 he presented the application to the Faculty of Philosophy and Natural Sciences, with the publication Axiomatisierung der Fregeschen Aussagenkalküle, to be admitted to his Habilitation. On the basis of the positive opinions of Heinrich Scholz and Adolf Kratzer, the degree of Doctor rerum naturalium habilitatus was awarded to him by certificate of May 22, 1943. On June 9, 1943, the report on the completed Habilitation was given to the Reich Minister. On July 1, 2and 3, 1943, he held a public trial lecture on the topic Der Nutzen der mathematischen Logik für die Mathematik as a prerequisite for a civil service position as a lecturer. On August 18, 1943, he was appointed lecturer with the authorisation to teach "Mathematical Logic and Fundamental Research", all the while still being employed in Berlin as a "scientific assistant worker" at Pers Z S. Karl Schröter remained at the University of Münster from 31 December 1943 until his contract was up on 31 April 1945, when he was taken prisoner by the Counterintelligence Corps. From early May to the September 30, 1945, he appeared before a joint Anglo-American Commission, first in London, then in Marburg, concerning his work at Pers Z S during the war. After completion, he was dismissed in Marburg after the CIC had determined his political attitude. In the winter semester of 1945/46 he was affiliated as a lecturer in Münster. From May 1946 until his appointment to Berlin, Schröter was working at Münster as a substitute for the Review Committee of the Denazification Main Committee at the Westfälische Landesuniversität. In 1948, Karl Schröter was appointed Professor Extraordinarius for mathematical logic at Humboldt University in Berlin. In 1967, he became director of the Institute for pure mathematics of the German Academy of Sciences at Berlin. He was elected corresponding member in 1962 and two years later ordinary member of the German Academy of Sciences at Berlin. In 1955, Schröter together with Günter Asser founded the Zeitschrift für Mathematische Logik und Grundlagen der Mathematik which since 1991 is known as Mathematical Logic Quarterly.
