In 1934, Hoffmann began his education in Indo-European studies, which he continued until he was called in for military service for Nazi Germany at the start of World War II in 1939. Hoffmann took his leave from the war during 1941, just long enough to receive his doctorate for his unpublished dissertation, titled Die altindoarischen Wörter mit -ṇḍ- besonders im Ṛgveda. Hoffmann was at the Russian front until 1943, after which he joined the Indian Legion (Indische Legion), together with other German Indologists, such as Paul Thieme and Gustav Roth.
After the war
Once World War II had ended in 1945, Hoffmann returned to Munich in Occupied Germany, and was able to continue his academic work in Indo-Iranian studies. In 1951, he qualified as a university lecturer with his habilitation thesis, Der Injunktiv im Veda.
Hoffmann, Karl, Der Injunktiv im Veda: Eine synchronische Funktionsuntersuchung (1967), C. Winter. ISBN3-8253-0681-X
Hoffmann, Karl, Aufsätze zur Indoiranistik (1975, 1976, 1992), Reichert. ISBN3-920153-47-2
Hoffmann, Karl; Narten, J., Der Sasanidische Archetypus: Untersuchungen zu Schreibung und Lautgestalt des Avestischen (1989), Wiesbaden. ISBN3-88226-470-5