Curtius studied law at Kiel, Strasbourg and Bonn and was awarded a doctorate at Berlin. In 1905, he started practicing law at Duisburg. After 1911, he began working on issues in the field of public policy ("Staatswissenschaften") at Heidelberg. He served in the First World War, finishing at the rank of "Hauptmann" (captain) of the "Landwehr" and "Batterieführer" and was awarded both Iron Crosses. He remained at Heidelberg where he also was a member of the city council ("Stadtverordneter") until 1921. He then worked as a lawyer at the "Kammergericht Berlin". He mainly represented (also as a member of supervisory boards) firms in the steel and coal, potash and railway rolling stock businesses. From 1920 to 1932, he was a member of the Reichstag for the German People's Party (DVP).