In 1873 Kurth became the first person to be awarded the "special doctorate in historical sciences", for a dissertation on Cato the Elder. The same year, he became chair of Medieval History and Belgian History at the University of Liège. One of his students, Henri Pirenne, became a noted historian. Léon-Ernest Halkin considered them the founders of the scientific method of history in Belgium. Kurth modelled his pedagogy on that instituted by the German historian Leopold von Ranke at the University of Berlin. On 7 May 1894 he was elected a member of the Royal Academy of Science, Letters and Fine Arts of Belgium. He was a member of the committee that organised the Exposition de l'art ancien au Pays de Liège for the 1905 International exposition in Liège.