[2] Riebesell studied mathematics and natural sciences in Munich, in Berlin, and at the University of Kiel, where he received his doctorate in 1905 under the supervision of Paul Stäckel.
In 1934 he was elected president of the Reichsverband des öffentlich-rechtlichen Versicherung (Reich Association of Public Insurance Companies).
In 19,48 he co-founded the Deutsche Gesellschaft für Versicherungsmathematik (German Society for Actuarial Mathematics) and became its first chairman.
He published, with Rudolf Lencer, the textbook and reference book "Deutsche Versicherungswirtschaft" (6 vols., 1936–39).
[3] During WWI, a thousand copies of Riebesell's booklet Mathematik im Krieg (Mathematics in war) were sent, free of charge, to the front.