Editing geometries: The geometry volumes in Klein’s encyclopedia

Abstract

In the present article I describe the structure of the volumes on geometry in the Encyclopedia of Mathematical Sciences designed by the German mathematician Felix Klein (1849-1925) and compare it to the one of the Jahrbuch über die Fortschritte der Mathematik. I will argue that some global features, like lack of opposition between synthetic and analytic geometry, were present in the very first volumes of Klein’s encyclopedia, thus foreshadowing similar changes later made in the Jahrbuch. The regular participation of young mathematicians as coauthors allowed for the inclusion of innovative subjects in the Encyclopedia. In addition, changes were made in the structure of this work along its 30 years of continuous publication. Finally, I included some information as to the reception and obsolescence of Klein’s publishing project.