50 years of Graßmann research: results, unresolved questions and misinterpretations.

Abstract

In the context of the 150th anniversary of Hermann Graßmann's death, the results of 50 years of recent Graßmann research, starting with Lewis's dissertation and his contribution to the Annals of Science, are reflected upon. The unexpected revision initiated by Schubring in 1996 of the research findings on the sources of Graßmann's mathematical creativity, which have been available since Friedrich Engel, is rejected as unfounded. New insights into the introduction of the negative in geometry and the significance of the concept of multiplication for Graßmann are presented. Biographical information about Graßmann's work receives a stronger contextualization, and a simplistic handling of material hermeneutics in the historiography of mathematics is criticized. As shown by the influence of Pestalozzi on mathematics education in Prussia in the first half of the nineteenth century, in the case of Justus and Hermann Graßmann, there are 'causally effective societal factors in the development of mathematics' [Hans Wußing, 'Externalismus - Internalismus', N.T.M., 15 (2007), [284-88]], which were historically intertwined with the inner-mathematical development potentials of their time.