The suppression thesis in Riemann's Habilitationsvortrag

Abstract

In 1854 Riemann presented his Habilitationsvortrag {\it Über die Hypothesen welche der Geometrie zu Grunde liegen} to the Faculty of Philosophy of the University of Göttingen. The lecture does not contain analytical developments and Riemann never explained the reason for this choice. According to Dedekind this choice was done in order to make the lecture understandable to the non-mathematician professors of the Faculty. This is the suppression thesis. Nevertheless, in 1851, three years before, Riemann has presented his Inauguraldissertation {\it Grundlagen für eine allgemeine Theorie der Functionen einer veränderlichen complexen Grösse} to the same professors of the Faculty of Philosophy. The Inauguraldissertation contains many analytical developments but, on that occasion, they were not suppressed. Therefore, the presence of non-mathematician professors is unrelated with the presence or absence of analytical developments in the lectures. The ideas contained in Riemann's Habilitationsvortrag --manifold, line element, curvature-- were so new at the time that there was not even a proper language to express them. Therefore, Riemann was forced to adopt a non-technical expository style. This explanation for the absence of analytical developments in Riemann's Habilitationsvortrag is more credible than the suppression thesis.