nLab On the hypotheses which underlie geometry

On the hypotheses which underlie geometry is the title of talk given on June 10, 1854 by Bernhard Riemann before the Göttingen Faculty that included Gauss, Dedekind, and Weber in the audience. Its original German title was Über die Hypothesen, welche der Geometrie zu Grunde liegen.

Now it seems that the empirical notions on which the metric determinations of Space are based, the concept of a solid body and a light ray, lose their validity in the infinitely small; it is therefore quite definitely conceivable that the metric relations of Space in the infinitely small do not conform to the hypotheses of geometry; and in fact, one ought to assume this as soon as it permits a simpler way of explaining phenomena…

References

Translation into English by William Clifford, pdf.