Thus the late Göttingen mathematics professor, Riemann, who—with his lack of originality except for Gaussian self-mystification—was also led astray by Herbart’s philosophistry, wrote (in his paper, “On the hypotheses that lie at the foundations of geometry, Göttinger Abhandlungen, Vol. 13,1868): ”But it seems that the empirical concepts on which the spatial definitions of the physical universe are based, the concept of a rigid body and of a light ray, are no longer valid on the infinitesimal level. Thus, it is permissible to think that physical relations in space in the infinitely small do not correspond to the axioms of geometry; and, in fact, this may be assumed if it leads to a simpler explanation of phenomena.” It is not surprising that the somewhat unclearly philosophizing physiological professor of physics, H. Helmholtz, also could not pass up the opportunity to meddle in these investigations. In the article, “On the facts that lie at the foundations of geometry,”1 he commented upon this curious absurdity in a favorable sense.
KeywordsRiemann Surface Trace Formula Automorphic Function Abelian Function Abelian Integral
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- 1.Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, June 1868.Google Scholar
- 2.A critique of many of Dühring’s ideas can be found in Friedrich Engels’, “Anti-Dühring.” For rather comical reasons Dühring’s name (but, of course, not his work) was well-known in the Soviet Union, where every student was required to read Engels’ work.Google Scholar