Posthumous Fate

  • Michael Monastyrsky
Part of the Modern Birkhäuser Classics book series (MBC)


While he lived, Riemann’s work did not procure their author the influence he had a right to claim. This is especially true of the works that today are considered perhaps his main contribution to science: the theory of Abelian integrals, Riemann surfaces, and Riemannian geometry. There are many objective and subjective reasons that explain this circumstance. His views on geometry were, of course, completely novel for a wide circle of mathematicians. One must not forget that the very idea of non-Euclidean geometry was accepted only with difficulty, even eliciting wild fury from a majority of philosophers. For example, here is what E.K. Dühring wrote in his essay, “Kritische Geschichte der allgemeinen Prinzipien der Mechanik” (A critical history of the general principles of mechanics), which earned the Benecke Prize in 1872 from the philosophical faculty of Göttingen University:

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which the spatial definitions of the physical universe are based, the concept of a rigid body and of a light ray, are no longer valid on the infinitesimal level.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.


Riemann Surface Trace Formula Automorphic Function Abelian Function Abelian Integral 


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  1. 1.
    Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, June 1868.Google Scholar
  2. 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

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© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Michael Monastyrsky
    • 1
  1. 1.Department of Theoretical PhysicsInsitute for Theoretical and Experimental PhysicsMoscowRussia

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