The Emergence of Mathematical Physics at the University of Leipzig
Except for the well-known blossoming of theoretical physics with the group around Werner Heisenberg at the University of Leipzig at the end of the 1920s, the tradition of mathematical physics had been analyzed in only a few aspects, in particular the work
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Abstract Except for the well-known blossoming of theoretical physics with the group around Werner Heisenberg at the University of Leipzig at the end of the 1920s, the tradition of mathematical physics had been analyzed in only a few aspects, in particular the work of Carl Neumann and his contributions to the shaping of mathematical physics in general and the theory of electrodynamics in particular. However, the establishment of mathematical physics and its strong position at the University of Leipzig, with Neumann as its leading figure in the last third of the nineteenth century, formed important preconditions for the later upswing. That process is analyzed in this article, focusing on the work of Neumann. It includes a discussion of his ideas on the structure of a physical theory and the role of mathematics in physics as well as his impact on the interaction of mathematics and physics.
1 Introduction Looking back upon the history of mathematics at the University of Leipzig we can state a long lasting tradition of mathematical physics. Mathematicians like August Ferdinand M¨obius (1790–1868), Carl Neumann (1832–1925), Leon Lichtenstein (1878–1933), Ernst H¨older (1901–1990), Herbert Beckert (1920–2004) and Paul G¨unther (1926–1996) were representatives of this tradition. Gustav Theodor Fechner (1801–1887) and Wilhelm Weber (1804–1891) could also be mentioned. However, the last two were known mostly for experimental results, Fechner for the first experimental confirmation of Ohm’s law by exact
K.-H. Schlote () Universit¨at Hildesheim, Institut f¨ur Mathematik und angewandte Informatik, Germany e-mail: [email protected] E. Barbin and R. Pisano (eds.), The Dialectic Relation Between Physics and Mathematics in the XIXth Century, History of Mechanism and Machine Science 16, DOI 10.1007/978-94-007-5380-8 6, © Springer ScienceCBusiness Media Dordrecht 2013
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measurements (published 1831)1 and Weber for geomagnetic measurements, as well as for constructing and using the first practical long-range galvanic telegraph, in collaboration with Carl Friedrich Gauss (1777–1855). Would it not be more correct to characterize both physicists as experimentalists? Certainly not, since both achieved substantial theoretical work too. This raises such questions as: What does the concept of mathematical physics mean? Can mathematical physics be distinguished from theoretical physics, and what are the differences between the two? It is very hard to answer these questions since the characterization of the concepts varied very much depending on the different times and the persons who gave the characterization. Therefore I will restrict myself to a rough description of mathematical physics at Leipzig that is orientated by the discussion in the second half of the nineteenth century, especially focused on the opinion of C. Neumann: Mathematical physics is understood in general as the mathematical treatment of physical problems and the deductive construction of a physical theory on the basis of existing fundamental pr
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