Scholz, Erhard Weyls search for a difference between ‘physical’ and ‘mathematical’ automorphisms. (English) Zbl 1382.81015 Stud. Hist. Philos. Sci., Part B, Stud. Hist. Philos. Mod. Phys. 61, 57-67 (2018). Summary: During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s [Hermann Weyl, “Similarity and congruence: a chapter in the epistemology of science”, ETH Bibliothek, Hochschularchiv Hs 91a:31 (1948); see also Hermann Weyl, Symmetry. Completed by the text ‘Symmetry and congruence’ from the inheritance and with comments from Domenico Giulini, Erhard Scholz and Klaus Volkert. 3rd edition. (Symmetrie. Ergänzt durch den Text ‘Symmetry and congruence’ aus dem Nachlass und mit Kommentaren von Domenico Giulini, Erhard Scholz und Klaus Volkert.) (German). Heidelberg: Springer Spektrum, vii, 232 p. (2017; Zbl 1349.20001)] he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories. Cited in 2 Documents MSC: 81P05 General and philosophical questions in quantum theory 00A79 Physics 00A30 Philosophy of mathematics 20F29 Representations of groups as automorphism groups of algebraic systems 22F50 Groups as automorphisms of other structures 70S15 Yang-Mills and other gauge theories in mechanics of particles and systems Biographic References: Weyl, Hermann Citations:Zbl 1349.20001 PDFBibTeX XMLCite \textit{E. Scholz}, Stud. Hist. Philos. Sci., Part B, Stud. Hist. Philos. Mod. 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