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During his whole scientific life Hermann Weyl was fascinated by theinterrelation of physical and mathematical theories. From the mid 1920s onwardhe reflected also on the typical difference between the two epistemic fieldsand tried to identify it by comparing their respective automorphism structures.In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the mostdetailed and coherent discussion of his thoughts on this topic. This paperpresents his arguments in the talk and puts it in the context of the laterdevelopment of gauge theories.

Weyl's search for a difference between `physical' and `mathematical' automorphisms