  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 (ETH, Hs 91a:31) 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.
