 The first motive–operationalism–is not so higly valued any more today, and for good reasons (see entry on Operationalism). Nevertheless, it was, not only in physics, very strong in and around the 1950s, when axiomatic reformulations of QFT entered the scene. Accordingly, the impact of operationalism must not by overlooked. Already in the 1930s the problem of perturbative infinities (see Supplement “The History of QFT”) as well as the potentially heuristic status of the Lagrangian formulation of QFT stimulated the search for concise and ideally axiomatic reformulations. About a dacade later it became clear that operationalism and mathematical rigour may go hand in hand, because the setting of conventional QFT—where quantum fields are basic, with field values being assigned to points in spacetime—is both mathematically ill-defined and in conflict with the “operational” idea that the core elements of an empirical theory should be observable quantities, which can be measured by means of certain physical operations.