Applying New Mathematics

Abstract

Here we present our first case study: the introduction of group theory into quantum mechanics in the 1920s and 1930s. It is helpful in this context to distinguish the ‘Weyl’ and ‘Wigner’ programmes, where the former is concerned with using group theory to provide secure foundations for the emerging quantum physics and the latter emphasizes its practical applications. We suggest the application of the mathematics to the physics depended on certain structural ‘bridges’ within the mathematics itself and also that both this mathematics and the physics were in a state of flux. Given those features, we argue that the partial structures approach offers a suitable framework for representing these developments. One can resist Steiner’s claim that the mathematics is doing all the work in these cases, as it is only because of prior idealizing moves on the physics side that the mathematics can be brought into play to begin with.