Dirac and the dispensability of mathematics

In this paper, I examine the role of the delta function in Dirac's formulation of quantum mechanics (QM), and I discuss, more generally, the role of mathematics in theory construction. It has been argued that mathematical theories play an indispensable role in physics, particularly in QM [Colyvan, M. (2001). The indispensability of mathematics. Oxford University Press: Oxford]. As I argue here, at least in the case of the delta function, Dirac was very clear about its dispensability. I first discuss the significance of the delta function in Dirac's work, and explore the strategy that he devised to overcome its use. I then argue that even if mathematical theories turned out to be indispensable, this wouldn't justify the commitment to the existence of mathematical entities. In fact, even in successful uses of mathematics, such as in Dirac's discovery of antimatter, there's no need to believe in the existence of the corresponding mathematical entities. An interesting picture about the application of mathematics emerges from a careful examination of Dirac's work.