At least since a famous 1960 paper by Wigner, the effectiveness of mathematics in the natural sciences has been the subject of ongoing debate. This paper argues that if we take nature to be consistent, then given that we have complete freedom short of inconsistency in choosing axioms to mathematically model reality, we \emph{should} expect mathematics to potentially be ``unreasonably'' effective in modeling reality. The reason why it actually turns out to be so, however, is attributable to human imagination.\\ As a case study to illustrate this, I present highlights of recent work which attempts to connect the foundations of mathematics to the foundations of quantum mechanics by means of a tentative novel axiom to be added to ZFC set theory. This axiom is meant to formally introduce into mathematics the intuitive distinction between actualities and potentialities by permitting the construction of novel mathematical objects which are in a certain sense incomplete. These objects exhibit quantum-like features, and a theorem directly connects them to the Feynman path integral for the simplest possible case.
Armin Nikkhah Shirazi