Mathematics: Intuition’s Consistency Check

Abstract

There is a well-noted overlap between mathematics and physics, and in many cases the relevant mathematics was developed without any thought of the eventual physical application. This essay argues that this is not a coincidental mystery, but naturally follows from (1) a self-consistency requirement for physical models, and (2) innate physical intuitions that guide us in the wrong directions, slowing the development of physical models more so than the related mathematics. A detailed example (concerning the flow of time in physical theories) demonstrates key parts of this argument.