Abstract
The development of mathematics used in physics is most likely to become concerned with finite elements that are measurable. This means that topology and the computation of topological charges and indices, quantum numbers, and connection to logical switching theory are likely to supplant concerns of geometry, metrics and infinitesimal structure of manifolds. This is examined, with a possible counter direction to this as well with super-Turing machines and second order $\lambda$-calculus. Mathematics and its deeper foundations may share a similar nature with physics in regards to quantum information.
Lawrence B Crowell