Pure mathematics can tell you ways long and what direction a path between 2 points are, Topology can tell you whether or not or not there's a path between 2 points. Visibly in native to world theorems in geometry, and results similar to the Gauss–Bonnet theorem and Chern–Weil theory. Sharp distinctions between pure mathematics and topology is drawn, however, as mentioned below. it is also the title of a journal pure mathematics & Topology that covers these topics. The terms are not used fully consistently: symplectic manifolds area unit a boundary case, and coarse pure mathematics is world, not local. Geometry has perpetually been tied closely to mathematical physics via the speculation of differential equations.
Published Date: 2020-08-29; Received Date: 2020-08-10