A Different Breed of Mathematics: Topology

Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects. Tearing, however, is not allowed[1]. Topology can be used to abstract the inherent connectivity of objects while ignoring their detailed form. Put simply, Topology is a mathematical discipline that studies shape and assumes that shape has meaning[2]. While Topology is certainly not new breed, it was restricted to the realms of physics and pure mathematics for a long time and only recently has started gathering applications in machine learning, finance and insurance.