In Trinity College we just have one Department of Pure and Applied Mathematics. Just as Pure Mathematics covers a multitude of areas, such as Algebra, Analysis, Geometry, Topology etc, so Applied Mathematics covers Theoretical Physics, Computing, Numerical Analysis etc. Mathematics has evolved as an abstract subject because of its usefulness as a tool in science and industry. The range of its applications is increasing all the time.
New applications demand new mathematics, which often leads to further applications, and so on.
Theoretical Physics has always been a fertile ground for this interaction. Recently physical considerations have led to speculative results in the geometry of four-dimensional manifolds. It is also true that over time mathematics seems to go through phases of divergence and convergence. In the divergent phase many seemingly independent theories are developed, motivated by particular problems. However, despite the fact that the problems have been totally different it often emerges that there is a unity underlying the mathematical theories that have been developed.