In this talk  we will discuss some topics related  to the interaction of physical and mathematical theories that have led to new points of view and new results in mathematics. The area where this is most evident is that of geometric topology of low dimensional manifolds. I coined the term Physical Mathematics to describe this new and fast growing area of research and used it in the title of my paper in Springer's book Mathematics Unlimited: 2001 and beyond.

We will discuss some recent developments in this area. General reference for this talk is my book Topics in Physical Mathematics, Springer (2010).