ABSTRACT
The modern increase in interaction between mathematics and physics began about twenty years ago. This chapter outlines some recent mathematical developments which have been strongly influenced by physics. It includes Elliptic Cohomology, Quantum Cohomology, Mirror Manifolds, Moduli Spaces, Jones-Witten Theory, and Donaldson and Floer Theory. The chapter illustrates how physical insight can suggest new methods, concepts and results in mathematics. It focuses on the developments in Donaldson and Seiberg-Witten theory over the last few years. This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book gives an overview of the interaction between geometry and physics. It first provides a historical survey. The book looks at several areas in mathematics which have benefited recently from interaction with physics. It focuses on a survey of some of the current challenges.
