Of Connections and Fields

We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These applications range from magnetic monopoles in electrodynamics to instantons in quantum chromodynamics to the geometric phase of quantum mechanics. The first part of this article is elementary and addressed to a general reader. The second part is somewhat more demanding and is addressed to advanced students of mathematics and physics.