In the last talk of this semester we will come back to the origin of global differential geometry. I will introduce Chern's proof of Gauss-Bonnet formula in detail, based on his two papers in the 1940's, and talk about the thoughts hidden in the proof. Chern's work usual integrate topology and differential geometry very well. In fact this proof is the first instance that shows the fiber bundles of a manifold to be indispensable in differential geometry.