During the 1930's and 1940's, several mathematicians--notably Stiefel, Whitney, Pontrjagin, and Chern--developed the basic ideas of characteristic classes. These cohomology classes of a bundle over a manifold measure how far that bundle is from being a product. The existence of non-zero classes proved the impossibility of certain embeddings of manifolds. While these results were being found, other results connected the characteristic classes to the curvature of the base manifold. Then, Andre Weil systematized that connection via classical invariant theory. His unification led to new developments in topology and geometry.