Symmetry and conservation laws: Noether's contribution to physics

A single result of Noether's is widely credited in physics papers as fundamental to the modern way of approaching physics. Two basic ideas are those of symmetry on the one side and the notion of quantities such as energy preserved under flows on the other. While parts of the theory were not new at the time, the 1918 paper of Noether related the two subjects in a beautiful, complete and definitive fashion. After giving some background and an outline of her proof, I will talk a little bit about the importance of symmetry in today's mathematics and physics.