Emmy Noether, hero of symmetry and conservation

The first of two Perimeter Institute public lectures this week. Emmy Noether was a giant of mathematics, whose work tied together two fundamental concepts: conservation laws and symmetries in nature. But who was she, and why does her work still have such impact?

When I gave a public lecture at the Perimeter Institute for Theoretical Physics in April, I mentioned Noether's theorem in an answer to a question, to the delight of my hosts. Unknown to me at the time, Noether is a key figure for the Institute, and the dinner afterwards included members of the Emmy Noether Council. Noether was a mathematician rather than a physicist, but her theorem, which states that for every continuous symmetry in nature, there is a conservation law, is now part of the bedrock of physics.

A "continuous symmetry" of some system means a variable that can be changed to any value without affecting the system. For example the laws of physics don't depend on where you are. There is a continuous symmetry with respect to changes of location. Noether's theorem says that because of this, there must be a conserved quantity.