Colloquium: A Century of Noether's Theorem

In the summer of 1918, Emmy Noether published the theorem that now bears her name, establishing a profound two-way connection between symmetries and conservation laws. The influence of this insight is pervasive in physics; it underlies all of our theories of the fundamental interactions and gives meaning to conservation laws that elevates them beyond useful empirical rules. Noether's papers, lectures, and personal interactions with students and colleagues drove the development of abstract algebra, establishing her in the pantheon of twentieth-century mathematicians. This essay traces her path from Erlangen through G\"ottingen to a brief but happy exile at Bryn Mawr College in Pennsylvania, illustrating the importance of "Noether's Theorem" for the way we think today. The text draws on a colloquium presented at Fermilab on 15 August 2018.