Colloquium: A Century of Noether's Theorem

TL;DR

This paper reviews the historical development and profound impact of Emmy Noether's 1918 theorem, which links symmetries to conservation laws and has shaped modern physics and mathematics.

Contribution

It provides a comprehensive historical overview of Noether's theorem and its influence on physics and algebra, highlighting her role in shaping contemporary scientific thought.

Findings

Noether's theorem established a fundamental link between symmetries and conservation laws.

Her work significantly influenced the development of abstract algebra and theoretical physics.

The theorem remains central to modern physics and mathematics.

Abstract

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.