The Noether theorems in context

TL;DR

This paper reviews Emmy Noether's 1918 work on invariance and conservation laws, exploring its historical context, originality, mathematical methods, influence, and lasting significance in physics and mathematics.

Contribution

It provides a comprehensive historical and conceptual analysis of Noether's theorems, highlighting their originality, mathematical techniques, and impact over time.

Findings

Noether's theorems linked symmetries to conservation laws.

Her use of Lie groups was innovative for her time.

The influence of her work extended from 1918 to modern physics and mathematics.

Abstract

I shall sketch the contents of Noether's 1918 article, "Invariante Variationsprobleme", in the context of the debate on the conservation of energy that had arisen from Einstein's general theory of relativity. How original was Noether's "Invariante Variationsprobleme"? how modern were her use of Lie groups and her introduction of generalized vector fields? and how influential was her article? I shall sketch the curious transmission of her results from 1918 to 1970, the history of the later developments of her theory in mathematics and in physics, and the ultimate recognition of the wide applicability of "the Noether theorems".