Excerpted from a more extensive biography in the UCLA archive, "CONTRIBUTIONS OF 20TH CENTURY WOMEN TO PHYSICS" (CWP)
Copyright © CWP and Regents of the University of California 1995 - 1998. .

Picture of Amalie Emmy Noether
 

Emmy Noether

1882 - 1935



"In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance... Pure mathematics is, in its way, the poetry of logical ideas. ... In this effort toward logical beauty, spiritual formulas are discovered necessary for deeper penetration into the laws of nature."
--- Albert Einstein, in a tribute to Emmy Noether

Noether's work is of paramount importance to physics and the interpretation of fundamental laws in terms of group theory. --- Feza Gursey

Important Contributions

Proved that a physical system described by a Lagrangian invariant with respect to the symmetry transformations of a Lie group has, in the case of a group with a finite (or countably infinite) number of independent, infinitesimal generators, a conservation law for each such generator, and certain `dependencies' in the case of a larger infinite number of generators. The latter case applies, for example, to the general theory of relativity and gives the Bianchi identities. These `dependencies' lead to understanding of energy-momentum conservation in the general theory. Her paper proves both the theorems described above and their converses. These are collectively referred to by physicists as Noether's Theorem.

The key to the relation of symmetry laws to conservation laws is Emmy Noether's celebrated Theorem. ... Before Noether's Theorem the principle of conservation of energy was shrouded in mystery, leading to the obscure physical systems of Mach and Ostwald. Noether's simple and profound mathematical formulation did much to demystify physics. --- Feza Gursey

An historical account of how she came to make this discovery is given in E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws.

End of excerpt from CWP.

Briefly, when she arrived in Goettingen in 1915 to be Hilbert's assistant, she was assigned by Hilbert to work with him and others in his group on Einstein's theory. She did not like the assignment much, and complains in a letter that she had to perform long and difficult calculations for Einstein and "none of us understands what they are good for". However, it was at that time that she discovered her famous theorem, and Hilbert was able to obtain the full, correct equations of General Relativity one week before Einstein, by a different and much more elegant method than Einstein did. Her contribution is aknowledged by Hilbert in his paper and by Einstein in a letter to Hilbert when he referred to Noether's penetrating mathematical thinking.

After 1919, Noether moved away from invariant theory to work on the theory of ideals, and was instrumental in developing ring theory into a major mathematical topic. This work has not found (yet) applications in physics, but pure mathematicians regard it as her most important.