Emmy Noether’s First Theorem


S.C. Kavassalis over at The Language of Bad Physics:

Ada Lovelace Day celebrates the life and achievements of women in science and technology through blogging in the name of Ada Byron – Countess of Lovelace, daughter of the romantic poet Lord Byron, analyst, metaphysician, the founder of scientific computing, and The Enchantress of Numbers.

In honour of Ada Lovelace Day, I’ll briefly profile the life of one of the most important women in the history of science and mathematics, born March 23rd, Emmy Noether, her brilliant (first) theorem, and how, perhaps surprisingly, there is still room for debate and discussion on it’s applicability today.

Emmy Noether (March 23rd, 1882 – April 14th, 1935)

“My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously.”

Amalie Emmy Noether was a German born, Jewish mathematician who is known for her fundamental contributions to the study of algebraic structures and considered by many to be the most important woman in the history of mathematics.

Born in Erlangen, the daughter of the noted mathematician Max Noether, Emmy studied mathematics at the University of Erlangen, completing her dissertation in 1907 with Paul Albert Gordan at the Mathematical Institute of Erlangen. In 1915, David Hilbert and Felix Klein invited her to join the mathematics department at the University of Göttingen despite the objections of the philosophical faculty there. Her seven years at the Mathematical Institute of Erlangen were spent unpaid and she had to spend four years lecturing at the University of Göttingen under Hilbert’s name. Despite this, her Habilitation process was approved in 1919 allowing her to obtain the rank of Privatdozent. She remained in Göttingen until 1933 as a leading member of the mathematical community, where her students were sometimes known as the “Noether boys”. Noether’s First Theorem

First proved in 1915 and published in 1918, Emmy Noether’s First Theorem gives a profound connection between continuous symmetries and conservation laws for certain classes of theories. The familiar consequences of Noether’s Theorem are that space translational symmetry gives us conservation of momentum, rotational symmetry gives us conservation of angular momentum, time translational symmetry gives us conservation of energy, etc.