Emmy Noether - Contributions To Mathematics and Physics

Contributions To Mathematics and Physics

First and foremost Noether is remembered by mathematicians as an algebraist and for her work in topology. Physicists appreciate her best for her famous theorem because of its far-ranging consequences for theoretical physics and dynamic systems. She showed an acute propensity for abstract thought, which allowed her to approach problems of mathematics in fresh and original ways. Her friend and colleague Hermann Weyl described her scholarly output in three epochs:

"Emmy Noether’s scientific production fell into three clearly distinct epochs:

(1) the period of relative dependence, 1907–1919;

(2) the investigations grouped around the general theory of ideals 1920–1926;

(3) the study of the non-commutative algebras, their representations by linear transformations, and their application to the study of commutative number fields and their arithmetics." (Weyl 1935)

In the first epoch (1907–19), Noether dealt primarily with differential and algebraic invariants, beginning with her dissertation under Paul Gordan. Her mathematical horizons broadened, and her work became more general and abstract, as she became acquainted with the work of David Hilbert, through close interactions with a successor to Gordan, Ernst Sigismund Fischer. After moving to Göttingen in 1915, she produced her seminal work for physics, the two Noether's theorems.

In the second epoch (1920–26), Noether devoted herself to developing the theory of mathematical rings.

In the third epoch (1927–35), Noether focused on noncommutative algebra, linear transformations, and commutative number fields.