She proved Noether's first and second theorems , which are fundamental in mathematical physics. In physics, Noether's theorem explains the connection between symmetry and conservation laws.
Noether was born to a Jewish family in the Franconian town of Erlangen ; her father was the mathematician Max Noether. She originally planned to teach French and English after passing the required examinations but instead studied mathematics at the University of Erlangen , where her father lectured.
After completing her doctorate in [ 9 ] under the supervision of Paul Gordan , she worked at the Mathematical Institute of Erlangen without pay for seven years. At the time, women were largely excluded from academic positions. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her habilitation was approved in , allowing her to obtain the rank of Privatdozent.
In , Dutch mathematician B. The following year, Germany's Nazi government dismissed Jews from university positions , and Noether moved to the United States to take up a position at Bryn Mawr College in Pennsylvania. Noether's mathematical work has been divided into three " epochs ". Her work on differential invariants in the calculus of variations , Noether's theorem , has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics".
She made elegant use of the ascending chain condition , and objects satisfying it are named Noetherian in her honor. In the third epoch — , she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals.
