Emmy Noether's father, Max Noether, was a distinguished mathematician and a professor at Erlangen. In school, she studied German, English, French, arithmetic and was given piano lessons. She loved dancing and intended to become a language teacher. After further study of English and French, in 1900 she became a certificated teacher of English and French in Bavarian girls schools.

However Noether never became a language teacher. Instead she decided to take the difficult route for a woman of that time and study mathematics at a university. Women were only allowed to study at German universities unofficially and each professor had to give permission for his course. Noether obtained permission to sit in on courses at the University of Erlangen from 1900 to 1902, and the University of Göttingen from 1902 to 1903. There she attended lectures by Blumenthal, Hilbert, Klein and Minkowski. In 1904 Noether was permitted to matriculate at Erlangen and in 1907 was granted a doctorate after working under Paul Gordan.

Having completed her doctorate, the normal progression to an academic post would have been the habilitation. However this route was not open to women so Noether remained at Erlangen, helping her father. Noether also worked on her own research. Noether's reputation grew quickly as her publications appeared. In 1908, she was elected to the Circolo Matematico di Palermo, then in 1909 she was invited to become a member of the Deutsche Mathematiker Vereinigung and in the same year she was invited to address the annual meeting of the Society in Salzburg. In 1913 she lectured in Vienna.

In 1915 Hilbert and Klein invited Noether to return to Göttingen. They persuaded her to remain there while they fought a battle to have her officially on the faculty. It was not until 1919 that permission was granted. During this time Hilbert had allowed Noether to lecture by advertising her courses under his own name.

Emmy Noether's first piece of work when she arrived in Göttingen in 1915 is a result in theoretical physics sometimes referred to as Noether's Theorem, which proves a relationship between symmetries in physics and conservation principles. It was her work in the theory of invariants which led to formulations for several concepts of Einstein's general theory of relativity.

After 1919, Noether moved away from invariant theory to work on ideal theory, producing an abstract theory which helped develop ring theory into a major mathematical topic. This paper was of fundamental importance in the development of modern algebra. In this paper she gave the decomposition of ideals into intersections of primary ideals in any commutative ring with ascending chain condition. Lasker (the world chess champion) had already proved this result for polynomial rings.

In 1924, van der Waerden came to Göttingen and spent a year studying with Noether. After returning to Amsterdam, van der Waerden wrote his book Moderne Algebra in two volumes. The major part of the second volume consists of Noether's work. From 1927 on Noether collaborated with Hasse and Brauer in work on non-commutative algebras.

In addition to teaching and research, Noether helped edit Mathematische Annalen. Much of her work appears in papers written by colleagues and students, rather than under her own name.

Further recognition of her outstanding mathematical contributions came with invitations to address the International Mathematical Congress at Bologna in 1928 and again at Zurich in 1932. In 1932 she also received, jointly with Artin, the Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge.

In 1933, her mathematical achievements counted for nothing when the Nazis caused her dismissal from the University of Göttingen because she was Jewish. She accepted a visiting professorship at Bryn Mawr College in the United States, and also lectured at the Institute for Advanced Study, Princeton.