Throughout the whole history of mathematics, the development and most significant contributions to this science were mostly made by the mind and ambitions of men. However, it is impossible to underestimate the role and importance of talented female mathematicians, who earned their glory and managed to change mathematics due to their hard work and ability to consider mathematical problems in a new unique perspective. Emmy Noether was a brilliant scientist, a Professor of Gottingen University, who contributed some significant ideas and discoveries to abstract algebra, commutative algebra and other fields of mathematics.
Noether was born in Germany, in 1882. She started demonstrating her natural endowments to mathematics in school, but in those times women were not allowed to be matriculated to a university, that’s why Noether insisted on becoming a free audit learner in Erlangen University. In 1907, after legalization of the enrollment of women, she became a student of Paul Gordan who assisted her in writing dissertation “On Complete Systems of Invariants for Ternary Biquadratic Forms” for obtaining a doctorate (Olsen, 1974, 142).
After working for some time in Erlangen, she was contacted by David Hilbert and Felix Klein, the Professors of Gottingen University, who were about to start their researches of relativity theory applications and needed some qualified specialist in invariant theory. Working together with Hilbert, Noether was inspired and heavily influenced by his approaches and axiomatic methods in mathematics. The attempts to make the young lady a Privatdozent in Gottingen University failed due to reluctance of the professorate to employ a woman, making Hilbert compare this university to a bath-house (Simon Fraser University).
That is why Noether continued her academic researches until 1922, when she was officially admitted as an associate professor. She worked in Gottingen and in the University of Moscow, where she was extremely appreciated for her efficient teaching styles and effective strategies to stimulate her students for creating their own ideas and own interpretations of known models or concepts in mathematics. Her innovative techniques, determination and passion made a tremendous influence on many Russian mathematicians.
Mainly, the works of Noether were dedicated to the development of algebra, where she created an entire new direction known as abstract algebra. Together with Emil Artin and B. van der Waerden, Noether made a considerable contribution to modern algebra. She introduced such important concepts as «Noetherian module» or «right- and left-Noetherian rings», as well as proved or generalized a number of theorems, including the Lasker–Noether theorem describing primary decomposition of ideals, and so on.
Besides, Noether made a series of theoretical researches related to central simple algebra and algebraic topology. She used Betti numbers for measuring the size of abelian (homology) groups and proved that these numbers are the ranks of such groups. Also, when researching invariant and ideal theories, Noether managed to prove a statement describing the relationship between the continuous symmetry and conservation laws. It is known as Noether’s theorem and is an important fundamental of modern theoretical physics.
In addition to her researching activities, Noether helped and inspired a great deal of other scientists and mathematicians in their scientific work. Her close associate, Hermann Weyl, in his memorial speech expressed the following idea: “…Her significance for algebra cannot be read entirely from her own papers, she had great stimulating power and many of her suggestions took shape only in the works of her pupils and co-workers” (O’Connor and Robertson, 1997). Emmy Noether spent the last years of her life in immigration in the U. S. and died in 1935 after a cancer removal surgery.