Born on March 23, 1882 in Erlangen, Bavaria (Germany), Emmy Noether was the eldest child of Max Noether and Ida Kaufmann.  Max Noether was a distinguished professor of mathematics at University of Erlangen and Ida was from a wealthy Cologne family.  Her younger siblings were all boys.  Her family was of Jewish descent.

At a young age Emmy studied languages (German, French and English), arithmetic and piano.  As she matured, her interests in languages and mathematics blossomed and she planned to become a teacher of the English and French languages.  Noether pursued this career and took examinations of the Bavarian State, and in 1900, she became a certified teacher of English and French in Bavarian girls schools.

However talented she was in languages, Noether never became a language teacher.  Instead, she pursued mathematics.  Emmy's father, Max, was an algebraist as was Paul Gordan, an associate of Max at the university and a close friend of the Noether family.  Following in their footsteps, Emmy Noether would later become an algebraist as well.

Noether matriculated at the University of Erlangen in 1904 and earned a doctorate in 1907 working under Gordan.  Her thesis, entitled "On Complete Systems of Invariants for Ternary Biquadratric Forms," followed a constructive approach for providing an existence result for the finiteness of invariants in n variables (after the work of Gordan) and listed systems of 331 covariant forms.  Gordan retired in 1910 and was followed by Ernst Fischer who, subsequently exerted major influence over Noether's work in algebra.  Under his direction, Noether's focus transitioned from the algorithmic aspects of Gordan's work to the abstract axiomatic approach of Hilbert.

Emmy Noether's reputation grew as she began to publish more of her work.  In 1908 and 1909 she was both elected to the Circolo Matematico di Palermo and invited to join the Deutsche Mathematiker Vereiningung, respectively.  She was also invited to address the annual meeting of the Society in Salzburg in 1909 and lectured in Vienna in 1913.

In 1915, both Hilbert and Klein struggled to have Noether return to the University of Gottingen.  Because she was a woman, she experienced major tribulation in the course of obtaining her habilitation at the university.  It was not until 1917 that permission was finally granted.  In the meantime, Noether lectured under Hilbert.  Hilbert would advertise Noether's lecture under his own name.  For example, a course given in the winter semester of 1916 appears in the course catalogue as:

"Mathematical Physics Seminar: Professor Hilbert, with the assistance of Dr. E. Noether, Mondays from 4-6, no tuition."

Noether's first significant piece of mathematical work (1915) is a result in theoretical physics and is sometimes referred to as 'Noether's Theorem.'  This theorem proves a relationship between symmetries in physics and conservation principles.  This was a basic result in the general theory of relativity and weas praised by Einstein in a letter to Hilbert.  It was her work in the theory of invariants which led to formulations for several concepts of Einstein's general theory of relativity.  In addition, the work that Noether did in ideal theory produced an abstract theory which was integral in developing ring theory into a major mathematical topic.  Her work, "Idealtheorie in Ringbereichen" (1921) was important to the development of modern algebra.  Noether also did work in non-commutative algebra.

Emmy Noether was one of the most outstanding mathematicians in the field of abstract algebra.  It is reported that Noether was a poor lecturer and lack a foundation of sound pedagogical skill.  Nevertheless, she inspired a surprising number of students who left their marks in the field of abstract algebra.  Throughout her career she worked with many mathematicians such as Emanuel Lasker, Bartel van der Waerden, Helmut Hasse and Richard Brauer.  Twice Noether was invited to address the International Mathematical Congress (1928, 1932).  In 1932 she received the Alfred Ackermann-Teubner Memorial Prize for the Advancement of Mathematical Knowledge.

Amalie Emmy Noether died April 14, 1935 in the Pennsylvania (U.S.A) a respected mathematician who, despite claims as to the matter of gender, made significant contribution to mathematics and science.

Author: Clarence L. Terry

References:
Eves, Howard.  An Introduction to the History of Mathematics. (Sixth edition)  Published by Saunders College (1990), a division of HBJ College Publishers.  Fort Worth, TX. (Pgs. 574, 575).

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