# Emmy Noether

## Pioneer in Modern Algebra

Noether was born in Erlangen, Germany, into a family of tradesmen on March 23, 1882. Crippled by polio, her father was excused from family business concerns and became a mathematics professor at University of Erlangen. Noether herself followed the usual educational path for women of her time, which culminated in language studies, piano practice, and dancing lessons. But all along she aspired to a more active career.

One of the few professional options for women was teaching children. After passing exams for certification as a teacher of English and French, Noether petitioned to audit math classes at the University of Erlangen. Women were not accepted as students in German universities at that time and could attend lectures only with the permission of individual professors. After several years of visiting classes, Noether and several other women were permitted to enroll at Erlangen in 1904. Noether earned her doctorate in mathematics, summa cum laude, in 1907.

Over the next 25 years, Noether worked at various universities as a privatdozent, a person who had earned the right to teach but was not paid. In 1915 she went to the University of Göttingen where she assisted David Hilbert and Felix Klein in work on general relativity theory. From 1923 to 1933 she finally got a small stipend as a lecturer and official permission to guide doctoral students.

During these lean years Noether developed her theorems in the areas of abstract algebra and physics. Her most famous theorem relates the physical laws of conservation to mathematical properties of symmetry. She generated foundations of the general theory of ideals, beginning in 1921, and vastly expanded the theory of non commutative systems. In the mathematical theory of ideals Noether developed a process of normalization in which all integers of a field are sorted so that any two elements of a class—and no two elements of different classes—are congruent. Her years of collaboration and editorial work with the journal Mathematische Annalen extended understanding of modern mathematics.

When the Nazis seized power in 1933, Noether’s university position was lost as were those of many of her friends and students. She represented all of the things Hitler despised; not only was she a woman but also she was a Jew and a pacifist. In this climate Noether accepted an invitation to go to Bryn Mawr College in Pennsylvania as a guest lecturer. While there she taught young women interested in mathematics and did some research at the Institute for Advanced Study in Princeton, New Jersey, meeting with ALBERT EINSTEIN on a regular basis.

After less than two years in the U.S., Noether died unexpectedly after routine surgery on April 14, 1935.

**Emmy Noether’s Legacy**

Noether’s investigations in abstract algebra proved to be crucial in changing what is known about numbers and their relationship to physical reality. She also helped to provide the necessary mathematical groundwork for the atomic age. Her contributions helped break down biases against women working in mathematics.

During her time in Germany Noether’s presence on university campuses caused many to question whether women could have a place in academic life. Her repeated attempts to enter the University of Erlangen eventually resulted in acceptance of women as students there, but coeducation was not generally accepted in Germany until 1908. Noether’s ideas became known and respected internationally, but she never did secure a position with benefits and pension rights that professors receive.

After World War II a new generation of German scholars recognized the scope and originality of Noether’s work. In 1958 the University of Erlangen sponsored a conference of her distinguished former students and their students to discuss her work, its applications, and its influence on research. In 1960 the city of Erlangen named one of its streets Noetherstrasse and in 1982 dedicated the Emmy Noether Gymnasium, a coeducational high school emphasizing mathematics and science.

In the decades since Noether’s death her technique of normalization evolved as a fundamental tool in commutative algebra. Topology, the study of properties of shapes and figures that remain unchanged as an object is distorted, is another area that advanced by use of Noether’s algebra.

Noether’s contributions to Einstein’s work and the development of nuclear energy are perhaps her most significant legacy. Her theory of symmetry and conservation was crucial to Einstein’s theory of relativity. She helped develop the mathematical bases that support Einstein’s elegant equation E = mc2.

Emmy Noether – 1882-1935