Noether, Emmy, 1882-1935

Emmy Noether was born in Wilhemine Nuremberg, Germany and raised the daughter of mathematician and Professor of Mathematics at the University of Erlangen, Max Noether. At the age of eighteen she decided to pursue a career in mathematics and began auditing her father's classes. In 1907 she received a doctorate in mathematics, which made her the second woman in history to receive a doctorate degree from a German University. Since women were still not allowed to teach at the university level in Germany, after receiving her degree Noether worked at the University of Erlangen for eight years as an unpaid supervisor of doctoral students and as an occasional lecturer.

Noether was then invited to Gottingen University to write and deliver a paper on the General Relativity theory. She was well received by colleagues Felix Kline, David Hilbert and Albert Einstein. In the second year of the First World War there was an attempt to put Noether on the faculty of mathematics at Gottingen University. The attempt was unsuccessful, though David Hilbert, her strongest advocate and close friend, circumvented the institution's rejection of Noether by setting up lecture courses in his name but allowing Noether to teach them. In 1919 Noether started teaching at Gottingen in her own right and in 1922 her position at the University became salaried. In the spring of 1933, with the rise of the Nazi party to power in Germany, Noether, then fifty-one, faced persecution as a woman academic and as an anti-Nazi Jew. She left Germany for the United States and a teaching job at Bryn Mawr College. During the 1934-1935 academic year Noether taught one graduate level course in Algebra in the department of mathematics. Noether died suddenly in 1935 at the Bryn Mawr Hospital. She was cremated and her ashes were buried beneath a memorial stone in the Cloisters of Bryn Mawr College. She was eulogized by colleague Albert Einstein in the New York Times following her death. Noether is today considered the most influential female mathematician of the twentieth century.

Amalie Emmy Noether[a] (US: /ˈnʌtər/, UK: /ˈnɜːtə/; German: [ˈnøːtɐ]; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She discovered Noether's First and Second Theorem, which are fundamental in mathematical physics.[1] She was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history of mathematics.[2][3] As one of the leading mathematicians of her time, she developed some theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.[4]

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 1907[5] 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. In 1915, she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.[5]

Noether remained a leading member of the Göttingen mathematics department until 1933; her students were sometimes called the "Noether boys". In 1924, Dutch mathematician B. L. van der Waerden joined her circle and soon became the leading expositor of Noether's ideas; her work was the foundation for the second volume of his influential 1931 textbook, Moderne Algebra. By the time of her plenary address at the 1932 International Congress of Mathematicians in Zürich, her algebraic acumen was recognized around the world. 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 where she taught, among others, doctoral and post-graduate women including Marie Johanna Weiss, Ruth Stauffer, Grace Shover Quinn and Olga Taussky-Todd. At the same time, she lectured and performed research at the Institute for Advanced Study in Princeton, New Jersey.[5]

Noether's mathematical work has been divided into three "epochs".[6] In the first (1908–1919), she made contributions to the theories of algebraic invariants and number fields. 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".[7] In the second epoch (1920–1926), she began work that "changed the face of [abstract] algebra".[8] In her classic 1921 paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains), Noether developed the theory of ideals in commutative rings into a tool with wide-ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor. In the third epoch (1927–1935), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.