Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra and mathematical physics. As one of the leading mathematicians of her time, she developed theories of rings, fields, and algebras. She also proved Noether's first and second theorems, which play a fundamental role in mathematical physics, by explaining the connection between symmetry and conservation laws. in
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–Nuremberg, where her father lectured. After completing her doctorate in 1907 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, David Hilbert and Felix Klein invited her to join the mathematics department at the University of Göttingen, a world-renowned center of mathematical research. The philosophical faculty objected, and she spent four years lecturing under Hilbert's name. Her habilitation was approved in 1919, allowing her to obtain the rank of Privatdozent.
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 worldwide. In 1933, Germany's Nazi government dismissed Jews from university positions, and Noether moved to the United States to take a position at Bryn Mawr College in Pennsylvania. There, she taught graduate and post-doctoral women including Marie Johanna Weiss and Olga Taussky-Todd. At the same time, she lectured and conducted research at the Institute for Advanced Study in Princeton, New Jersey.
Noether's mathematical work has been divided into three "epochs". In the first (1908–1919), she made contributions to the theories of algebraic invariants and number fields. Noether's theorem, a result in differential invariants in the calculus of variations, has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics". In the second epoch (1920–1926), she began work that "changed the face of [abstract] algebra". 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. Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl, and Norbert Wiener as the most important woman in the history of mathematics. Transcribed online at the MacTutor History of Mathematics Archive. Biography Early life
Amalie Emmy Noether was born on 23 March 1882 in Erlangen, Bavaria. She was the first of four children of mathematician Max Noether and Ida Amalia Kaufmann, both from wealthy Jewish merchant families. Her first name was "Amalie", but she began using her middle name at a young age and continued to do so in her adult life and her publications.
In her youth, Noether did not stand out academically, but she was known for being clever and friendly. She was nearsighted and had a minor lisp during her childhood. A family friend recounted a story years later about young Noether quickly solving a brain teaser at a children's party, showing logical acumen at an early age. She was taught to cook and clean, as were most girls of the time, and took piano lessons. She pursued none of these activities with passion, but loved to dance.
Noether had three younger brothers. The eldest, Alfred Noether, was born in 1883 and was awarded a doctorate in chemistry from Erlangen in 1909, but died nine years later. Fritz Noether was born in 1884, studied at the Ludwig-Maximilians-Universität München, and made contributions to applied mathematics. He was likely executed in the Soviet Union in 1941 during the Second World War.. The youngest, Gustav Robert Noether, was born in 1889. Very little is known about his life; he suffered from chronic illness and died in 1928.
Education Noether showed early proficiency in French and English. In 1900, she took the examination for teachers of these languages and received an overall score of sehr gut (very good). Her performance qualified her to teach languages at schools reserved for girls, but she chose instead to continue her studies at the University of Erlangen–Nuremberg, where her father was a professor.
This was an unconventional decision; two years earlier, the Academic Senate of the university had declared that allowing mixed-sex education would "overthrow all academic order". One of just two women in a university of 986 students, Noether was allowed only to audit classes rather than participate fully, and she required the permission of individual professors whose lectures she wished to attend. Despite these obstacles, on 14 July 1903 she passed the graduation exam at a Realgymnasium in Nuremberg.
During the 1903–04 winter semester, Noether studied at the University of Göttingen, attending lectures given by astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert.
In 1903, restrictions on women's full enrollment in Bavarian universities were rescinded. Noether returned to Erlangen and officially reentered the university in October 1904, declaring her intention to focus solely on mathematics. She was one of six women in her year (two auditors) and the only woman in her chosen school. Under the supervision of Paul Gordan, she wrote her dissertation, Über die Bildung des Formensystems der ternären biquadratischen Form (On Complete Systems of Invariants for Ternary Biquadratic Forms), in 1907, graduating summa cum laude that year. Gordan was a member of the "computational" school of invariant researchers, and Noether's thesis ended with a list of over 300 explicitly worked-out invariants. This approach to invariants was later superseded by the more abstract and general approach pioneered by Hilbert. It was well received, but Noether later called her thesis and some subsequent similar papers of hers "crap". All her later work was in a completely different field.
University of Erlangen–Nuremberg From 1908 to 1915, Noether taught at Erlangen's Mathematical Institute without pay, occasionally substituting for her father, Max Noether, when he was too ill to lecture. She joined the Circolo Matematico di Palermo in 1908 and the Deutsche Mathematiker-Vereinigung in 1909. In 1910 and 1911, she published an extension of her thesis work from three variables to n variables.
Gordan retired in 1910, and Noether taught under his successors, Erhard Schmidt and Ernst Fischer, who took over from Schmidt in 1911. According to her colleague Hermann Weyl and her biographer Auguste Dick, Fischer was an important influence on Noether, in particular by introducing her to David Hilbert's work. Noether and Fischer shared lively enjoyment of mathematics and often discussed lectures long after they were over; Noether is known to have sent Fischer postcards continuing her train of mathematical thoughts.
From 1913 to 1916, Noether published several papers extending and applying Hilbert's methods to mathematical objects such as fields of rational functions and the invariants of finite groups. This phase marked Noether's first exposure to abstract algebra, a field to which she made groundbreaking contributions.
In Erlangen, Noether advised two doctoral students: Hans Falckenberg and Fritz Seidelmann, who defended their theses in 1911 and 1916. Despite Noether's significant role, they were both officially under her father's supervision. After completing his doctorate, Falckenberg spent time in Braunschweig and Königsberg before becoming a professor at the University of Giessen. Seidelmann became a professor at the Ludwig-Maximilians-Universität München.
University of Göttingen Habilitation and Noether's theorem In early 1915, Noether was invited to return to the University of Göttingen by Hilbert and Felix Klein. Their effort to recruit her was initially blocked by the philologists and historians among the philosophical faculty, who insisted that women should not become privatdozenten. In a joint department meeting on the matter, one faculty member protested: "What will our soldiers think when they return to the university and find that they are required to learn at the feet of a woman?" Hilbert, who believed Noether's qualifications were the only important issue and that gender was irrelevant, objected with indignation and scolded those protesting her habilitation. His exact words have not been preserved, but his objection is often said to have included the remark that the university was "not a bathhouse". Pavel Alexandrov recalled that faculty members' opposition to Noether was based not just in sexism, but also in their objections to her social-democratic political beliefs and Jewish ancestry.
Noether left for Göttingen in late April; two weeks later her mother died suddenly in Erlangen. She had previously received medical care for an eye condition, but its nature and relation to her death is unknown. Around the same time, Noether's father retired and her brother joined the German Army to serve in World War I. She returned to Erlangen for several weeks, mostly to care for her aging father.
During her first years teaching at Göttingen, she had no official position and was not paid. Her lectures often were advertised under Hilbert's name, with Noether providing "assistance".
Soon after arriving at Göttingen, she demonstrated her capabilities by proving the theorem now known as Noether's theorem, which shows that a conservation law is associated with any differentiable symmetry of a physical system. The paper, Invariante Variationsprobleme, was presented by Felix Klein on 26 July 1918 at a meeting of the Royal Society of Sciences at Göttingen. Noether presumably did not present it herself because she was not a member of the society. In their book Symmetry and the Beautiful Universe, physicists Leon M. Lederman and Christopher T. Hill write that Noether's theorem is "certainly one of the most important mathematical theorems ever proved in guiding the development of modern physics, possibly on a par with the Pythagorean theorem".
When World War I ended, the German Revolution of 1918–19 brought a significant change in social attitudes, including more rights for women. In 1919, the University of Göttingen allowed Noether to proceed with her habilitation (eligibility for tenure). Her oral examination was in May, and she successfully delivered her habilitation lecture in June. Noether became a privatdozent, and that fall delivered the first lectures listed under her name. She was still not paid for her work.