Born on the 23rd of March in 1882 in Bavaria, Germany, Amalie “Emmy” Noether was the daughter of mathematics professor Max Noether. As she was not allowed to study at regular college preparatory schools, she attended a finishing school instead. When she was teaching, she specialized in English and French. However, she became very passionate only about mathematics, which is believed to be the reason why she never married. Nevertheless, she had a lot of friends who were fellow mathematicians and colleagues, among which was Anna Pell Wheeler, who was her closest friend and fellow at Bryn Mawr College. Another dear friend of her was Hermann Weyl, who was also working at the same college. To know more about this mathematics icon, here is a round-up of her accomplishments.
Education
Noether was a graduate from Höhere Töchter Schule in Erlangen, Bavaria, and in 1990, she passed the exams of the State of Bavaria, certifying her to teach English and French at women’s schools. But soon after teaching language, she decided to pursue mathematics, which was considered as a challenging path for women during her time. She took math classes for a couple of years from the University of Erlangen after she obtained permission from the German professors at the institution. After she passed the matriculation exam in Nürnberg in 1903, she then joined the University of Göttingen and attended lectures of some of the leading mathematicians during such time, like David Hilbert, Hermann Minkowski and Felix Klien. Afterwards, she went back to the University of Erlangen to finish her doctorate degree and be awarded Ph. D in Mathematics.
Career in Mathematics
Noether worked at the Mathematical Institute of Erlangen from 1908 to 1915 without pay, but she piloted her research there. Klien and Hilbert invited her to join the University of Göttingen mathematics department in 1915, and though she was criticized by many people for being at this university, she offered lectures to students for 4 years under Hilbert’s name. After she was given the title “Privatdozent”, she was then permitted to give her own lectures in 1919, but was still not receiving any pay for it. But in 1922, Noether finally became an associate professor, including her to the roster of people in the university to receive a menial salary for their service.
Despite her brilliant knowledge and works, Noether was still not given the status of a professor as she was a woman, social democrat and a Jew. From 1928 to 1929, she became a guest lecturer at the University of Moscow. In 1930, she was given the chance to teach at the University of Frankfurt, and in 1932, she gave a lecture at the International Mathematical Congress in Zurich. She became a member of the Göttingen mathematics department until 1933 when the Nazis took over. Because of this, she was not able to continue her profession in Germany, so she moved to the US in 1933 and taught at Pennsylvania’s Bryn Mawr College as a guest professor. Here, she received full salary and was eventually accepted as a regular faculty member. Aside from these, she also taught at the Institute of Advanced Study at Princeton.
Withal her intellectual achievements and recognitions from notable mathematicians, such as Hilbert and Hermann Weyl, Noether did endure years of unfavorable treatment by universities in Germany. Stating his opinion about the Nazis preventing Noether from lecturing, he wrote, “Her courage, her frankness, her unconcern about her own fate, her conciliatory spirit, were, in the midst of all the hatred and meanness, despair and sorrow… a moral solace.” But after Germany, she did soon collected many colleagues and students around her in the US, but then died there just 2 years later at 53 years old.
Contributions in Mathematics
During the year of Noether’s death, which is 1935, Albert Einstein wrote in a letter to the New York Times, stating, “In the judgement of the most competent living mathematicians, Fraulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.” Well, as previously mentioned, she conquered tremendous obstacles to become one of the 18th century’s greatest algebraists.
Noether was primarily known for her beautiful and profound theorems in ring theory, where her most significant achievement runs deep—she was able to change how mathematicians think about their subject. As what her colleague, P.S. Alexandroff, said during a memorial service after her death, “She taught us to think in simple, and thus general, terms… homomorphic image, the group or ring with operators, the ideal… and not in complicated algebraic calculations.” In some way, she opened the door for the discovery of new algebraic patterns, which were previously obscured.
The work of Noether was divided into 3 epochs. The first one was created between 1907-1919, when she devoted her time in the area of algebraic invariant theory, physics and the Galois Theory. This time, she proved 2 theorems that were fundamental for general relativity and elementary particle physics. One of these theorems, which is called Noether’s Theorem, is one of her most significant contributions to the development of modern physics.
As for the second epoch, it was from 1920-1926, when she concentrated on the mathematical rings theory. It was during this time when she developed the conceptual and abstract approach to algebra that resulted in many principles, which unify algebra, logic, topology, geometry and linear algebra. Her works became a breakthrough in abstract algebra, where her study on chain conditions on the ideals of commutative rings was honored by several mathematicians from around the world. Her paper entitled “Theory of Ideals in Ring Domains” (originally “Idealtheorie in Ringbereichen”), which was published 1921, became the foundation for the theory of commutative ring. The Noetherian ideals and Noetherian rings formed part of her mathematical contributions. Her ideas and insights in topology had made a great impact on the field of math.
The third epoch started from 1927 and ended in 1935, where non-commutative algebras, hyper-complex numbers, representation theory and linear transformations became her primary focus in research. In 1932, Noether received the Ackermann-Teubner Memorial Prize in Mathematics.