Men have always dominated in the field of mathematical studies, but some women managed to achieve there more success than their male colleagues. One of such outstanding women was Emmy Noether. Amalie Emmy Noether was a Jewish German mathematician and one of the most famous female scholars in the history of mathematics. She made significant contributions to theoretical physics and abstract algebra and established the theories of fields, rings, and algebras and famous Noether’s theorem that demonstrated bindings between conservation laws and symmetry. As Nathan Jacobson said, “Emmy Noether was one of the most influential mathematicians of the century” (Noether 1). The aim of this paper is to describe the life of Emmy Noether and her outstanding mathematical and physical achievements.
Emmy Noether was born on 23 March 1882 in the family of mathematician Max Noether and Ida Amalia Kaufmann. She was the eldest child and had three brothers, Alfred, who got a Ph.D. degree in chemistry but soon died, Fritz, who also became a mathematician, and Gustav, who had a chronic illness and died around forty years old. At first, Emmy planned to teach French and English languages. In 1900, she successfully passed exams for teachers and received a qualification for teaching at a school for girls. However, she changed her mind and decided to continue her education at the University of Erlangen.
Those days, mixed-sex university education was not encouraged. Emmy was one of two female students, and even despite this fact she could visit audit classes only having permission from lecturers. However, this did not prevent her from achieving her purpose. In 1903, Noether successfully passed graduation exams at a Realgymnasium in Nuremberg, and she spent the next winter semester at the University of Göttingen. In 1904, she returned to Erlangen and wrote there her dissertation “On Complete Systems of Invariants for Ternary Biquadratic Forms, 1907” (Dick 14). For the next seven years, Noether had read lectures at the University’s Mathematical Institute for free substituting her father who could not teach due illness.
In 1915, Emmy Noether was invited back to the University of Göttingen. Mathematicians Felix Klein and David Hilbert insisted on recruiting her but faced refusal because women could not become privatdozents. Nevertheless, Noether started to read lectures at the University of Göttingen, and again without any pay. When Einstein published the general theory of relativity, Noether started to apply her invariance works to some of the theory’s complexities. She achieved success establishing the theorem that proved a connection between differential symmetries of physical systems and conservation laws, or Noether’s theorem. Talking about significance of Noether’s theorem, physicists Leon Lederman and Christopher Hill said that it was “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” (Lederman 73), and Ransom Stephens states, “You can make a strong case that her theorem is the backbone on which all of modern physics is built” (Angier). At the end of the First World War, the society experienced social changes and the increase of women’s rights, and Noether got an opportunity to prove her qualification and to take an exam for habilitation. She successfully passed it but continued to be unpaid. Three years later, in 1922, she was advanced to “an untenured professor with limited internal administrative rights and functions” (Dick 188) but started to draw salary only in 1923 when got a position of lecturer in algebra.
Quoting the information from the 1964 World Fair in New York, Dick states, “Emmy’s early work on invariants gave no hint that she would become one of the creators of abstract axiomatic algebra” (Dick 2). Indeed, it is hard to underestimate Noether’s contributions to abstract algebra. She started her researches in 1920 and together with W. Shmeidler published a paper regarding the theory of ideals. One year later, she published another paper dedicated to an analysis of the connection between ascending chain conditions and mathematical ideals. Her works were called revolutionary and mothered such “Noetherian” mathematical objects as Noetherian ring, Noetherian induction, Noetherian group, etc. In 1924, Noether started to work with L. van der Waerden, who had come to Göttingen from the Netherlands. In 1931, he published two-volume book “Moderne Algebra,” and the whole second book was dedicated to Noether’s studies.
In Göttingen, Emmy Noether supervised dozens of doctorate students. She was a brilliant person with an outstanding mind but sometimes could be rude to those who disagreed with her opinion. In spite of this trait of her character, Noether gained a reputation of patient and helpful lecturer and curator. Due to low salaries and parental upbringing, she led a frugal life and, even when started to get more money, saved half of them for her nephew, Gottfried Noether. Emmy was unconcerned about her manners and looks fully concentrating on her mathematical studies and never had lessons plans. Noether used her lectures for students’ discussions and careful thinking about key mathematical issues.
In 1928-1929, Emmy Noether was invited to Moscow State University to work with the Soviet mathematician Pavel Alexandrov and read lectures in algebraic geometry and abstract algebra. She supported the Russian Revolution of 1917 and the Bolsheviks, which became a reason for her problems in Germany as some people started to name her "a Marxist-leaning Jewess" (Alexandrov 106). In 1932, together with Emil Artin, Noether received the Ackermann-Teubner Memorial Award for the Promotion of Mathematical Sciences. It was an official recognition of her mathematical contributions. However, in 1933, when Hitler became the German Reichskanzler and gave birth to the humiliation of Jews, Noether’s physical and mathematical contributions became “unimportant,” and she was forced to leave Germany. Alexandrov tried to help her to get a job in Moscow but failed. Emmy Noether moved to the USA. In 1933, she started to work at Bryn Mawr College and one year later, began to read her lectures at the Institute for Advanced Study in Princeton.
In 1935, Noether developed a tumor in her pelvis. She underwent surgery and started to recover but suddenly felt unconscious. On 14 April 1935, Emmy Noether died from the disease. She was fifty-four years old.
All Noether’s mathematical works could be divided into three “epochs.” During the first one (1908-1919), she concentrated on number fields and algebraic invariants. Those days, she developed Noether’s theorem and worked on the calculus of variations. The second epoch (1920-1926) was marked by contributions to abstract algebra. Noether established the theory of ideals in commutative rings, studied ascending chain conditions, and discovered “Noetherian” mathematical objects. During the third epoch (1927-1935), Emmy Noether published papers about hypercomplex numbers and noncommutative algebras and proved the connection between the representation theory of groups and the theory of ideals and modules. She had never sought for recognition, and some of her studies constituted a part of papers published by other mathematicians and her students.
Amalie Emmy Noether was a widely recognized respected scholar. As Einstein said, “Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began” (Cavna). Her mathematical and physical contributions played an important role in further discoveries and completely changed an opinion about female scholars in the mathematical sphere.
Works Cited
Alexandrov, Pavel Sergeevich. “In Memory of Emmy Noether.” In Brewer, James W., and Martha K. Smith, Emmy Noether: A Tribute to Her Life and Work. New York, NY: Marcel Dekker, 1981. Print.
Angier, Natalie. “The Mighty Mathematician You’ve Never Heard Of.” The New York Times. The New York Times, 26 Mar 2012. Web. Accessed 15 Apr 2016.
Cavna, Michael. “Emmy Noether Google Doodle: Why Einstein called her a ‘creative mathematical genius.’” The Washington Post. The Washington Post, 23 Mar 2015. Web. Accessed 15 Apr 2016.
Dick, Auguste. Emmy Noether 1882-1935. Trans. H. I. Blocher. Boston, MA: Springer Science & Business Media, 2012. Print.
Lederman, Lean M., and Christopher T. Hill. Symmetry and the Beautiful Universe. Amherst, NY: Prometheus Books, 2004. Print.
Noether, Emmy. Collected Papers. Introduction by Nathan Jacobson. Berlin: Springer-Verlag, 1983. Print.
