Emmy Noether

Emmy Noether

Emmy Noether was an influential German mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Albert Einstein described her as the most important woman in mathematical history. She lived and worked in Germany during the same period that Ramanujan worked in England and India, but whereas Ramanujan’s contributions were in analysis and number theory, hers were in abstract algebra and in the application of algebra to theoretical physics. She revolutionized the theories of rings, fields and algebras. In physics Noether’s theorem explains the fundamental connection between symmetry and conservation laws. The innovative approach to modern abstract algebra of Emmy Noether not only produced major new results, but also inspired highly productive work by students and colleagues who emulated her techniques.

Amalie Emmy Noether to give her the full name was born on March 23, 1882 in Erlangen in Germany. Her father Max Noether was professor of mathematics at the University of Erlangen while her mother Ida Amalia was the daughter of a wealthy Jewish family of Cologne. She was better known as Emmy. She loved to dance and enjoyed music. She attended the Municipal school for the Higher Education of Daughters until she was 18. Emmy Noether showed early proficiency in French and English. In the spring of 1900 she took the examination for teachers of these languages and received an overall score of 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. This was an unconventional decision because as late as 1900, women were not allowed to enroll in Universities in Germany. Professors frequently refused permission for women event to attend their lectures, and only very rarely women allowed taking university examination. The obstacle in a way could not deter her to enroll in a university, she had to get permission of the professors to take an entrance exam -- she did and she passed, after sitting in on mathematics lectures at the University of Erlangen. She was then allowed to audit courses -- first at the University of Erlangen and then the University of Göttingen, neither of which would permit a woman to attend classes for credit. Finally, in 1904, the University of Erlangen decided to permit women to enroll as regular students, and Emmy Noether returned there. She began to focus solely on mathematics. 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). Her dissertation in algebraic math earned her a doctorate summa cum laude in 1908.

Having obtained her doctorate, Noether was well qualified for a position at a university, but the persistent sexiest atmosphere in Germany prevented the brilliant young woman from being able to even apply for a job. This depressed her greatly, but she began helping her father in his research. She also started publishing papers on her own, which were so well received that she was invited to join a number of European Mathematical Societies, including the German Mathematical Association, which had been founded by George Cantor, but still she could not obtain a paying position at a University in Germany. By 1915 Noether was a famous mathematician in her own right and her papers were read with interest throughout the world. They dealt primarily with algebra.

In 1915, Emmy Noether's mentors, Felix Klein and David Hilbert, invited her to join them at the Mathematical Institute in Gottingen, again without compensation. There, she pursued important mathematical work that confirmed key parts of the general theory of relativity. Noether arrived at Gottingen and began her work on invariance in mathematical physics. Meanwhile, Klein rallied to get her appointed a professor at Gottingen, but he had to struggle with the administration until 1919, when his request was finally granted. She became a privatdozent allowing her to teach students and students would pay her directly. In 1922, the University gave her a position as an adjunct professor with a small salary and no tenure or benefits. Soon after arriving at Göttingen, however, 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. 

American physicists Leon M. Lederman and Christopher T. Hill argue in their book Symmetry and the Beautiful Universe 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". Her work went far beyond mathematical physics. She made important contributions to Galois Theory, to many other areas of abstract algebra and to topology. Noether was, in fact the greatest algebraist of her time.

Noether’s groundbreaking work in algebra began in 1920 with a paper on non commutative fields. Her work earned her enough recognition that she was invited as a visiting professor in 1928-1929 at the University of Moscow and in 1930 at the University of Frankfurt. In 1932 Emmy Noether and Emil Artin received the Ackermann Teubner Memorial Award for their contributions to mathematics.  Though she was never able to gain a regular faculty position at Göttingen, she was one of many Jewish faculty members who were purged by the Nazis in 1933.  

In America, the Emergency Committee to Aid Displaced German Scholars obtained for Emmy Noether an offer of a professorship at Bryn Mawr College in America, and they paid, with the Rockefeller Foundation, her first year's salary. The grant was renewed for two more years in 1934. This was the first time that Emmy Noether was paid a full professor's salary and accepted as a full faculty member. In 1934, Noether began lecturing at the Institute for Advanced Study in Princeton upon the invitation of Abraham Flexner and Oswald Veblen. She also worked with and supervised Abraham Albert and Harry Vandiver. Her time in the United States was pleasant, surrounded as she was by supportive colleagues and absorbed in her favorite subjects. 

In April 1935 doctors discovered a tumor in Noether's pelvis. She was admitted to hospital for surgery to remove a uterine tumor. Although the operation was successful but on April 14, she fell unconscious and she developed a high fever resulting to her death.

Weyl said to her funeral – The memory of her work in science and of her personality among her fellows will not soon pass away. She was a great mathematician, the greatest, I firmly believe, her sex has ever produced, and a great woman.