Of all of the women mathematicians, Emmy Noether is generally the best known. Often described as a loving, intelligent woman, she was impressive by many standards. She was faced with gender issues and political tensions in her lifetime, but her passion for mathematics remained strong.
Amalie `Emmy' Noether was born in Erlangen Germany on March 23, 1882 and was the eldest of four children. Her father, Max Noether, was a professor of Mathematics at the University of Erlangen. Initially her interests were mainly languages, and upon graduation of high school she became eligible to teach French and English at a school for young girls. However, when she was 18 she became interested in mathematics. She was not allowed to enroll at the University at the time, because she was a woman. She was able to audit classes, and she did so for two years at the Universities of Erlangen and Gottingen. She worked closely with Paul Gordon, a friend at the University. Under his supervision, she wrote her doctoral thesis: On Complete Systems of Invariants for Ternary Biquadratic Forms. In 1907 she was granted a doctorate at Erlangen.
After Gordon's retirement, she began to work with the algebraists Ernst Fischer and Erhard Schmidt on the topic of finite relational and integral bases. Around this time she periodically substituted for her father at the University.
Felix Klein and David Hilbert took an interest in her knowledge in the area they were studying, which was one of Einstein's theories. They persuaded her to remain at Gottingen and after a three year battle she was allowed to be officially named to the faculty. There was vast opposition to the idea of a woman professor, so this was a difficult battle.
While she was at Gottingen, Emmy did some notable work in establishing a completely general theory of ideals on an axiomatic basis. Her efforts helped bring ring theory into stronger mathematical prominence. In 1920 she co-authored an impressive paper on differential operators. In 1921 She published Ideal theorie in Ringberiechen which became fundamental to modern algebra. In 1924 B.L. van der Waerden came to Gottingen to work with her. The second part of his book Moderne Algebra largely contains her work.
Later in the decade she began to investigate many aspects of non-commutative algebras. She, H. Hasse and Richard Brauer collaborated on several occasions to investigate properties of non-commutative algebras, the hypercomplex quantities and the theory of class fields, norm rests, and the principal genus theorem. They proved that every simple algebra over an ordinary algebraic number field is cyclic.
She also became known as an extraordinary professor, with students travelling from as far away as Russia to be taught in her stimulating, innovative style. She motivated a great many others with her energy. By 1930 she had clearly made a reputation for herself at Gottingen. She acquired a following at Gottingen known as `Noether's Boys'.
In 1933, under Nazi pressure she, a Jewish, liberal, woman, was released from Gottingen. From there she went on to a visiting professorship at Bryn College in the United States. In the USA, she was in great demand since there were fewer traditional forces to oppose her. This was her first opportunity to work with women colleagues.
By the time of her sudden death in 1935 she had published over 40 papers and had inspired a great many students.
Her colleagues called her ``the most creative abstract algebraist in the world.'' Emmy Noether brought much to the mathematical world with her work in algebra and in the development of axiomatic theory. She also put much life and imagination into her work. Hers was a life passionately devoted to mathematics. Clearly, she was not only a dynamic person, but a brilliant mathematician. To think, so many opposed her solely on the basis of her gender. I cannot help but find myself inspired by her story.
Marni Mishna
mjmishna@undergrad.math.uwaterloo.ca
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