Within the world mathematical community, Emmy Noether is widely regarded as the greatest of all woman mathematicians. She was born in the German university town of Erlangen, where her father, Max Noether, was a professor of mathematics. After receiving the Ph.D. degree from the University of Erlangen under Paul Gordan, Dr. Noether moved to the University of Göttingen, known in those days as the Mecca of Mathematics. There she developed as a world-class algebraist and taught a number of doctoral students who eventually became leading algebraists. Noether came to the United States in 1933, where she taught at Bryn Mawr College near Philadelphia and lectured at the Institute for Advanced Study in Princeton, New Jersey.
Emmy Noether's name is known to many physicists through Noether's Theorem, described by Peter G. Bergmann as a cornerstone of work in general relativity as well as in certain aspects of elementary particles physics. For details, see Brewer and Smith, page 16.
Her name is known to mathematicians largely in connection with the adjective noetherian, which applies in ring theory to properties associated with ascending chains of subrings. Specifics are given in Brewer and Smith, page 18.
It is probably true that most algebraists have never heard of Noether's Theorem in physics and that most physicists have never heard of noetherian rings.
I first became interested in Emmy Noether while struggling with one of her famous ring-theoretic theorems in Zariski and Samuel's book, Commutative Algebra. The professor for the course said something superlative about Noether's proof and then mentioned that noetherian rings were named for a woman. This happened in 1965 at Louisiana State University, where the library owned next to nothing about Emmy Noether. Over the years, that has certainly changed!
In 1965, Emmy Noether's former students and collegues were aging. I wrote to them and obtained valuable information that served as a basis for articles and a chapter of a book. These are included in the following list of publications:
Emmy Noether, Gesammelte Abhandlungen (Collected Publications), edited by Nathan Jacobson, Springer Verlag, New York, 1983.
Auguste Dick, Emmy Noether, 1882-1935, (published in German in 1971), translation by H. I. Blocher, Birkhauser, Boston, 1981.
C. Kimberling, "Emmy Noether," Amer. Math. Monthly 79 (1972) 136-149. This article contains a translation of Russian topologist P. S. Alexandroff's memorial tribute to his friend and colleague, Emmy Noether. The article also tells of the recovery of letters from Noether's estate file, lost in a law office for thirty years, written by R. Dedekind, G. Cantor, G. Frobenius, and H. Weber.
C. Kimberling, "Emmy Noether," in James W. Brewer and Martha K. Smith, editors, Emmy Noether, A Tribute to Her Life and Work, Marcel Dekker, New York, 1981, Chapter 1, pages 1-61.
C. Kimberling, "Emmy Noether, greatest woman mathematician" in Mathematics Teacher 75 (1982) 53-57. This article quotes an interview of Natascha Artin Brunswick, who recalled vivid memories of Emmy Noether from visits in Hamburg. Mrs. Brunswick's first husband, the algebraist, Emil Artin, was one of Emmy Noether's colleagues.
For a longer list of references on Emmy Noether and other women in mathematics and the sciences, see
Louise S. Grinstein and Paul J. Campbell, editors, Women of Mathematics, Greenwood Press, New York, 1987. This book contains a chapter on Emmy Noether written by her nephew, Gottfried E. Noether.
Sharon Bertsch McGrayne, Nobel Prize Women in Science, Their Lives, Struggles and Momentous Discoveries, Carol Publishing Group, New York, 1993. New edition in softback with an additional chapter, 1998.