98 4. WOMEN MATHEMATICIANShowever, finding work at a university, was formidable. Emmy Noether spent many
years working without salary at the Mathematical Institute in Erlangen. This po-
sition enabled her to look after her father, who had been frail since he contracted
polio at the age of 14. It also allowed her to continue working on mathematical
ideas. For nearly two decades she corresponded with Ernst Fischer (1875-1954,
Gordan's successor in Erlangen), who is best remembered for having discovered
the Riesz-Fischer theorem independently of F. Riesz (1880-1956). By staying in
touch with the mathematical community and giving lectures on her discoveries,
she kept her name before certain influential mathematicians, namely David Hilbert
(1862-1943) and Felix Klein,^16 and in 1915 she was invited to work as a Privat-
dozent in Gottingen. (This was the same rank originally offered to Kovalevskaya
at Stockholm in 1883.) Over the next four years Klein and Hilbert used all their
influence to get her a regular appointment at Gottingen; during part of that time
she lectured for Hilbert in mathematical physics. That work led her to a theorem
in general relativity that was highly praised by both Hilbert and Einstein. Despite
this brilliant work, however, she was not allowed to pass the Habituation needed to
acquire a professorship. Only after the German defeat in World War I, which was
followed by the abdication of the Kaiser and a general spirit of reform in Germany,
was she allowed to "habilitate." Between Sof'ya Kovalevskaya and Emmy Noether
there was a curious kind of symmetry: Kovalevskaya was probably aided in her ef-
forts to become a student in Berlin because many of the students were away at war
at the time. Noether was aided in her efforts to become a professor by an influx of
returning war veterans. She began lecturing in courses offered under the name Dr.
Emmy Noether (without any mention of Hilbert) in the fall of 1919. Through the
efforts of Richard Courant (1888-1972) she was eventually granted a small salary
for her lectures.
In the 1920s she moved into the area of abstract algebra, and it is in this area
that mathematicians know her work best. Noctherian rings became a basic area
of study after her work, which became part of a standard textbook by her student
Bartel Leendert van der Waerden (1903 1996). He later described her influence on
this work (1975, p. 32):
When I came to Gottingen in 1924, a new world opened up be-
fore me. I learned from Emmy Noether that the tools by which
my questions could be handled had already been developed by
Dedekind and Weber, by Hilbert, Lasker, and Macaulay, by Steinitz
and by Emmy Noether herself.
Of all the women we have discussed Emmy Noether was unquestionably the
most talented mathematically. Her work, both in quantity and quality, places her
in the elite of twentieth-century mathematicians, and it was recognized as such
during her lifetime. She became an editor of Mathematische Annalen, one of the
two or three most prestigious journals in the world. She was invited to speak at
the International Congress of Mathematicians in Bologna in 1928 and in Zurich
in 1932, when she shared with Emil Artin (1898-1962) a prestigious prize for the
advancement of mathematical knowledge. This recognition was clear and simple
(^16) Klein wrote to Hilbert, "You know that FVaulein Noether is continually advising me in my
projects and that it is really through her that I have become competent in the subject." (Dick,
1981, p. 31)