Teaching
University of Erlangen
For the next seven years (1908–1915) she taught at the
University of Erlangen's Mathematical Institute without pay, occasionally
substituting for her father when he was too ill to lecture. In 1910 and 1911
she published an extension of her thesis work from three variables to n
variables.
Gordan retired in the spring of 1910, but continued to teach
occasionally with his successor, Erhard Schmidt, who left shortly afterward for
a position in Breslau. Gordan retired from teaching altogether in 1911 when
Schmidt's successor Ernst Fischer arrived; Gordan died a year later in December
1912.
According to Hermann Weyl, Fischer was an important
influence on Noether, in particular by introducing her to the work of David
Hilbert. From 1913 to 1916 Noether published several papers extending and
applying Hilbert's methods to mathematical objects such as fields of rational
functions and the invariants of finite groups. This phase marks the beginning
of her engagement with abstract algebra, the field of mathematics to which she
would make groundbreaking contributions.
Noether and Fischer shared lively enjoyment of mathematics
and would often discuss lectures long after they were over; Noether is known to
have sent postcards to Fischer continuing her train of mathematical thoughts.
University of
Göttingen
In the spring of 1915, Noether was invited to return to the
University of Göttingen by David Hilbert and Felix Klein. Their effort to
recruit her, however, was blocked by the philologists and historians among the
philosophical faculty: Women, they insisted, should not become privatdozenten.
One faculty member protested: "What will our soldiers think when they
return to the university and find that they are required to learn at the feet
of a woman?" Hilbert responded
with indignation, stating, "I do not see that the sex of the candidate is
an argument against her admission as privatdozent. After all, we are a
university, not a bath house."
In 1915 David Hilbert invited Noether to join the Göttingen
mathematics department, challenging the views of some of his colleagues that a
woman should not be allowed to teach at a university.
Noether left for Göttingen in late April; two weeks later
her mother died suddenly in Erlangen. She had previously received medical care
for an eye condition, but its nature and impact on her death is unknown. At
about the same time Noether's father retired and her brother joined the German
Army to serve in World War I. She returned to Erlangen for several weeks,
mostly to care for her aging father.
During her first years teaching at Göttingen she did not
have an official position and was not paid; her family paid for her room and
board and supported her academic work. Her lectures often were advertised under
Hilbert's name, and Noether would provide "assistance".
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. The paper was
presented by a colleague, F. Klein on 26 July 1918 to a meeting of the Royal
Society of Sciences at Göttingen. Noether presumably did not present it herself
because she was not a member of the society.
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".
The mathematics department at the University of Göttingen
allowed Noether's habilitation in 1919, four years after she had begun
lecturing at the school.
When World War I ended, the German Revolution of 1918–1919
brought a significant change in social attitudes, including more rights for
women. In 1919 the University of Göttingen allowed Noether to proceed with her
habilitation (eligibility for tenure). Her oral examination was held in late
May, and she successfully delivered her habilitation lecture in June 1919.
Three years later she received a letter from Otto Boelitz
[de], the Prussian Minister for Science, Art, and Public Education, in which he
conferred on her the title of nicht beamteter ausserordentlicher Professor (an
untenured professor with limited internal administrative rights and functions).
This was an unpaid "extraordinary" professorship, not the higher
"ordinary" professorship, which was a civil-service position.
Although it recognized the importance of her work, the position still provided
no salary. Noether was not paid for her lectures until she was appointed to the
special position of Lehrbeauftragte für Algebra a year later.
Work in abstract algebra
Although Noether's theorem had a significant effect upon
classical and quantum mechanics, among mathematicians she is best remembered
for her contributions to abstract algebra. In his introduction to Noether's
Collected Papers, Nathan Jacobson wrote that:
The development of
abstract algebra, which is one of the most distinctive innovations of twentieth
century mathematics, is largely due to her – in published papers, in lectures,
and in personal influence on her contemporaries.
She sometimes allowed her colleagues and students to receive
credit for her ideas, helping them develop their careers at the expense of her
own.
Noether's work in algebra began in 1920. In collaboration
with W. Schmeidler, she then published a paper about the theory of ideals in
which they defined left and right ideals in a ring.
The following year she published a paper called Idealtheorie
in Ringbereichen, analyzing ascending chain conditions with regard to
(mathematical) ideals. Noted algebraist Irving Kaplansky called this work
"revolutionary"; the
publication gave rise to the term "Noetherian ring" and the naming of
several other mathematical objects as Noetherian.
In 1924 a young Dutch mathematician, B.L. van der Waerden,
arrived at the University of Göttingen. He immediately began working with
Noether, who provided invaluable methods of abstract conceptualization. Van der
Waerden later said that her originality was "absolute beyond
comparison". In 1931 he published Moderne Algebra, a
central text in the field; its second volume borrowed heavily from Noether's
work. Although Noether did not seek recognition, he included as a note in the
seventh edition "based in part on lectures by E. Artin and E.
Noether".
Van der Waerden's visit was part of a convergence of
mathematicians from all over the world to Göttingen, which became a major hub
of mathematical and physical research. From 1926 to 1930 Russian topologist
Pavel Alexandrov lectured at the university, and he and Noether quickly became
good friends. He began referring to her as der Noether, using the masculine
German article as a term of endearment to show his respect. She tried to
arrange for him to obtain a position at Göttingen as a regular professor, but
was only able to help him secure a scholarship from the Rockefeller
Foundation. They met regularly and enjoyed discussions
about the intersections of algebra and topology. In his 1935 memorial address,
Alexandrov named Emmy Noether "the greatest woman mathematician of all
time".
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