Graduate students and
influential lectures
In addition to her mathematical insight, Noether was
respected for her consideration of others. Although she sometimes acted rudely
toward those who disagreed with her, she nevertheless gained a reputation for
constant helpfulness and patient guidance of new students. Her loyalty to
mathematical precision caused one colleague to name her "a severe
critic", but she combined this demand for accuracy with a nurturing
attitude. A colleague later described
her this way:
Completely
unegotistical and free of vanity, she never claimed anything for herself, but
promoted the works of her students above all.
Göttingen
In Göttingen, Noether supervised more than a dozen doctoral
students; her first was Grete Hermann, who defended her dissertation in
February 1925. She later spoke reverently of her
"dissertation-mother". Noether
also supervised Max Deuring, who distinguished himself as an undergraduate and
went on to contribute significantly to the field of arithmetic geometry; Hans
Fitting, remembered for Fitting's theorem and the Fitting lemma; and Zeng
Jiongzhi (also rendered "Chiungtze C. Tsen" in English), who proved
Tsen's theorem. She also worked closely with Wolfgang Krull, who greatly
advanced commutative algebra with his Hauptidealsatz and his dimension theory
for commutative rings.
Her frugal lifestyle at first was due to being denied pay
for her work; however, even after the university began paying her a small
salary in 1923, she continued to live a simple and modest life. She was paid
more generously later in her life, but saved half of her salary to bequeath to
her nephew, Gottfried E. Noether.
Mostly unconcerned about appearance and manners, biographers
suggest she focused on her studies. A distinguished algebraist Olga
Taussky-Todd described a luncheon, during which Noether, wholly engrossed in a
discussion of mathematics, "gesticulated wildly" as she ate and
"spilled her food constantly and wiped it off from her dress, completely
unperturbed". Appearance-conscious
students cringed as she retrieved the handkerchief from her blouse and ignored
the increasing disarray of her hair during a lecture. Two female students once
approached her during a break in a two-hour class to express their concern, but
they were unable to break through the energetic mathematics discussion she was
having with other students.
According to van der Waerden's obituary of Emmy Noether, she
did not follow a lesson plan for her lectures, which frustrated some students.
Instead, she used her lectures as a spontaneous discussion time with her
students, to think through and clarify important problems in mathematics. Some
of her most important results were developed in these lectures, and the lecture
notes of her students formed the basis for several important textbooks, such as
those of van der Waerden and Deuring.
Several of her colleagues attended her lectures, and she
allowed some of her ideas, such as the crossed product (verschränktes Produkt
in German) of associative algebras, to be published by others. Noether was
recorded as having given at least five semester-long courses at Göttingen:
Winter 1924/1925:
Gruppentheorie und hyperkomplexe Zahlen [Group Theory and Hypercomplex Numbers]
Winter 1927/1928:
Hyperkomplexe Grössen und Darstellungstheorie [Hypercomplex Quantities and
Representation Theory]
Summer 1928:
Nichtkommutative Algebra [Noncommutative Algebra]
Summer 1929:
Nichtkommutative Arithmetik [Noncommutative Arithmetic]
Winter 1929/30:
Algebra der hyperkomplexen Grössen [Algebra of Hypercomplex Quantities]
These courses often
preceded major publications on the same subjects.
Noether spoke quickly – reflecting the speed of her
thoughts, many said – and demanded great concentration from her students.
Students who disliked her style often felt alienated. Some pupils felt that she relied too much on
spontaneous discussions. Her most dedicated students, however, relished the
enthusiasm with which she approached mathematics, especially since her lectures
often built on earlier work they had done together.
She developed a close circle of colleagues and students who
thought along similar lines and tended to exclude those who did not.
"Outsiders" who occasionally visited Noether's lectures usually spent
only 30 minutes in the room before leaving in frustration or confusion. A
regular student said of one such instance: "The enemy has been defeated;
he has cleared out."
Noether showed a devotion to her subject and her students
that extended beyond the academic day. Once, when the building was closed for a
state holiday, she gathered the class on the steps outside, led them through
the woods, and lectured at a local coffee house. Later, after she had been dismissed by the
Third Reich, she invited students into her home to discuss their plans for the
future and mathematical concepts.
Moscow
Pavel Alexandrov
In the winter of 1928–1929 Noether accepted an invitation to
Moscow State University, where she continued working with P.S. Alexandrov. In
addition to carrying on with her research, she taught classes in abstract
algebra and algebraic geometry. She worked with the topologists Lev Pontryagin
and Nikolai Chebotaryov, who later praised her contributions to the development
of Galois Theory.
Noether taught at the Moscow State University during the
winter of 1928–1929.
Although politics was not central to her life, Noether took
a keen interest in political matters and, according to Alexandrov, showed
considerable support for the Russian Revolution. She was especially happy to
see Soviet advances in the fields of science and mathematics, which she
considered indicative of new opportunities made possible by the Bolshevik
project. This attitude caused her problems in Germany, culminating in her
eviction from a pension lodging building, after student leaders complained of
living with "a Marxist-leaning Jewess".
Noether planned to return to Moscow, an effort for which she
received support from Alexandrov. After she left Germany in 1933 he tried to
help her gain a chair at Moscow State University through the Soviet Education
Ministry. Although this effort proved unsuccessful, they corresponded
frequently during the 1930s, and in 1935 she made plans for a return to the
Soviet Union. Meanwhile, her brother
Fritz accepted a position at the Research Institute for Mathematics and
Mechanics in Tomsk, in the Siberian Federal District of Russia, after losing
his job in Germany, and was subsequently executed during the Great Purge.
Recognition
In 1932 Emmy Noether and Emil Artin received the
Ackermann–Teubner Memorial Award for their contributions to mathematics. The prize included a monetary reward of 500
Reichsmarks and was seen as a long-overdue official recognition of her
considerable work in the field. Nevertheless, her colleagues expressed
frustration at the fact that she was not elected to the Göttingen Gesellschaft
der Wissenschaften (academy of sciences) and was never promoted to the position
of Ordentlicher Professor (full professor).
Noether's colleagues celebrated her fiftieth birthday in
1932, in typical mathematicians' style. Helmut Hasse dedicated an article to
her in the Mathematische Annalen, wherein he confirmed her suspicion that some
aspects of noncommutative algebra are simpler than those of commutative
algebra, by proving a noncommutative reciprocity law. This pleased her immensely. He also sent her a
mathematical riddle, which he called the "mμν-riddle of syllables".
She solved it immediately, but the riddle has been lost.
In November of the same year, Noether delivered a plenary
address (großer Vortrag) on "Hyper-complex systems in their relations to
commutative algebra and to number theory" at the International Congress of
Mathematicians in Zürich. The congress was attended by 800 people, including
Noether's colleagues Hermann Weyl, Edmund Landau, and Wolfgang Krull. There
were 420 official participants and twenty-one plenary addresses presented.
Apparently, Noether's prominent speaking position was a recognition of the
importance of her contributions to mathematics. The 1932 congress is sometimes
described as the high point of her career.
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