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Sophia Korvin-Krukovsky, later known as Sonja Kovalevsky, was born into a
family of Russian nobility in Moscow in 1850. When she was seventeen, she
went to St. Petersberg and studied calculus with a teacher of the naval school
there. Barred because of her sex, from pursuing advanced studies in a Russian
university, she contracted a nominal marriage with the sympathetic Vladimir
Kovalevsky (later to become a noted
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paleontologist) to be free of parental
objections to studying abroad. The marriage took place in 1868, and in the
following spring, the pair went to Heidelberg.
At Heidelberg, Kovalevsky attended the mathematics lectures of Leo
Konigsberger (1837-1921)and du Bois-Reymond (1831-1889) and the physics
lectures of Kirchhoff(1824-1887)and Helmholz(1821-1894). Konigsberger had
earlier studied under Karl Weierstrass of the University of Berlin, and his
enthusiastic reports of his mentor instilled in Kovalevsky a desire to study
under the great teacher. She arriver in Berlin in 1870, but found the University
adamant in its exclusion of women students. She accordingly approached
Weierstrass directly, who, upon receiving a strong recommendation from
Konigsberger, accepted her as a private student. Kovalevsky soon became
Weierstrass' favorite pupil, and he repeated his university lectures to her. She
won Weierstrass' admiration and studied under the master for four years
(1870-1874), during which time she not only covered the university course in
mathematics, but also wrote three important papers, one on the theory of
partial differential equations, one on the reduction of Abelian integrals of the
third kind, and one supplemention Laplace's research on the form of Saturn's
rings.
In 1874, Sonja Kovalevsky was awarded, in absentia, the degree of Doctor
of Philosophy by Gottingen University and, because of the outstanding quality
of a submitted paper on partial differential equations, was excused from taking
the oral examination. In 1888, when thirty-eight years old she achieved her
greatest success when the French Academy awarded her the prestigious Prix
Bordin for her memoir "On the Problem of the Rotation of a Solid Body about a
Fixed Point." Of the fifteen papers submitted for the prize. Kovalevsky's was
judged the best;it was considered so exceptional that the prize was raised from
3000 francs to 5000 francs.
From 1884 until her death in 1891, Kovalevsky served as a professor of
higher mathematics at Stockholm University. Her motto was: "Say what you
know, do what you must, come what may."
There is an oft-told story about an early influence, other than her mathematically
inclined father and uncle, that attracted Kovalevsky to mathematics
when she was only a child. It seems that one of the children's rooms of her
home was temporarily papered with sheets of calculus lecture notes dating
from her father's student days. There sheets fascinated her, and she spent
hours trying to decipher them and to put them in proper order.
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Amalie Emmy Noether, one of the most outstanding mathematicians in the
field of abstract algebra, was born in Erlangen, Germany, in 1882. Although she
was born in the late nineteenth century, she did her work in the first half of the
twentieth century. Her father, Max Noether(1844-1921), was a distinguished
mathematician at the University of Erlangen. Max Noether was an algebraist,
as was Paul Gordan (1837-1921) who also was associated with the university
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and was a close friend of the Noether family. It is no wonder that Emmy
Noether, who studied at the University, also became an algebraist.
She wrote
her doctoral thesis, "On Complete Systems of Invariants for Ternary
Biquadratic Forms," under Gordan in 1907. When Gordan retired in 1910, he was
followed one year later by Ernst Fischer (1875-1959), another algebraist with
particular interests in the theory of elimination and the theory of invariants. His
influence on Noether was great, and under his direction, her preoccupation
passed From the algorithmic aspect of Gordan's work to the abstract axiomatic
approach of Hilbert.
After leaving Erlangern Emmy Noether studied at Gottingen, where she
passed her habilitation examination in 1919, after overcoming objections of
some of the faculty who were opposed to women lecturers. "What will our
soldiers think" they queried "when they return to the University and find that
they are expected to learn at the feet of a woman?" David Hilbert was very and
annoyed at the question, and responded, "Meine Herren, I do not see that the
sex of the candidate is an argument against her admission as a Privatdozent.
After all, the Senate is not a bathhouse." In 1922, she became extraordinary
professor at Gottingen a position she held until 1933, when, under the excesses
of the German national revolution, she, as well as many others, was prohibited
from academic participation. She thereupon left Germany to accept a professorship
at Bryn Mawr College in Pennsylvania and to become a member of the
Institute for Advanced Study at Princeton. Her short time in America was
perhaps her happiest and most productive period. She died in 1935, at the age
of fifty-three and at the height of her creative powers.
Although Noether was a poor lecturer and lacked pedagogical skill, she
managed to inspire a surprising number of students who also left marks in the
field of abstract algebra. Her studies on abstract rings and ideal theory have
been particularly important in the development of modern algebra.
In the ceremonies following her death, Emmy Noether received a glowing
tribute from Albert Einstein. Someone once described her as the daughter of
Max Noether. To this Edmund Landau replied: "Max noether was the father
of Emmy Noether. Emmy is the origin of coordinates in the Noether family."
Hermann Weyl characterized her as "warm, like a loaf of bread." A centenary
celebration of Emmy Noether's birth was held at Bryn Mawr College in 1982.
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