Amalie Emmy Noether[a] (German: [ˈnøːtɐ]; 23 March 1882 – 14
April 1935) was a Jewish-German mathematician who made important contributions
to abstract algebra and theoretical physics.
She invariably used the name "Emmy Noether" in her life and
publications. She was described by Pavel
Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as
the most important woman in the history of mathematics. As one of the leading mathematicians of her
time, she developed the theories of rings, fields, and algebras. In physics,
Noether's theorem explains the connection between symmetry and conservation
laws.
Noether was born to a Jewish family in the Franconian town
of Erlangen; her father was a mathematician, Max Noether. She originally
planned to teach French and English after passing the required examinations,
but instead studied mathematics at the University of Erlangen, where her father
lectured. After completing her dissertation in 1907 under the supervision of Paul
Gordan, she worked at the Mathematical Institute of Erlangen without pay for
seven years. At the time, women were largely excluded from academic positions.
In 1915, she was invited by David Hilbert and Felix Klein to join the
mathematics department at the University of Göttingen, a world-renowned center
of mathematical research. The philosophical faculty objected, however, and she
spent four years lecturing under Hilbert's name. Her habilitation was approved
in 1919, allowing her to obtain the rank of Privatdozent.
Noether remained a leading member of the Göttingen
mathematics department until 1933; her students were sometimes called the
"Noether boys". In 1924, Dutch mathematician B. L. van der Waerden
joined her circle and soon became the leading expositor of Noether's ideas; her
work was the foundation for the second volume of his influential 1931 textbook,
Moderne Algebra. By the time of her plenary address at the 1932 International
Congress of Mathematicians in Zürich, her algebraic acumen was recognized
around the world. The following year, Germany's Nazi government dismissed Jews
from university positions, and Noether moved to the United States to take up a
position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery
for an ovarian cyst and, despite signs of a recovery, died four days later at
the age of 53.
Noether's mathematical work has been divided into three
"epochs".[5] In the first (1908–1919), she made contributions to the
theories of algebraic invariants and number fields. Her work on differential
invariants in the calculus of variations, Noether's theorem, has been called
"one of the most important mathematical theorems ever proved in guiding
the development of modern physics".[6] In the second epoch (1920–1926),
she began work that "changed the face of [abstract] algebra". In her classic 1921 paper Idealtheorie in
Ringbereichen (Theory of Ideals in Ring Domains) Noether developed the theory
of ideals in commutative rings into a tool with wide-ranging applications. She
made elegant use of the ascending chain condition, and objects satisfying it
are named Noetherian in her honor. In the third epoch (1927–1935), she
published works on noncommutative algebras and hypercomplex numbers and united
the representation theory of groups with the theory of modules and ideals. In
addition to her own publications, Noether was generous with her ideas and is
credited with several lines of research published by other mathematicians, even
in fields far removed from her main work, such as algebraic topology.
Personal life
Emmy's father, Max Noether, was descended from a family of
wholesale traders in Germany. At age 14, he had been paralyzed by polio. He
regained mobility, but one leg remained affected. Largely self-taught, he was
awarded a doctorate from the University of Heidelberg in 1868. After teaching
there for seven years, he took a position in the Bavarian city of Erlangen,
where he met and married Ida Amalia Kaufmann, the daughter of a prosperous
merchant.
Max Noether's mathematical contributions were to algebraic
geometry mainly, following in the footsteps of Alfred Clebsch. His best known
results are the Brill–Noether theorem and the residue, or AF+BG theorem;
several other theorems are associated with him; see Max Noether's theorem.
Emmy Noether was born on 23 March 1882, the first of four
children. Her first name was
"Amalie", after her mother and paternal grandmother, but she began
using her middle name at a young age.
As a girl, Noether was well liked. She did not stand out
academically although she was known for being clever and friendly. She was
near-sighted and talked with a minor lisp during her childhood. A family friend
recounted a story years later about young Noether quickly solving a brain
teaser at a children's party, showing logical acumen at that early age. She was taught to cook and clean, as were
most girls of the time, and she took piano lessons. She pursued none of these
activities with passion, although she loved to dance.
She had three younger brothers: The eldest, Alfred, was born
in 1883, was awarded a doctorate in chemistry from Erlangen in 1909, but died
nine years later. Fritz Noether, born in 1884, is remembered for his academic
accomplishments; after studying in Munich he made a reputation for himself in
applied mathematics. The youngest, Gustav Robert, was born in 1889. Very little
is known about his life; he suffered from chronic illness and died in 1928.
University education
Noether showed early proficiency in French and English. In
the spring of 1900, she took the examination for teachers of these languages
and received an overall score of sehr gut (very good). Her performance
qualified her to teach languages at schools reserved for girls, but she chose
instead to continue her studies at the University of Erlangen.
This was an unconventional decision; two years earlier, the
Academic Senate of the university had declared that allowing mixed-sex
education would "overthrow all academic order". One of only two women in a university of 986
students, Noether was only allowed to audit classes rather than participate
fully, and required the permission of individual professors whose lectures she
wished to attend. Despite these obstacles, on 14 July 1903 she passed the
graduation exam at a Realgymnasium in Nuremberg.
During the 1903–1904 winter semester, she studied at the
University of Göttingen, attending lectures given by astronomer Karl
Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix
Klein, and David Hilbert. Soon thereafter, restrictions on women's
participation in that university were rescinded.
Noether returned to Erlangen. She officially reentered the
university in October 1904, and declared her intention to focus solely on
mathematics. Under the supervision of Paul Gordan she wrote her dissertation,
Über die Bildung des Formensystems der ternären biquadratischen Form (On
Complete Systems of Invariants for Ternary Biquadratic Forms, 1907). Gordan was
a member of the "computational" school of invariant researchers, and
Noether's thesis ended with a list of over 300 explicitly worked out
invariants. This approach to invariants was later superseded by the more
abstract and general approach pioneered by Hilbert. Although it had been well received, Noether later
described her thesis and a number of subsequent similar papers she produced as
"crap".
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