Emmy Noether (nonfiction)

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Emmy Noether.

Amalie Emmy Noether (23 March 1882 – 14 April 1935) was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics.

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's work in abstract algebra and topology was influential in mathematics, while in physics, Noether's theorem has far-ranging consequences for theoretical physics and dynamic systems. She showed an acute propensity for abstract thought, which allowed her to approach problems of mathematics in fresh and original ways.

Noether's mathematical work has been divided into three "epochs":

  • In the first (1908–19), 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".
  • In the second epoch (1920–26), she began work that "changed the face of [abstract] algebra". In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) 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 (1927–35), 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.

Noether was born on March 23, 1882 to a Jewish family in the Franconian town of Erlangen. Her father Max was a mathematician. 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.

On December 13, 1907, Noether received her Ph.D. degree, summa cum laude, from the University of Erlangen, for a dissertation on algebraic invariants directed by Paul Gordan.

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.

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. 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". 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.

In the winter of 1928–29 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.

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.

There is no record of Noether ever marrying or having children.

She had three younger brothers. The eldest, Alfred, was born in 1883, was awarded a doctorate in chemistry from Erlangen in 1909; he died nine years later. Fritz Noether, born in 1884, is remembered for his academic accomplishments: he made a reputation for himself in applied mathematics; he was arrested (1937) during the Great Purge, and shot (1941). The youngest, Gustav Robert, was born in 1889. Very little is known about his life; he suffered from chronic illness and died in 1928.

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 cutting-edge 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.

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.

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