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Amalie Emmy Noether
(1882 – 1935)

Was a German-born Jewish mathematician who is known mainly for her seminal contributions to abstract algebra. Often described as the most important woman mathematician of all time, she revolutionized the mathematical theories of rings and fields, as well as commutative and noncommutative algebras. In modern theoretical physics, her two Noether's theorems, which explain the connections between symmetry and conservation laws, are essential tools of research.

Born in the Bavarian town of Erlangen to the noted mathematician Max Noether and his wife, Emmy showed intellectual promise at a young age. Although she passed the examinations required to teach French and English, she continued her studies in mathematics at the University of Erlangen, where her father lectured. After completing her dissertation in 1907 under the supervision of Paul Albert Gordan, she worked at the Mathematical Institute without pay for seven years.

In 1915 she was invited by David Hilbert and Felix Klein to join the mathematics department at the University of Göttingen. The Philosophical faculty objected, however, and she spent four years lecturing under Hilbert's name. Her Habilitation process was approved after that time, paving the way for her to obtain the rank of Privatdozent. She spent the next fourteen years gaining respect for her groundbreaking mathematics work, culminating with a major address at the 1932 International Congress of Mathematicians in Zürich, Switzerland. The following year, Germany's Nazi government fired her from Göttingen, and she moved to the United States, where she took a position at Bryn Mawr College in Pennsylvania. In 1935 she underwent surgery for an ovarian cyst and, despite signs of speedy recovery, died four days later at the age of 53.

Most of Noether's mathematical work was focused on algebra, and has been divided into three "epochs". In the first epoch (1908–1919), she made important contributions to invariant theory, most notably her famous Noether's theorem, which has been called "one of the most important mathematical theorems ever proved in guiding the development of modern physics".In the second epoch (1920–1926), Noether studied commutative rings, most notably working out the theory of ideals in such rings. Her paper Idealtheorie in Ringbereichen (1921) is considered a classic of mathematics. In it, she gave the first definition of a commutative ring and used ascending chain conditions to prove an analog of the fundamental theorem of arithmetic. Rings and modules which satisfy the ascending chain condition are called Noetherian in her honor. In the third epoch (1927–1935), she worked on noncommutative algebras and on uniting hypercomplex numbers and the representation theory of groups with the modules and ideals of rings. She is credited with formulating a theory of modules and ideals in rings that satisfy certain finiteness conditions. Her papers Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern (1927), Hyperkomplexe Größen und Darstellungstheorie (1929) and Beweis eines Hauptsatzes in der Theorie der Algebren (1932) are considered milestones of modern abstract algebra. Noether was generous with her ideas, and is credited with several novel lines of research by other mathematicians, even in disparate fields such as algebraic topology.