Emmy Noether

Emmy Noether
Portrait of Emmy Noether in her 20s with her hand resting on a chair
Noether c. 1900–1910
Born
Amalie Emmy Noether

(1882-03-23)23 March 1882
Erlangen, Bavaria, German Empire
Died14 April 1935(1935-04-14) (aged 53)
Bryn Mawr, Pennsylvania, United States
NationalityGerman
Alma materUniversity of Erlangen
Known for
AwardsAckermann–Teubner Memorial Award (1932)
Scientific career
FieldsMathematics and physics
Institutions
ThesisOn Complete Systems of Invariants for Ternary Biquadratic Forms (1907)
Doctoral advisorPaul Gordan
Doctoral students

Amalie Emmy Noether[a] (US: /ˈnʌtər/, UK: /ˈnɜːtə/; German: [ˈnøːtɐ]; 23 March 1882 – 14 April 1935) was a German mathematician who made many important contributions to abstract algebra. She proved Noether's first and second theorems, which are fundamental in mathematical physics.[4] 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.[5][6][7] As one of the leading mathematicians of her time, she developed theories of rings, fields, and algebras. In physics, Noether's theorem explains the connection between symmetry and conservation laws.[8]

Noether was born to a Jewish family in the Franconian town of Erlangen; her father was the 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 doctorate in 1907[9] 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.[9]

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. There, she taught graduate and post-doctoral women including Marie Johanna Weiss, Ruth Stauffer, Grace Shover Quinn, and Olga Taussky-Todd. At the same time, she lectured and performed research at the Institute for Advanced Study in Princeton, New Jersey.[9]

Noether's mathematical work has been divided into three "epochs".[10] 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".[11] In the second epoch (1920–1926), she began work that "changed the face of [abstract] algebra".[12] 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.

  1. ^ Noether 1983, p. iii.
  2. ^ Tollmien, Cordula. "Emmy Noether (1882–1935) – Lebensläufe". physikerinnen.de. Archived from the original on 29 September 2007. Retrieved 13 April 2024.
  3. ^ Smolin, Lee (21 March 1999). "Lee Smolin on 'Special Relativity: Why Cant You Go Faster Than Light?' by W. Daniel Hillis; Hillis Responds". Edge.org. Edge Foundation, Inc. Archived from the original on 30 July 2012. Retrieved 6 March 2012. But I think very few non-experts will have heard either of it or its maker – Emily Noether, a great German mathematician. ... This also requires Emily Noether's insight, that conserved quantities have to do with symmetries of natural law.
  4. ^ Conover, Emily (12 June 2018). "In her short life, mathematician Emmy Noether changed the face of physics". Science News. Archived from the original on 26 March 2023. Retrieved 2 July 2018.
  5. ^ Einstein, Albert (1 May 1935). "The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician". The New York Times (published 4 May 1935). Retrieved 13 April 2008. Transcribed online at the MacTutor History of Mathematics Archive.
  6. ^ Alexandrov 1981, p. 100.
  7. ^ Kimberling 1982.
  8. ^ Ne'eman, Yuval, The Impact of Emmy Noether's Theorems on XXIst Century Physics in Teicher 1999, pp. 83–101.
  9. ^ a b c Ogilvie & Harvey 2000, p. 949.
  10. ^ Weyl 1935
  11. ^ Lederman & Hill 2004, p. 73.
  12. ^ Cite error: The named reference weyl_128 was invoked but never defined (see the help page).


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