Editing Emmy Noether (section)

{{Short description|German mathematician (1882–1935)}}
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{{Infobox scientist
| name              = Emmy Noether
| image             = Emmy Noether (3x4 cropped).jpg
| alt               = Portrait of Emmy Noether in her 20s with her hand resting on a chair
| caption           = Noether {{circa|1900–1910}}
| birth_name        = Amalie Emmy Noether
| birth_date        = {{birth date|1882|03|23|df=y}}
| birth_place       = [[Erlangen]], [[Kingdom of Bavaria|Bavaria]], [[German Empire]]
| death_date        = {{death date and age|1935|04|14|1882|03|23|df=y}}
| death_place       = [[Bryn Mawr, Pennsylvania]], [[United States]]
| nationality       = German
| fields            = [[Mathematics]] and [[physics]]
| workplaces        = {{unbulleted list|[[University of Göttingen]]|[[Bryn Mawr College]]}}
| alma_mater        = [[University of Erlangen–Nuremberg]]
| thesis_title      = {{lang|de|Über die Bildung des Formensystems der ternären biquadratischen Form}} (On Complete Systems of Invariants for Ternary Biquadratic Forms)
| thesis_url        = https://gdz.sub.uni-goettingen.de/id/PPN243919689_0134
| thesis_year       = 1907
| doctoral_advisor  = [[Paul Gordan]]
| doctoral_students = {{plainlist|
* [[Max Deuring]]
* [[Hans Fitting]]
* [[Grete Hermann]]
* [[Jacob Levitzki]]
* [[Otto Schilling]]
* [[Chiungtze C. Tsen]]
* [[Werner Weber (mathematician)|Werner Weber]]
* [[Ernst Witt]]
}}
| known_for         = {{unbulleted list|[[Abstract algebra]]|[[Noether's theorem]]|[[Noetherian]]|[[List of things named after Emmy Noether|List of namesakes]]}}
| awards            = [[Ackermann–Teubner Memorial Award]] (1932)
}}
'''Amalie Emmy Noether'''{{refn|group=lower-alpha|name=Rufname|[[Emmy (given name)|Emmy]] is the ''[[German name#Forenames|Rufname]]'', the second of two official given names, intended for daily use. This can be seen in the résumé submitted by Noether to the [[University of Erlangen–Nuremberg]] in 1907.{{sfn|Noether|1983|p=iii}}<ref>{{Cite web|last=Tollmien|first=Cordula|website=physikerinnen.de|title=Emmy Noether (1882–1935) – Lebensläufe|url=http://www.physikerinnen.de/noetherlebenslauf.html|archive-url=https://web.archive.org/web/20070929100418/http://www.physikerinnen.de/noetherlebenslauf.html|archive-date=29 September 2007|access-date=13 April 2024}}</ref> Sometimes ''Emmy'' is mistakenly reported as a short form for ''Amalie'', or misreported as ''Emily''; for example, the latter was used by [[Lee Smolin]] in a letter for [[The Reality Club]].<ref>{{Cite web | url = http://www.edge.org/documents/archive/edge52.html | author-link = Lee Smolin | first = Lee | last = Smolin | website = Edge.org |publisher=[[Edge.org|Edge Foundation, Inc.]] | title = Lee Smolin on 'Special Relativity: Why Cant You Go Faster Than Light?' by W. Daniel Hillis; Hillis Responds| date=21 March 1999 | access-date = 6 March 2012 | archive-url =https://web.archive.org/web/20120730103108/http://www.edge.org/documents/archive/edge52.html | archive-date = 30 July 2012 | url-status = dead |quote=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.}}</ref>}} ({{IPAc-en|US|ˈ|n|ʌ|t|ər|audio=LL-Q1860 (eng)-Naomi Persephone Amethyst (NaomiAmethyst)-Noether.wav}}, {{IPAc-en|UK|ˈ|n|ɜː|t|ə}}; {{IPA|de|ˈnøːtɐ|lang}}; 23 March 1882 – 14 April 1935) was a German [[mathematician]] who made many important contributions to [[abstract algebra]]. She also proved Noether's [[Noether's theorem|first]] and [[Noether's second theorem|second theorems]], which are fundamental in [[mathematical physics]].<ref>{{cite web |first=Emily |last=Conover |author-link=Emily Conover |date=12 June 2018 |title=In her short life, mathematician Emmy Noether changed the face of physics |url=https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math |access-date=2 July 2018 |website=[[Science News]] |url-status=live |archive-url=https://web.archive.org/web/20230326222502/https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math |archive-date=26 March 2023}}</ref> Noether was described by [[Pavel Alexandrov]], [[Albert Einstein]], [[Jean Dieudonné]], [[Hermann Weyl]] and [[Norbert Wiener]] as the most important [[List of women in mathematics|woman in the history of mathematics]].<ref name="einstein">{{cite news |last=Einstein |first=Albert |author-link=Albert Einstein |title=The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician |date=1 May 1935 |url=http://select.nytimes.com/gst/abstract.html?res=F70D1EFC3D58167A93C6A9178ED85F418385F9 |newspaper=[[The New York Times]] |publication-date=4 May 1935 |access-date=13 April 2008 |url-access=subscription}} Transcribed [https://mathshistory.st-andrews.ac.uk/Obituaries/Noether_Emmy_Einstein/ online] at the [[MacTutor History of Mathematics Archive]].</ref>{{sfn|Alexandrov|1981|p=100}}{{sfn|Kimberling|1982}} As one of the leading mathematicians of her time, she developed theories of [[ring (mathematics)|rings]], [[field (mathematics)|fields]], and [[algebra over a field|algebras]]. In physics, [[Noether's theorem]] explains the connection between [[Symmetry (physics)|symmetry]] and [[conservation law]]s.<ref name="neeman_1999">{{citation |last=Ne'eman |first=Yuval |title=The Impact of Emmy Noether's Theorems on XXIst Century Physics |author-link=Yuval Ne'eman}} in {{Harvnb|Teicher|1999|pp=83–101}}.</ref>

Noether was born to a [[Jews|Jewish family]] in the [[Franconia]]n 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–Nuremberg]], where her father lectured. After completing her doctorate in 1907 under the supervision of [[Paul Gordan]], she worked at the Mathematical Institute of Erlangen without pay for seven years.{{sfn|Ogilvie|Harvey|2000|p=949}} 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]]''.{{sfn|Ogilvie|Harvey|2000|p=949}}

Noether remained a leading member of the [[Göttingen]] mathematics department until 1933; her students were sometimes called the "Noether Boys". In 1924, Dutch mathematician [[Bartel Leendert van der Waerden|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 [[Anti-Jewish legislation in pre-war Nazi Germany|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]] and [[Olga Taussky-Todd]]. At the same time, she lectured and performed research at the [[Institute for Advanced Study]] in [[Princeton, New Jersey]].{{sfn|Ogilvie|Harvey|2000|p=949}}

Noether's mathematical work has been divided into three "[[epoch]]s".<ref name=Weyl>{{Harvnb|Weyl|1935}}</ref> In the first (1908–1919), she made contributions to the theories of [[algebraic invariant]]s and [[field (mathematics)|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".{{Sfn |Lederman|Hill|2004|p=73}} In the second epoch (1920–1926), she began work that "changed the face of [abstract] algebra".<ref name="weyl_128"/> In her classic 1921 paper ''Idealtheorie in Ringbereichen'' (''Theory of Ideals in Ring Domains''), Noether developed the theory of [[ideal (ring theory)|ideals]] in [[commutative ring]]s 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 algebra]]s and [[hypercomplex number]]s and united the [[representation theory]] of [[group (mathematics)|groups]] with the theory of [[module (mathematics)|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]].