„Emmy Noether“: Munur á milli breytinga

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Lína 1:
'''Amalie Emmy Noether'''<ref name="Rufname" group="lower-alpha">[[Emmy (given name)|Emmy]] er ''[[Rufname]]'', þ.e.a.s. millinafn, en það er ætlað til frjálslegri notkunnar en fornafn eða eftirnafn. Cf. til dæmis notaði ferilskráin sem Noether sendi til Erlangen háskóla árið 1907 það (Erlangen University archive, ''Promotionsakt Emmy Noether'' (1907/08, NR. 2988); reproduced in: ''Emmy Noether, Gesammelte Abhandlungen – Collected Papers,'' ed. N. Jacobson 1983; online facsimile at [http://www.physikerinnen.de/noetherlebenslauf.html physikerinnen.de/noetherlebenslauf.html]). Stundum er ''Emmy'' ruglað við styttingu á ''Amalie'', eða "Emily". e.g. {{Citation/CS1-Prufa|url=http://www.edge.org/documents/archive/edge52.html|author-link=Lee Smolin|first=Lee|last=Smolin|work=Edge|title=Special Relativity – Why Can't You Go Faster Than Light?|quote=Emily Noether, a great German mathematician}}</ref> (Borið fram {{IPA|ˈnøːtɐ}} á þýsku; 23 Mars 1882 – 14 Apríl 1935) var þýskur [[Stærðfræði|stærðfræðingur]] sem gerði mikilvæg framlög til [[Hrein algebra|algebru]] og [[eðlisfræði]].<ref>{{cite web|url=https://www.sciencenews.org/article/emmy-noether-theorem-legacy-physics-math|title=Emmy Noether changed the face of physics; Noether linked two important concepts in physics: conservation laws and symmetries|author=Emily Conover|date=12 June 2018|website=[[Sciencenews.org]]|publisher=|access-date=2 July 2018}}</ref> Hún notaði ávallt nafnið "Emmy Noether" bæði í daglegu lífi og í skrifum. Henn var lýst af [[Pavel Alexandrov]], [[Albert Einstein]], [[Jean Dieudonné]], [[Hermann Weyl]] og [[Norbert Wiener]] sem mikilvægustu konu í sögu stærðfræðinnar.<ref name="einstein" /> Sem einn af leiðtogum stærðfræðinga sinnar tíðar, þróaði hún forsendukerfi [[Baugur (stærðfræði)|bauga]] og [[Svið (stærðfræði)|sviða]] en hún átti einnig önnur mikilvæg framlög til [[Hrein algebra|algebru]]. Kenning Noether í [[eðlisfræði]] útskýrir tengingu [[Samhverfa|samhverfna]] og [[Varðveislulögmál|varðveislulögmála]].<ref name="neeman_1999" />
 
Noether fæddist í [[Gyðingar|gyðingafjölskyldu]] í bænum [[Erlangen]] sem er í [[Franconia|Franconian]] héraði [[Þýskaland|Suður-Þýskalands]]; faðir hennar var stærðfræðingur, [[Max Noether]]. Upphaflega ætlaði hún sér að kenna frönsku og ensku eftir að standast þau próf sem til þurfti, henni snerist þó hugur og ákvað að læra stærðfræði í [[Háskóli Erlangen|háskóla Erlangen]] í staðinn, þar sem pabbi hennar var kennari. Eftir að hún lauk lokaritgerð sinni árið 1907 undir handleiðslu [[Paul Gordan]] þá vann hún við Stærðfræðideild Erlangen án launa í 7 ár. Á þeim tíma fengu konur yfirleitt ekki að vinna sem fræðimenn, en árið 1915 var henni boðið af [[David Hilbert]] og [[Felix Klein]] að ganga til liðs við stærðfræðideild [[Háskóli Göttingen|Göttingen Háskóla]], sem var heimsfræg miðstöð stærðfræðirannsókna. Hinsvegar mótmælti heimspekideild háskólans þannig að Noether gaf fyrirlestra undir nafni Hilberts í fjögur ár. Henni var loks leyft að gegna stöðu ''[[Privatdozent]]'' árið 1919 eftir að Hilbert lét þau orð falla að þetta væri háskóli ekki baðhús.<ref>Haft eftir Reyni Axelsyni stærðfræðing við Háskóla Íslands.</ref>
Lína 6:
 
Framlagi Noether til stærðfræðinnar hefur verið skipt í þrjú tímabil,<ref name="Weyl">{{Harvnb|Weyl|1935}}</ref> það fyrsta á árunum 1908-1919, var þegar hún setti fram kenningar um [[algebraísk fastaskilyrði]] og [[Svið (stærðfræði)|talnasvið]]. Setning hennar um óbreytileika deildana í [[Hnikareikningar|hnikareikningum]], [[setning Noether]], hefur verið kölluð "eitt mikilvægasta og áhrifamesta framlag stærðfræðinnar til nútímaeðlisfræði". Næsta tímabil var á árunum 1920-1926, en á þeim tíma breytti hún því sem var kallað abstrakt algebra með því að búa til þau fræði sem eru grunnur fagsins nú til dags. Í klassískri fræðigrein hennar frá 1921, ''Idealtheorie in Ringbereichen'' (''Íðöl yfir bauga'') þróar Noether [[Íðal|íðöl]] í [[Baugur (stærðfræði)|víxlbaugum]] í verkfæri sem nýtast í alskyns samhengjum. Hún notfærði sér [[vaxandi keðjuskilyrði]] svo glæsilega að hlutir sem mæta þeim eru nefndir eftir henni. Þriðja tímabilið var svo á árunum 1927-1935, þá gaf hún út greinar um [[Óvíxlin algebra|óvíxlnar algebrur]] og [[Svið (stærðfræði)|rauntalnasvið]] þar sem hún sameinaði [[Grúpa|útsetningarfræði grúpa]] og fræði [[Íðal|íðala]] og [[Mótull|mótla]]. Þó Noether væri jafn dugleg að gefa út greinar og raun ber vitni þá var hún einnig mjög gjafmild á hugmyndirnar sýnar og er eignaður heiðurinn af mörgum fræðigreinum sem gefnar voru út af öðrum stærðfræðingum þar á meðal í [[Algebraísk grannfræði|algebraískri grannfræði]] sem sótti margt í [[Svipalgebra|svipalgebru]].
 
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== Einkalíf ==
Lína 91 ⟶ 89:
 
Þessir kúrsar komu oft á undan mikilvægum greinum sem hún gaf út um sama efni.
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Noether talaði hratt - eins og hún hugsaði - og krafðist mikillar einbeitingar frá nemendum sínum. Sumum nemendum líkaði illa við þetta sniðmát og leið eins og þeir væru ekki velkomnir. Öðrum fannst hún reiða sig of mikið á hvatvísa umræðu. Uppáhaldsnemendur hennar hinsvegar, elskuðu hvaða hún var áhugasöm og
Lína 218:
For illustration, if a physical system behaves the same, regardless of how it is oriented in space, the physical laws that govern it are rotationally symmetric; from this symmetry, Noether's theorem shows the [[angular momentum]] of the system must be conserved.<ref name="ledhill">{{Harvnb|Lederman|Hill|2004|pp=97–116}}.</ref> The physical system itself need not be symmetric; a jagged asteroid tumbling in space [[Conservation of angular momentum|conserves angular momentum]] despite its asymmetry. Rather, the symmetry of the ''physical laws'' governing the system is responsible for the conservation law. As another example, if a physical experiment has the same outcome at any place and at any time, then its laws are symmetric under continuous translations in space and time; by Noether's theorem, these symmetries account for the [[Conservation law (physics)|conservation laws]] of [[Momentum|linear momentum]] and [[energy]] within this system, respectively.
 
Noether's theorem has become a fundamental tool of modern [[theoretical physics]], both because of the insight it gives into conservation laws, and also, as a practical calculation tool.<ref name="neeman_1999">{{Citation/CS1-Prufa|author-link=Yuval Ne'eman|last=Ne'eman|first=Yuval|title=The Impact of Emmy Noether's Theorems on XXIst Century Physics}} in Teicher (1999){{Harvnb|Teicher|1999|pp=83–101}}.</ref> Her theorem allows researchers to determine the conserved quantities from the observed symmetries of a physical system. Conversely, it facilitates the description of a physical system based on classes of hypothetical physical laws. For illustration, suppose that a new physical phenomenon is discovered. Noether's theorem provides a test for theoretical models of the phenomenon:<blockquote>If the theory has a continuous symmetry, then Noether's theorem guarantees that the theory has a conserved quantity, and for the theory to be correct, this conservation must be observable in experiments.</blockquote>
 
=== Second epoch (1920–1926): Ascending and descending chain conditions ===
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{{quote|When ... she first became acquainted with a systematic construction of combinatorial topology, she immediately observed that it would be worthwhile to study directly the [[group (mathematics)|groups]] of algebraic complexes and cycles of a given polyhedron and the [[subgroup]] of the cycle group consisting of cycles homologous to zero; instead of the usual definition of [[Betti number]]s, she suggested immediately defining the Betti group as the [[quotient group|complementary (quotient) group]] of the group of all cycles by the subgroup of cycles homologous to zero. This observation now seems self-evident. But in those years (1925–1928) this was a completely new point of view.{{Sfn | Dick | 1981|p= 174}}}}
 
Noether's suggestion that topology be studied algebraically was adopted immediately by Hopf, Alexandrov, and others,{{Sfn|Dick|1981|p=174}} and it became a frequent topic of discussion among the mathematicians of Göttingen.<ref name="Hirzebruch">[[Friedrich Hirzebruch|Hirzebruch, Friedrich]]. "Emmy Noether and Topology" in {{Harvnb|Teicher|1999|pp=57–61}}.</ref> Noether observed that her idea of a [[Betti group]] makes the [[Euler characteristic|Euler–Poincaré formula]] simpler to understand, and Hopf's own work on this subject{{Sfn|Hopf|1928}} "bears the imprint of these remarks of Emmy Noether".{{Sfn|Dick|1981|pp=174–75}} Noether mentions her own topology ideas only as an aside in a 1926 publication,{{Sfn|Noether|1926b}} where she cites it as an application of [[group theory]].<ref>{{Citation/CS1-Prufa|last=Hirzebruch|first=Friedrich|title=Emmy Noether and Topology}} in {{Harvnb|Teicher|1999|p=63}}</ref>
 
This algebraic approach to topology was also developed independently in [[Austria]]. In a 1926–1927 course given in [[Vienna]], [[Leopold Vietoris]] defined a [[homology group]], which was developed by [[Walther Mayer]], into an axiomatic definition in 1928.<ref>Hirzebruch, Friedrich, "Emmy Noether and Topology" in {{Harvnb|Teicher|1999|pp=61–63}}.</ref>
Lína 284:
Noether's work continues to be relevant for the development of theoretical physics and mathematics and she is consistently ranked as one of the greatest mathematicians of the twentieth century. In his obituary, fellow algebraist [[Bartel Leendert van der Waerden|BL van der Waerden]] says that her mathematical originality was "absolute beyond comparison",{{Sfn|Dick|1981|p=100}} and Hermann Weyl said that Noether "changed the face of [[Abstract algebra|algebra]] by her work".<ref name="weyl_128">{{Harvnb|Dick|1981|p=128}}</ref> During her lifetime and even until today, Noether has been characterized as the greatest woman mathematician in recorded history by mathematicians{{Sfn|Osen|1974|p=152}}{{Sfn|Alexandrov|1981|p=100}}{{Sfn|James|2002|p=321}} such as [[Pavel Alexandrov]],{{Sfn|Dick|1981|p=154}} [[Hermann Weyl]],{{Sfn|Dick|1981|p=152}} and [[Jean Dieudonné]].<ref name="g_noether_p167">{{Harvnb|Noether|1987|p=167}}.</ref>
 
In a letter to ''[[The New York Times]]'', [[Albert Einstein]] wrote:<ref name="einstein">{{Citation/CS1-Prufa|last=Einstein|first=Albert|title=Professor Einstein Writes in Appreciation of a Fellow-Mathematician|date=1 May 1935|url=http://select.nytimes.com/gst/abstract.html?res=F70D1EFC3D58167A93C6A9178ED85F418385F9|publication-date=5 May 1935|newspaper=[[The New York Times]]|accessdate=13 April 2008}}. Also [http://www-history.mcs.st-andrews.ac.uk/Obits2/Noether_Emmy_Einstein.html online] at the [[MacTutor History of Mathematics archive]].</ref>
{{Quote|In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical [[genius]] thus far produced since the higher education of women began. In the realm of algebra, in which the most gifted mathematicians have been busy for centuries, she discovered methods which have proved of enormous importance in the development of the present-day younger generation of mathematicians.}}
 
Lína 290:
{{quote|Miss Noether is ... the greatest woman mathematician who has ever lived; and the greatest woman scientist of any sort now living, and a scholar at least on the plane of [[Marie Curie|Madame Curie]].}}
 
At an exhibition at the [[1964 World's Fair]] devoted to [[Mathematica: A World of Numbers ... and Beyond|Modern Mathematicians]], Noether was the only woman represented among the notable mathematicians of the modern world.<ref>{{Citation/CS1-Prufa|last=Duchin|first=Moon|authorlink=Moon Duchin|url=http://www.math.lsa.umich.edu/~mduchin/UCD/111/readings/genius.pdf|title=The Sexual Politics of Genius|format=PDF|date=December 2004|publisher=University of Chicago|accessdate=23 March 2011|deadurl=yes|archiveurl=https://web.archive.org/web/20110718033431/http://www.math.lsa.umich.edu/~mduchin/UCD/111/readings/genius.pdf|archivedate=18 July 2011|df=dmy}} (Noether's birthday).</ref>
 
Noether has been honored in several memorials,
 
* The [[Association for Women in Mathematics]] holds a [[Noether Lecture]] to honor women in mathematics every year; in its 2005 pamphlet for the event, the Association characterizes Noether as "one of the great mathematicians of her time, someone who worked and struggled for what she loved and believed in. Her life and work remain a tremendous inspiration".<ref>{{Citation/CS1-Prufa|chapter-url=http://www.awm-math.org/noetherbrochure/Introduction.html|chapter=Introduction|title=Profiles of Women in Mathematics|series=The Emmy Noether Lectures|publisher=[[Association for Women in Mathematics]]|year=2005|accessdate=13 April 2008}}</ref>
* Consistent with her dedication to her students, the [[University of Siegen]] houses its mathematics and physics departments in buildings on ''the Emmy Noether Campus''.<ref>{{Citation/CS1-Prufa|url=http://www.uni-siegen.de/uni/campus/wegweiser/emmy.html|title=Emmy-Noether-Campus|publisher=Universität Siegen|place=[[Germany|DE]]|accessdate=13 April 2008}}</ref>
* The German Research Foundation ([[Deutsche Forschungsgemeinschaft]]) operates the ''Emmy Noether Programme'', providing funding to early-career researchers to rapidly qualify for a leading position in science and research by leading an independent junior research group.<ref>[http://www.dfg.de/en/research_funding/programmes/individual/emmy_noether/index.html "Emmy Noether Programme"]. ''Research Funding''. [[Deutsche Forschungsgemeinschaft]]. n.d. Retrieved on 25 May 2016.</ref>
* A street in her hometown, Erlangen, has been named after Emmy Noether and her father, Max Noether.
Lína 304:
* In 2013, The European Physical Society established the Emmy Noether Distinction for Women in Physics.<ref>{{Cite web|url=https://www.eps.org/page/distinction_prize_en|title=EPS Emmy Noether Distinction for Women in Physics – European Physical Society (EPS)|website=www.eps.org|access-date=2018-09-14}}</ref> Winners have included Dr [[Catalina Curceanu]], Prof [[Sibylle Günter]] and Prof [[Anne L'Huillier]].
 
In fiction, Emmy Nutter, the physics professor in "The God Patent" by [[Ransom Stephens]], is based on Emmy Noether.<ref>{{Citation/CS1-Prufa|url=http://ransomstephens.com/the-god-patent.htm|title=The God Patent|first=Ransom|last=Stephens}}</ref>
 
Farther from home,
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* [[Timeline of women in science]]
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== Notes ==
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{{reflist|20em}}
 
=== Frekari heimildir ===
=== Selected works by Emmy Noether (in German) ===
{{main|List of publications by Emmy Noether}}
 
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|title=Über die Bildung des Formensystems der ternären biquadratischen Form|trans-title=On Complete Systems of Invariants for Ternary Biquadratic Forms|journal=Journal für die Reine und Angewandte Mathematik|volume=134|issue=134|year=1908|pages=23–90 and two tables|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=261200|place=[[Germany|DE]]|language=German|doi=10.1515/crll.1908.134.23|deadurl=yes|archiveurl=https://web.archive.org/web/20130308102907/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=261200|archivedate=8 March 2013|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Rationale Funktionenkörper|trans-title=Rational Function Fields|journal=J. Ber. D. DMV|volume=22|year=1913|pages=316–19|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=244058|place=DE|language=German|deadurl=yes|archiveurl=https://web.archive.org/web/20130308102912/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=244058|archivedate=8 March 2013|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|year=1915|url=http://www.digizeitschriften.de/download/PPN235181684_0077/log12.pdf|title=Der Endlichkeitssatz der Invarianten endlicher Gruppen|trans-title=The Finiteness Theorem for Invariants of Finite Groups|journal=Mathematische Annalen|volume=77|pages=89–92|doi=10.1007/BF01456821|place=DE|language=German}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Gleichungen mit vorgeschriebener Gruppe|trans-title=Equations with Prescribed Group|journal=[[Mathematische Annalen]]|volume=78|year=1918|pages=221–29|doi=10.1007/BF01457099|language=German|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002266733&L=1|deadurl=yes|archiveurl=https://web.archive.org/web/20140903092131/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002266733&L=1|archivedate=3 September 2014|df=dmy-all}}
* {{cite journal|last=Noether|first=Emmy|author-mask=3|year=1918b|title=Invariante Variationsprobleme|trans-title=Invariant Variation Problems|journal=Nachr. D. König. Gesellsch. D. Wiss.|place=Göttingen|volume=918|issue=3|pages=235–57|language=de|translator-first=M.A.|translator-last=Tavel|arxiv=physics/0503066|bibcode=1971TTSP....1..186N|doi=10.1080/00411457108231446}}
* {{cite journal|last=Noether|first=Emmy|author-mask=3|year=1918c|title=Invariante Variationsprobleme|trans-title=Invariant Variation Problems|journal=Nachr. D. König. Gesellsch. D. Wiss.|place=Göttingen|volume=918|pages=235–57|language=de|url=https://web.archive.org/web/20080705175409/http://www.physics.ucla.edu/~cwp/articles/noether.trans/german/emmy235.html|deadurl=yes|archiveurl=https://web.archive.org/web/20140903092131/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002266733&L=1|archivedate=5 July 2008|df=dmy-all}} Original German image with link to Tavel's English translation
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Idealtheorie in Ringbereichen|trans-title=The Theory of Ideals in Ring Domains|format=PDF|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002267829&L=1|year=1921|journal=Mathematische Annalen|volume=83|issue=1|pages=24–66|language=German|doi=10.1007/bf01464225|bibcode=1921MatAn..83...24N|deadurl=yes|archiveurl=https://web.archive.org/web/20140903092135/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002267829&L=1|archivedate=3 September 2014|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|year=1923|title=Zur Theorie der Polynomideale und Resultanten|url=http://www.digizeitschriften.de/download/PPN235181684_0088/log7.pdf|journal=Mathematische Annalen|volume=88|pages=53–79|doi=10.1007/BF01448441|place=DE|language=de}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|year=1923b|title=Eliminationstheorie und allgemeine Idealtheorie|url=http://www.digizeitschriften.de/download/PPN235181684_0090/log25.pdf|journal=Mathematische Annalen|volume=90|pages=229–61|doi=10.1007/BF01455443|issue=3–4|place=Germany|language=de}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|year=1924|title=Eliminationstheorie und Idealtheorie|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248880|journal=Jahresbericht der Deutschen Mathematiker-Vereinigung|volume=33|pages=116–20|place=DE|language=German|deadurl=yes|archiveurl=https://web.archive.org/web/20130308102926/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248880|archivedate=8 March 2013|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Der Endlichkeitsatz der Invarianten endlicher linearer Gruppen der Charakteristik ''p''|trans-title=Proof of the Finiteness of the Invariants of Finite Linear Groups of Characteristic ''p''|journal=Nachr. Ges. Wiss|pages=28–35|year=1926|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=63971|place=DE|language=German|deadurl=yes|archiveurl=https://web.archive.org/web/20130308102929/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=63971|archivedate=8 March 2013|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Ableitung der Elementarteilertheorie aus der Gruppentheorie|trans-title=Derivation of the Theory of Elementary Divisor from Group Theory|journal=Jahresbericht der Deutschen Mathematiker-Vereinigung|volume=34 (Abt. 2)|year=1926b|page=104|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248861|place=DE|language=German|deadurl=yes|archiveurl=https://web.archive.org/web/20130308102932/http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=248861|archivedate=8 March 2013|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern|trans-title=Abstract Structure of the Theory of Ideals in Algebraic Number Fields|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002270951&L=1|year=1927|format=PDF|journal=Mathematische Annalen|volume=96|issue=1|pages=26–61|doi=10.1007/BF01209152|language=German|deadurl=yes|archiveurl=https://web.archive.org/web/20140903095147/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002270951&L=1|archivedate=3 September 2014|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Brauer|first=Richard|last2=Noether|first2=Emmy|author1-link=Richard Brauer|title=Über minimale Zerfällungskörper irreduzibler Darstellungen|trans-title=On the Minimum Splitting Fields of Irreducible Representations|journal=Sitz. Ber. D. Preuss. Akad. D. Wiss.|year=1927|pages=221–28|language=de}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|year=1929|title=Hyperkomplexe Größen und Darstellungstheorie|trans-title=Hypercomplex Quantities and the Theory of Representations|journal=Mathematische Annalen|volume=30|pages=641–92|doi=10.1007/BF01187794|language=German|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002371448&L=1|deadurl=yes|archiveurl=https://web.archive.org/web/20160329230805/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002371448&L=1|archivedate=29 March 2016|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Brauer|first=Richard|first2=Helmut|last2=Hasse|first3=Emmy|last3=Noether|author2-link=Helmut Hasse|year=1932|title=Beweis eines Hauptsatzes in der Theorie der Algebren|trans-title=Proof of a Main Theorem in the Theory of Algebras|journal=Journal für die Reine und Angewandte Mathematik|volume=167|pages=399–404|url=http://gdz.sub.uni-goettingen.de/no_cache/dms/load/img/?IDDOC=260847|place=DE|language=German}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|year=1933|title=Nichtkommutative Algebren|trans-title=Noncommutative Algebras|journal=Mathematische Zeitschrift|volume=37|pages=514–41|doi=10.1007/BF01474591|language=German}}
* {{Citation/CS1-Prufa|last=Noether|first=Emmy|author-mask=3|title=Gesammelte Abhandlungen|trans-title=Collected papers|editor-first=Nathan|editor-last=Jacobson|publisher=Springer-Verlag|place=Berlin; New York|year=1983|pages=viii, 777|isbn=978-3-540-11504-5|mr=0703862|language=German}}
 
=== Additional sources ===
 
* {{cite web|last=Phillips|first=Lee|title=The female mathematician who changed the course of physics—but couldn't get a job|url=https://arstechnica.com/science/2015/05/the-female-mathematician-who-changed-the-course-of-physics-but-couldnt-get-a-job/|website=Ars Technica|publisher=Condé Nast|location=California|date=May 2015}}
Lína 525 ⟶ 503:
* {{cite conference|last=Blue|first=Meredith|year=2001|title=Galois Theory and Noether's Problem|conference=34th Annual Meeting of the Mathematical Association of America|publisher=MAA Florida Section|access-date=2018-06-09|archiveurl=https://web.archive.org/web/20080529020714/http://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf|archivedate=29 May 2008|url=http://mcc1.mccfl.edu/fl_maa/proceedings/2001/blue.pdf|dead-url=yes|format=PDF|df=dmy}}
* {{cite conference|author-link=Nina Byers|first=Nina|last=Byers|title=E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws|conference=Proceedings of a Symposium on the Heritage of Emmy Noether|date=December 1996|publisher=[[Bar-Ilan University]]|place=Israel|arxiv=physics/9807044|bibcode=1998physics...7044B}}
* {{Citation/CS1-Prufa|last=Byers|first=Nina|authorlink=Nina Byers|chapter=Emmy Noether|title=Out of the Shadows: Contributions of 20th Century Women to Physics|year=2006|editor1-first=Nina|editor1-last=Byers|editor2-first=Gary|editor2-last=Williams|place=Cambridge|publisher=Cambridge University Press|isbn=978-0-521-82197-1}}
* {{Citation/CS1-Prufa|author-last=Dick|author-first=Auguste|authorlink=Auguste Dick|title=Emmy Noether: 1882–1935|place=Boston|publisher=Birkhäuser|year=1981|isbn=978-3-7643-3019-4|translator-first=H.I.|translator-last=Blocher}}
* {{Citation/CS1-Prufa|last1=Fleischmann|first1=Peter|title=The Noether bound in invariant theory of finite groups|doi=10.1006/aima.2000.1952|mr=1800251|year=2000|journal=Advances in Mathematics|volume=156|issue=1|pages=23–32}}
* {{Citation/CS1-Prufa|last1=Fogarty|first1=John|title=On Noether's bound for polynomial invariants of a finite group|url=http://www.ams.org/era/2001-07-02/S1079-6762-01-00088-9/|accessdate=16 June 2008|mr=1826990|year=2001|journal=Electronic Research Announcements of the American Mathematical Society|volume=7|issue=2|pages=5–7|doi=10.1090/S1079-6762-01-00088-9}}
* {{Citation/CS1-Prufa|last=Gilmer|first=Robert|chapter=Commutative Ring Theory|title=Emmy Noether: A Tribute to Her Life and Work|editor1-first=James W.|editor1-last=Brewer|editor2-first=Martha K.|editor2-last=Smith|pages=131–43|place=New York|publisher=Marcel Dekker|year=1981|isbn=978-0-8247-1550-2}}
* {{Citation/CS1-Prufa|last1=Gordan|first1=Paul|title=Die simultanen Systeme binärer Formen|language=German|doi=10.1007/BF01444021|year=1870|journal=[[Mathematische Annalen]]|volume=2|issue=2|pages=227–80|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002240513&L=1|deadurl=yes|archive-url=https://web.archive.org/web/20140903095153/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002240513&L=1|archive-date=3 September 2014|df=dmy-all}}
* {{Citation/CS1-Prufa|authorlink=William Haboush|first=W.J.|last=Haboush|title=Reductive groups are geometrically reductive|volume=102|year=1975|pages=67–83|doi=10.2307/1970974|issue=1|journal=Annals of Mathematics|jstor=1970974}}
* {{Citation/CS1-Prufa|last=Hasse|first=Helmut|authorlink=Helmut Hasse|title=Die Struktur der R.&nbsp;Brauerschen Algebrenklassengruppe über einem algebraischen Zahlkörper|year=1933|language=de|doi=10.1007/BF01448916|journal=Mathematische Annalen|volume=107|pages=731–60|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002276062&L=1|dead-url=yes|archive-url=https://web.archive.org/web/20160305072945/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=GDZPPN002276062&L=1|archive-date=5 March 2016|df=dmy-all}}
* {{cite journal|last1=Hilbert|first1=David|author1-link=David Hilbert|title=Ueber die Theorie der algebraischen Formen|language=German|date=December 1890|journal=[[Mathematische Annalen]]|volume=36|issue=4|pages=473–534|doi=10.1007/BF01208503|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0036&DMDID=DMDLOG_0045&L=1|dead-url=yes|archive-url=https://web.archive.org/web/20140903165407/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0036&DMDID=DMDLOG_0045&L=1|archive-date=3 September 2014|df=dmy-all}}
* {{cite journal|last=Hilton|first=Peter|year=1988|title=A Brief, Subjective History of Homology and Homotopy Theory in this Century|journal=Mathematics Magazine|volume=60|issue=5|pages=282–91|jstor=2689545}}
* {{cite journal|last1=Hopf|first1=Heinz|author1-link=Heinz Hopf|url=http://www.digizeitschriften.de/index.php?id=loader&tx_jkDigiTools_pi1%5BIDDOC%5D=465901|title=Eine Verallgemeinerung der Euler-Poincaréschen Formel|language=de|year=1928|journal=Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse|volume=2|pages=127–36}}
* {{cite book|authorlink=Ioan James|last=James|first=Ioan|year=2002|title=Remarkable Mathematicians from Euler to von Neumann|publisher=Cambridge University Press|location=Cambridge|isbn=978-0-521-81777-6}}
* {{Citation/CS1-Prufa|last=Kimberling|first=Clark|chapter=Emmy Noether and Her Influence|pages=3–61|title=Emmy Noether: A tribute to her life and work|editor1-first=James W.|editor1-last=Brewer|editor2-first=Martha K.|editor2-last=Smith|place=New York|publisher=Marcel Dekker|year=1981|isbn=978-0-8247-1550-2}}
* {{Citation/CS1-Prufa|last=Lam|first=Tsit Yuen|chapter=Representation Theory|pages=145–56|title=Emmy Noether: A tribute to her life and work|editor1-first=James W.|editor1-last=Brewer|editor2-first=Martha K.|editor2-last=Smith|place=New York|publisher=Marcel Dekker|year=1981|isbn=978-0-8247-1550-2}}
* {{Citation/CS1-Prufa|author1-link=Leon M. Lederman|last1=Lederman|first1=Leon M.|author2-link=Christopher T. Hill|first2=Christopher T.|last2=Hill|title=Symmetry and the Beautiful Universe|place=Amherst, MA|publisher=Prometheus Books|year=2004|isbn=978-1-59102-242-8}}
* {{Citation/CS1-Prufa|last=Mac Lane|first=Saunders|author-link=Saunders Mac Lane|chapter=Mathematics at the University of Göttingen 1831–1933|title=Emmy Noether: A tribute to her life and work|editor1-first=James W.|editor1-last=Brewer|editor2-first=Martha K.|editor2-last=Smith|pages=65–78|place=New York|publisher=Marcel Dekker|year=1981|isbn=978-0-8247-1550-2}}
* {{Citation/CS1-Prufa|last1=Malle|first1=Gunter|last2=Matzat|first2=Bernd Heinrich|title=Inverse Galois theory|publisher=[[Springer-Verlag]]|location=Berlin, New York|series=Springer Monographs in Mathematics|isbn=978-3-540-62890-3|mr=1711577|year=1999}}
* {{Citation/CS1-Prufa|authorlink=Gottfried E. Noether|last=Noether|first=Gottfried E.|year=1987|title=Women of Mathematics|editor1-last=Grinstein|editor1-first=L.S.|editor2-last=Campbell|editor2-first=P.J.|publisher=Greenwood Press|location=New York|isbn=978-0-313-24849-8}}
* {{Citation/CS1-Prufa|last=Noether|first=Max|authorlink=Max Noether|title=Paul Gordan|journal=Mathematische Annalen|volume=75|issue=1|year=1914|pages=1–41|doi=10.1007/BF01564521|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0075&DMDID=DMDLOG_0007&L=1|dead-url=yes|archive-url=https://web.archive.org/web/20140904002613/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0075&DMDID=DMDLOG_0007&L=1|archive-date=4 September 2014|df=dmy-all}}
* {{Citation/CS1-Prufa|last=Osen|first=Lynn M.|chapter=Emmy (Amalie) Noether|title=Women in Mathematics|publisher=MIT Press|year=1974|isbn=978-0-262-15014-9|pages=141–52}}
* {{Citation/CS1-Prufa|last=Schmadel|first=Lutz D.|authorlink=Lutz D. Schmadel|title=Dictionary of Minor Planet Names|edition=5th revised and enlarged|place=Berlin|publisher=Springer-Verlag|year=2003|isbn=978-3-540-00238-3}}
* {{cite conference|last1=Srinivasan|first1=Bhama|last2=Sally|first2=Judith D.|title=Emmy Noether in Bryn Mawr|conference=Proceedings of a Symposium Sponsored by the Association for Women in Mathematics in Honor of Emmy Noether's 100th Birthday|date=2012|publisher=Springer Science & Business Media|isbn=978-1-4612-5547-5|url=https://books.google.com/books?id=8iPoBwAAQBAJ|language=en}}
* {{cite journal|first=Richard G|last=Swan|title=Invariant rational functions and a problem of Steenrod|journal=Inventiones Mathematicae|year=1969|volume=7|issue=2|pages=148–58|doi=10.1007/BF01389798|bibcode=1969InMat...7..148S}}
* {{cite book|last=Taussky|first=Olga|authorlink=Olga Taussky-Todd|chapter=My Personal Recollections of Emmy Noether|pages=79–92|title=Emmy Noether: A Tribute to Her Life and Work|editor1-first=James W.|editor1-last=Brewer|editor2-first=Martha K|editor2-last=Smith|place=New York|publisher=Marcel Dekker|year=1981|isbn=978-0-8247-1550-2}}
* {{cite conference|title=The Heritage of Emmy Noether|editor-first=M.|editor-last=Teicher|editor-link=Mina Teicher|conference=Israel Mathematical Conference Proceedings|publisher=[[Bar-Ilan University]], [[American Mathematical Society]], [[Oxford University Press]]|year=1999|isbn=978-0-19-851045-1|oclc=223099225}}
* {{Citation/CS1-Prufa|authorlink=M. B. W. Tent|author-first=M.B.W.|author-last=Tent|title=Emmy Noether: The Mother of Modern Algebra|year=2008|publisher=[[CRC Press]]}}
* {{Citation/CS1-Prufa|authorlink=Bartel Leendert van der Waerden|last=van der Waerden|first=B.L.|title=Nachruf auf Emmy Noether|trans-title=obituary of Emmy Noether|journal=Mathematische Annalen|volume=111|year=1935|language=German|pages=469–74|doi=10.1007/BF01472233|url=http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0111&DMDID=DMDLOG_0038&L=1|deadurl=yes|archiveurl=https://web.archive.org/web/20140903172427/http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0111&DMDID=DMDLOG_0038&L=1|archivedate=3 September 2014|df=dmy-all}}. Reprinted in {{harvnb|Dick|1981}}
* {{Citation/CS1-Prufa|last=van der Waerden|first=B.L.|author-mask=3|year=1985|title=A History of Algebra: from al-Khwārizmī to Emmy Noether|publisher=Springer-Verlag|location=Berlin|isbn=978-0-387-13610-3}}
* {{Citation/CS1-Prufa|first=Hermann|last=Weyl|authorlink=Hermann Weyl|title=Emmy Noether|journal=Scripta Mathematica|volume=3|issue=3|pages=201–20|year=1935}} Reprinted as an appendix in {{Harvtxt|Dick|1981}}.
* {{Citation/CS1-Prufa|last1=Weyl|first1=Hermann|title=David Hilbert and his mathematical work|doi=10.1090/S0002-9904-1944-08178-0|mr=0011274|year=1944|journal=[[Bulletin of the American Mathematical Society]]|volume=50|issue=9|pages=612–54}}
 
== External links ==
{{Wikiquote}}
{{Commonscat}}
{{Library resources box|by=yes|onlinebooksby=yes|viaf=73918294}}
 
* {{Citation/CS1-Prufa|contribution=Emmy Noether|url=http://cwp.library.ucla.edu/Phase2/Noether,_Amalie_Emmy@861234567.html|title=CWP|publisher=UCLA|deadurl=yes|archiveurl=https://web.archive.org/web/20080212093356/http://cwp.library.ucla.edu/Phase2/Noether,_Amalie_Emmy@861234567.html|archivedate=12 February 2008|df=dmy-all}}
* {{MathGenealogy|id=6967}}
* {{Citation/CS1-Prufa|url=http://www.agnesscott.edu/lriddle/women/noether.htm|contribution=Emmy Noether|title=Biographies of Women Mathematicians|publisher=[[Agnes Scott College]]}}.
* {{MacTutor Biography|id=Noether_Emmy}}
* {{Citation/CS1-Prufa|url=http://www.physikerinnen.de/noetherlebenslauf.html|title=Noether Lebensläufe|place=[[Germany|DE]]|language=German|publisher=Physikerinnen}}. Noether's application for admission to the [[University of Erlangen]] and three [[Curriculum vitae|curricula vitae]], two of which are shown in handwriting, with transcriptions. The first of these is in Emmy Noether's own handwriting.
* {{Citation/CS1-Prufa|url=http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=39728|title=Über die Bildung des Formensystems der ternären biquadratischen Form|edition=unpublished|last=Noether|first=Emmy|year=1908|type=[[doctoral dissertation]]|place=Erlangen|deadurl=yes|archiveurl=https://web.archive.org/web/20130309165251/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=39728|archivedate=9 March 2013|df=dmy-all}}; [https://web.archive.org/web/20130308103120/http://gdz.sub.uni-goettingen.de/dms/load/img/?IDDOC=261200 published version].
* {{Citation/CS1-Prufa|url=http://faculty.evansville.edu/ck6/bstud/enmc.html|title=Emmy Noether, Mentors & Colleagues|type=photogram|first=Clark|last=Kimberling|publisher=Evansville|deadurl=yes|archiveurl=https://web.archive.org/web/20070222010607/http://faculty.evansville.edu/ck6/bstud/enmc.html|archivedate=22 February 2007|df=dmy}}
* {{Citation/CS1-Prufa|url=http://owpdb.mfo.de/search?term=noether|title=Oberwolfach|type=collection of photograms|contribution=Noether|publisher=MFO|place=Germany}}
* {{Citation/CS1-Prufa|url=http://univerlag.uni-goettingen.de/handle/3/isbn-3-938616-35-0|title=Helmut Hasse und Emmy Noether – Die Korrespondenz 1925–1935|trans-title=Helmut Hasse and Emmy Noether – Their Correspondence 1925–1935|editor1-last=Lemmermeyer|editor1-first=Franz|editor2-last=Roquette|editor2-first=Peter|year=2006|publisher=Göttingen University|place=DE|format=PDF|doi=10.17875/gup2006-49|isbn=978-3-938616-35-2}}
* {{Citation/CS1-Prufa|url=https://www.nytimes.com/2012/03/27/science/emmy-noether-the-most-significant-mathematician-youve-never-heard-of.html|title=The Mighty Mathematician You've Never Heard Of|first1=Natalie|last1=Angier|newspaper=The New York Times|date=26 March 2012}}
* [http://triarte.brynmawr.edu/Obj188671?sid=318669&x=31763304 Photograph of Emmy Noether]
* [http://triarte.brynmawr.edu/Obj188672?sid=318669&x=31763306 Letter from Emmy Noether to Dr. Park, President of Bryn Mawr College]
 
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