„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 220:
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">{{
=== Second epoch (1920–1926): Ascending and descending chain conditions ===
Lína 265:
{{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>{{
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 286:
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 292:
{{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 306:
* 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,
Lína 502:
{{main|List of publications by Emmy Noether}}
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* {{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
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=== Additional sources ===
Lína 527:
* {{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}}
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* {{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}}
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* {{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}}
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* {{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}}
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* {{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}}
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* {{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}}
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== External links ==
Lína 563:
{{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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