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van der Waerden, Bartel L. (1985). A History of Algebra: From al-Khwārizmī to Emmy Noether. Berlin: Springer-Verlag. p. 244. ISBN 978-0-387-13610-3.
Noether, Emmy (1929), "Hyperkomplexe Größen und Darstellungstheorie" [Hypercomplex Quantities and the Theory of Representations], Mathematische Annalen (in German), 30: 641–92, doi: 10.1007/BF01187794, S2CID 120464373, archived from the original on 2016-03-29, retrieved 2016-01-14
This publication has had a profound influence on the development of modern algebra. I shall now summarize its content. In the introduction Emmy Noether states that in recent publications the structure theory of algebras and the representation theory of finite groups have been separated completely. She, on the other hand, aims at a purely arithmetical foundation, in which the structure theory and the representation theory of groups and algebras appear as a unified whole, namely as a theory of modules and ideals in rings satisfying finiteness conditions.—van der Waerden
Roselló, Joan.
Hilbert, Göttingen and the Development of Modern Mathematics. Cambridge Scholars Publishing. pp. 205–213.
ISBN
978-1-5275-2762-1. Chapter Twenty-One: The Noether School and the Rise of Modern Algebra
The maxim by which Emmy Noether was guided throughout her work might be formulated as follows: "Any relationships between numbers, functions and operations only become transparent, generally applicable, and fully productive after they have been isolated from their particular objects and been formu1ated as universally valid concepts."—van der Waerden, Bartel L. (Emmy Noether obituary)
Ernst Fischer at Erlangen influenced her away from Gordan's constructivist style, dominated by forms and formulas, toward Hilbert's more axiomatic and abstract style, characterized by existence proofs.
— Clark Kimberling https://faculty.evansville.edu/ck6/bstud/enmc.html
Noether’s work on factorization properties of ideals in abstract rigs, beginning in 1921, marks a turning point in the history of mathematics, because of its influence on shaping this view and in displaying its power. The spread of this view and its tremendous impact on mathematics at large over the 20th century came through the mediation of a famous textbook, Moderne Algebra, published in 1930 by Bartel L. van der Waerden under the decisive influence of Noether’s lectures in Göttingen (as well as of Emil Artin’s courses in Hamburg)— Leo Corry, Tel-Aviv University
My methods are working methods and perception methods and therefore penetrated anonymously everywhere. (Noether, 1931)
Emmy Noether, one of the most important mathematicians in the world, shaped modern algebra with her “working and perception methods” and made a decisive contribution to the algebraization of mathematical disciplines. Noether opened up new mathematical ways of thinking by developing a structural perspective on mathematics. With her habilitation thesis published in 1918, she solved central mathematical problems of general relativity. On June 4, 1919, Emmy Noether gave her habilitation lecture; she was the first woman to be qualified as a professor in Prussia.—Interdisciplinary conference on the occasion of the 100th anniversary of Emmy Noether's habilitation
The following Wikimedia Commons file used on this page or its Wikidata item has been nominated for deletion:
Participate in the deletion discussion at the nomination page. — Community Tech bot ( talk) 22:57, 22 January 2021 (UTC)
I am reviewing this article as part of WP:URFA/2020, and initiative to review older featured articles to ensure that they still meet the featured article criteria. After reviewing this article, I have some concerns:
Is anyone interested in resolving these, or should this article go to FAR? Z1720 ( talk) 14:14, 20 August 2023 (UTC)
In 1919 the University of Göttingen allowed Noether to proceed with her habilitation. These could easily be given inline citations but may not need them.
Although the results of Noether's first epoch were impressive and useful, her fame among mathematicians rests more on the groundbreaking work she did in her second and third epochs, as noted by Hermann Weyl and B.L. van der Waerden in their obituaries of her.
An example of an invariant is the discriminant B2 − 4 A C of a binary quadratic form. See Wikipedia:Scientific citation guidelines#Uncontroversial knowledge. Some of this may still need inline citations.
This phase marks the beginning of her engagement with abstract algebra, the field of mathematics to which she would make groundbreaking contributions.
Leaving notes here as they come up. Haven't found a citation for §University of Erlangen: "In 1910 and 1911 she published an extension of her thesis work from three variables to n variables", but Dick p. 20 could at least support her giving a lecture to the DMV on the topic in 1909. Rowe 2021 talks a bit abstractly about her work during this period on that topic. Firefangledfeathers ( talk / contribs) 22:11, 8 March 2024 (UTC)
In her next article, 'On the theory of invariants of forms of n variables' [1911], which had been announced the year before its publication (Noether [1910]), she extended the arguments of her thesis to the case of forms in n variables.— David Eppstein ( talk) 02:22, 10 March 2024 (UTC)
No luck yet on the "This phase marks the beginning ..." tag in §University of Erlangen, but Dick and Rowe at least seem to dance around it, and I could probably come up with a solidly sourced similar phrase. Firefangledfeathers ( talk / contribs) 03:47, 10 March 2024 (UTC)
I went through Rowe 2021, Rowe & Koreuber 2020, Dick 1981 to try and find a source for the phrase 'Her family paid for her room and board and supported her academic work' but couldn't find anything. There's plenty showcasing how she wasn't paid until 1923 but nothing specifically on her family financially supporting her. I finally found something in Page 99 of Emmy Noether: The Mother of Modern Algebra by Margaret B. W. Tent. I'm a little wary of using it a source, however, as it's aimed at young teenagers and the author creatively makes up conversations between historical figures. Does anyone know of a better source or would it be better to just remove the statement entirely? Sgubaldo ( talk) 19:46, 14 April 2024 (UTC)
The current article has a sentence starting
with a footnote undermining the quotation. If the quotation is not reliable it should not be used; if it is reliable it should not be qualified in a footnote. The exchange can be summarized rather than quoted if that is all the references support. Johnjbarton ( talk) 04:00, 25 April 2024 (UTC)