Article ID: CBB619659341

Zur Einführung einer begrifflichen Perspektive in die Mathematik: Dedekind, Noether, van der Waerden (2015)

unapi

For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden. „She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine – of all that is characterized by the term ‚Begriffliche Mathematik‘.“2 The aim of this paper is to illuminate this “new direction”, which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831–1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a “free creation of the human spirit”3. They thus stand for an abstract perspective of mathematics in their entirety, described as ‘modern algebra’ in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on “general mathematical concepts” [allgemein-mathematische Begriffe]4, was the success of a cultural movement whose most important protagonists included Emmy Noether (1882–1935) and her pupil Bartel L. van der Waerden (1903–1996). With the use of the term ‘conceptual’, a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the “working and conceptual methods” [Arbeits- und Auffassungsmethoden]5 of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term “conceptual world” [Begriffswelt]6 in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB619659341/

Similar Citations

Book Gray, Jeremy; Parshall, Karen Hunger; (2007)
Episodes in the History of Modern Algebra (1800--1950) (/isis/citation/CBB000774194/)

Chapter McLarty, Colin; (2006)
Emmy Noether's “Set Theoretic” Topology: From Dedekind to the Rise of Functors (/isis/citation/CBB000800122/)

Book Mechthild Koreuber; (2015)
Emmy Noether, die Noether-Schule und die moderne Algebra - | Mechthild Koreuber | Springer (/isis/citation/CBB818238242/)

Article J. Climent Vidal; J. Soliveres Tur; (2018)
The Modernity of Dedekind’s Anticipations Contained in what Are Numbers and What Are They Good for? (/isis/citation/CBB477696384/)

Article Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David; (2013)
Ten Misconceptions from the History of Analysis and Their Debunking (/isis/citation/CBB001252715/)

Article Emmylou Haffner; (2019)
From Modules to Lattices: Insight into the Genesis of Dedekind's Dualgruppen (/isis/citation/CBB728342102/)

Book Gray, Jeremy; (2008)
Plato's Ghost: The Modernist Transformation of Mathematics (/isis/citation/CBB000950298/)

Article J. Climent Vidal; J. Soliveres Tur; (2018)
Correction to: The modernity of Dedekind’s anticipations contained in What are numbers and what are they good for? (/isis/citation/CBB267654318/)

Article Lambert, Kevin; (2013)
A Natural History of Mathematics: George Peacock and the Making of English Algebra (/isis/citation/CBB001320192/)

Book Thomas Sonar; Karin Reich; (2014)
Der Briefwechsel, Richard Dedekind-Heinrich Weber (/isis/citation/CBB718714957/)

Article Parshall, Karen Hunger; (2004)
Defining a Mathematical Research School: The Case of Algebra at The University of Chicago, 1892--1945 (/isis/citation/CBB000470897/)

Chapter Mehrtens, Herbert; (1979)
Das Skelett der modernen Algebra: Zur Bildung mathematischer Begriffe bei Richard Dedekind (/isis/citation/CBB000000294/)

Article Purkert, Walter; (1976)
Ein Manuskript Dedekinds über Galois-Theorie (/isis/citation/CBB000027163/)

Article Toti Rigatelli, Laura; (1989-90)
Le lezioni sulla teoria di Galois di Richard Dedekind (/isis/citation/CBB000053670/)

Article Scharlau, Winfried; (1982)
Unveröffentlichte algebraische Arbeiten Richard Dedekinds aus seiner Göttinger Zeit, 1855-1858 (/isis/citation/CBB000001378/)

Article Nastasi, Tina; (2008)
La storia del pensiero scientifico e il suo significato nell'opera di Federigo Enriques (/isis/citation/CBB001024085/)

Authors & Contributors
Tur, J. Soliveres
Vidal, J. Climent
Parshall, Karen V. Hunger
McLarty, Colin
Gray, Jeremy
Mechthild Koreuber
Concepts
Mathematics
Algebra
Set theory
Mathematicians
Science and culture
Infinitesimals
Time Periods
19th century
20th century, early
Edo period (Japan, 1603-1868)
Modern
18th century
17th century
Places
Germany
Japan
Italy
Great Britain
Institutions
University of Chicago
Göttingen. Universität
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment