Article ID: CBB095893246

Why Did Weyl Think That Emmy Noether Made Algebra the Eldorado of Axiomatics? (2021)

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The article attempts to clarify Weyl’s metaphorical description of Emmy Noether’s algebra as the Eldorado of axiomatics. It discusses Weyl’s early view on axiomatics, which is part of his criticism of Dedekind and Hilbert, as motivated by Weyl’s acquiescence to a phenomenological epistemology of correctness. The article then describes Noether’s work in algebra, emphasizing in particular its ancestral relation to Dedekind’s and Hilbert’s works, as well as her mathematical methods, characterized by nonelementary reasoning—that is, reasoning detached from mathematical objects. The article then turns to Weyl’s remarks on Noether’s work and argues against assimilating her use of the axiomatic method in algebra to his late view on axiomatics, on the ground of the latter’s resistance to Noether’s principle of detachment.

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Authors & Contributors
Gray, Jeremy
McLarty, Colin
Mechthild Koreuber
Colyvan, Mark
Eckes, Christophe
Jankvist, Uffe Thomas
Journals
Historia Mathematica
Archive for History of Exact Sciences
Berichte zur Wissenschaftsgeschichte
British Journal for the Philosophy of Science
British Society for the History of Mathematics Bulletin
HOPOS
Publishers
Cambridge University Press
American Mathematical Society
Carocci Editore
Oxford University Press
Presses Universitaires de Nancy
Springer International
Concepts
Mathematics
Philosophy of mathematics
Algebra
Geometry
Philosophy of science
Controversies and disputes
People
Noether, Emmy
Weyl, Hermann
Hilbert, David
Minkowski, Hermann
Poincaré, Jules Henri
Quine, Willard Van Orman
Time Periods
20th century, early
20th century
19th century
Modern
Places
Germany
Denmark
Institutions
University of Chicago
Universität Göttingen
Göttingen. Universität
Göttingen Academy
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