{"title":"Why Did Weyl Think that Emmy Noether Made Algebra the Eldorado of Axiomatics?","authors":"Iulian D. Toader","doi":"arxiv-2408.08552","DOIUrl":null,"url":null,"abstract":"The paper attempts to clarify Weyl's metaphorical description of Emmy\nNoether's algebra as the Eldorado of axiomatics. It discusses Weyl's early view\non axiomatics, which is part of his criticism of Dedekind and Hilbert, as\nmotivated by Weyl's acquiescence to a phenomenological epistemology of\ncorrectness, then it describes Noether's work in algebra, emphasizing in\nparticular its ancestral relation to Dedekind's and Hilbert's works, as well as\nher mathematical methods, characterized by non-elementary reasoning, i.e.,\nreasoning detached from mathematical objects. The paper turns then to Weyl's\nremarks on Noether's work, and argues against assimilating her use of the\naxiomatic method in algebra to his late view on axiomatics, on the ground of\nthe latter's resistance to Noether's principle of detachment.","PeriodicalId":501462,"journal":{"name":"arXiv - MATH - History and Overview","volume":"181 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.08552","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The paper 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, then it 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 non-elementary reasoning, i.e.,
reasoning detached from mathematical objects. The paper turns then 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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