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

Abstract

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.