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

TL;DR

The paper explores Weyl's metaphorical praise of Emmy Noether's algebra as the pinnacle of axiomatics, contrasting his early views with his later criticisms and analyzing Noether's innovative methods.

Contribution

It clarifies Weyl's perspective on Noether's algebra and distinguishes his early axiomatic views from his later criticisms, highlighting her methodological innovations.

Findings

Weyl's early view linked axiomatics to phenomenological correctness.

Noether's algebraic methods are rooted in non-elementary reasoning.

Weyl's late critique resists equating Noether's approach with his axiomatic principles.

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.