Mathematical modernity, goal or problem? The opposing views of Felix Hausdorff and Hermann Weyl

TL;DR

This paper examines the contrasting perspectives of Hausdorff and Weyl on mathematical methodology, highlighting their diverging views during the rise of modern mathematics and challenging traditional classifications of their positions.

Contribution

It provides a detailed case study analyzing the work and self-definition of Hausdorff and Weyl, questioning the simplistic modernist versus countermodernist dichotomy.

Findings

Hausdorff exemplifies mathematical modernism.

Weyl's work challenges the countermodernist label.

The traditional dichotomy oversimplifies their positions.

Abstract

This paper contains a case study of the work and self-definition of two important mathematicians during the rise of modern mathematics: Felx Hausdorff (1868--1942) and Hermann Weyl (1885--1955). The two had strongly diverging positions with regard to basic questions of mathematical methodology, which is reflected in the style and content of their mathematical research. Herbert Mehrtens (1990) describes them as protagonists of what he sees as the two opposing camps of ``modernists'' (Hilbert, Hausdorff et al.) and ``countermodernists'' (Brouwer, Weyl et al.). There is no doubt that Hausdorff may be described as a mathematical ``modernist''', while the qualification of Weyl as ``countermodern'' is rather off the track, once his work is taken into account.