On Jordan's measurements

TL;DR

This paper explores Camille Jordan's diverse mathematical contributions and their historical context, analyzing how his work was organized and circulated before the rise of modern object-oriented disciplines.

Contribution

It provides a comprehensive review of Jordan's works and their collective organization within mathematical knowledge from 1860 to 1940.

Findings

Jordan's work spanned multiple mathematical fields.

Pre-object-oriented knowledge organizations influenced Jordan's research.

Jordan's contributions predate modern algebraic and topological disciplines.

Abstract

The Jordan measure, the Jordan curve theorem, as well as the other generic references to Camille Jordan's (1838-1922) achievements highlight that the latter can hardly be reduced to the "great algebraist" whose masterpiece, the Trait\'e des substitutions et des equations alg\'ebriques, unfolded the group-theoretical content of \'Evariste Galois's work. The present paper appeals to the database of the reviews of the Jahrbuch \"uber die Fortschritte der Mathematik (1868-1942) for providing an overview of Jordan's works. On the one hand, we shall especially investigate the collective dimensions in which Jordan himself inscribed his works (1860-1922). On the other hand, we shall address the issue of the collectives in which Jordan's works have circulated (1860-1940). Moreover, the time-period during which Jordan has been publishing his works, i.e., 1860-1922, provides an opportunity to investigate some collective organizations of knowledge that pre-existed the development of object-oriented disciplines such as group theory (Jordan-H\"older theorem), linear algebra (Jordan's canonical form), topology (Jordan's curve), integral theory (Jordan's measure), etc. At the time when Jordan was defending his thesis in 1860, it was common to appeal to transversal organizations of knowledge, such as what the latter designated as the "theory of order." When Jordan died in 1922, it was however more and more common to point to object-oriented disciplines as identifying both a corpus of specialized knowledge and the institutionalized practices of transmissions of a group of professional specialists.