La fonte alg\'ebrique des M\'ethodes nouvelles de la m\'ecanique c\'eleste d'Henri Poincar\'e

TL;DR

This paper analyzes Poincaré's methods in celestial mechanics, revealing their algebraic foundations and collective aspects, which shed light on the novelty and mathematical practices underlying his approach to the three-body problem.

Contribution

It uncovers the algebraic practices embedded in Poincaré's methods, highlighting their collective and innovative nature in celestial mechanics.

Findings

Algebraic practices underpin Poincaré's approach

The methods reveal collective mathematical dimensions

The algebraic cast contributes to the novelty of his methods

Abstract

Poincar\'e's approach to the three body problem has often been celebrated as a starting point of chaos theory in relation to the investigation of dynamical systems. Yet, Poincar\'e's strategy can also be analyzed as molded on - or casted in - some specific algebraic practices for manipulating systems of linear equations. These practices shed new light on both the novelty and the collective dimensions of Poincar\'e's M\'ethodes nouvelles. As the structure of a cast-iron building may be less noticeable than its creative fa\c{c}ade, the algebraic cast of Poincar\'e's strategy is broken out of the mold in generating the novel methods of celestial mechanics. But as the various components that are mixed in some casting process can still be detected in the resulting alloy, the algebraic cast of the M\'ethodes nouvelles points to some collective dimensions of Poincar\'e's methods. An edited version of the present preprint is to be published in the journal \textit{L'astronomie} under the title "L'approche de Poincar\`E sur le probl\"Eme des trois corps". This publication is an abstract in French language of a forthcoming paper - "The algebraic cast of Poincar\`E's \textit{M\`Ethodes nouvelles}" - which will develop its main claims as well as the historiographical and mathematical issues raised in section 4 and section 5.