Mathematics – History and Overview
Scientific paper
2007-04-23
Sciences et Techniques en Perspective IIe s\'erie, fasc. 1 (2007) (2008) p. 5-85
Mathematics
History and Overview
Il s'agit d'une version pr\'e publication ant\'erieure de plusieurs mois \`a la version publi\'ee (r\'ef\'erence jointe). Les
Scientific paper
What did "algebra" mean before the development of the algebraic theories of the 20th century ? This paper stresses the identities taken by the algebraic practices developped during the century long discussion around the equation around the equation of secular inequalities (1766- 1874). In 1874, a strong controversy on the theory of bilinear and quadratic forms opposed Camille Jordan and Leopold Kronecker. The arithmetical ideal of Kronecker faced Jordan's claim for the simplicity of his algebraic canonical form. As the controversy combined mathematical and historical arguments, it gave rise to the writing of a history of the methods used by Lagrange, Laplace and Weierstrass in a century long mathematical discussion around the "equation of secular inequalities".
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