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date: 15 August 2020

Abstract and Keywords

This article revisits the 1874 controversy between Camille Jordan and Leopold Kronecker over two theorems, namely Jordan’s canonical forms and Karl Weierstrass’s elementary divisors theorem. In particular, it compares the perspectives of Jordan and Kronecker on generality and how their debate turned into an opposition over the algebraic or arithmetic nature of the ‘theory of forms’. It also examines the ways in which the various actors used the the categories of algebraic generality and arithmetic generality. After providing a background on the Jordan-Kronecker controversy, the article explains Jordan’s canonical reduction and Kronecker’s invariant computations in greater detail. It argues that Jordan and Kronecker aimed to ground the ‘theory of forms’ on new forms of generality, but could not agree on the types of generality and on the treatments of the general they were advocating.

Keywords: Camille Jordan, Leopold Kronecker, canonical forms, Karl Weierstrass, elementary divisors theorem, theory of forms, algebraic generality, arithmetic generality, canonical reduction, invariant computations

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