Article ID: CBB000930655

La controverse de 1874 entre Camille Jordan et Leopold Kronecker (2007)

unapi

The 1874 Controversy between Camille Jordan and Leopold Kronecker During the whole of 1874, Camille Jordan and Leopold Kronecker quarrelled vigorously over the organisation of the theory of bilinear forms. That theory promised a general and homogeneous treatment of numerous questions arising in various 19th-century theoretical contexts, and it hinged on two theorems, stated independently by Jordan and Weierstrass, that would today be considered equivalent. It was, however, the perceived difference between those two theorems that sparked the 1874 controversy. Focusing on this quarrel allows us to explore the algebraic identity of the polynomial practices of the manipulations of forms in use before the advent of structural approaches to linear algebra. The latter approaches identified these practices with methods for the classification of similar matrices. We show that the practices---Jordan's canonical reduction and Kronecker's invariant computation---reflect identities inseparable from the social context of the time. Moreover, these practices reveal not only tacit knowledge, local ways of thinking, but also---in light of a long history tracing back to the work of Lagrange, Laplace, Cauchy, and Hermite---two internal philosophies regarding the significance of generality which are inseparable from two disciplinary ideals opposing algebra and arithmetic. By interrogating the cultural identities of such practices, this study aims at a deeper understanding of the history of linear algebra without focusing on issues related to the origins of theories or structures. Keywords : Algebraic practices. Generality. Jordan. Kronecker. Weierstrass. Canonical forms. Invariants; Elementary divisors. Invariant factors. Linear substitutions. Bilinear forms. Matrices. Spectral theory. Linear algebra. Algebra. Arithmetic. Mechanics.

...More

Description On their quarrels over the organization of the theory of bilinear forms, and “the algebraic identity of the polynomial practices of the manipulations of forms.” (from the abstract)


Citation URI
https://data.isiscb.org/isis/citation/CBB000930655/

Similar Citations

Book Boniface, Jacqueline; (2002)
Les constructions des nombres réels dans le mouvement d'arithmétisation de l'analyse (/isis/citation/CBB000771381/)

Article Cédric Vergnerie; (2020)
Une controverse entre Émile Picard et Leopold Kronecker (/isis/citation/CBB977640957/)

Book Gray, Jeremy; Parshall, Karen Hunger; (2007)
Episodes in the History of Modern Algebra (1800--1950) (/isis/citation/CBB000774194/)

Article Radu, Mircea; (2003)
A Debate about the Axiomatization of Arithmetic: Otto Hölder against Robert Graßmann (/isis/citation/CBB000340654/)

Article Schubring, Gert; (2007)
Hüseyin Tevfik Pasha: The Inventor of “Linear Algebra” (/isis/citation/CBB000931430/)

Book Gauthier, Yvon; (2002)
Internal Logic: Foundations of Mathematics from Kronecker to Hilbert (/isis/citation/CBB000301820/)

Book Cantor, Georg; Ferreirós, José; (2006)
Fundamentos para una teoría general de conjuntos: Escritos y correspondencia selecta (/isis/citation/CBB000930382/)

Article Archibald, T.; Tazzioli, R.; (2014)
Integral Equations between Theory and Practice: The Cases of Italy and France to 1920 (/isis/citation/CBB001202206/)

Article Grattan-Guinness, Ivor; (2008)
Differential Equations and Linearity in the 19th and Early 20th Centuries (/isis/citation/CBB001021149/)

Article Hawkins, Thomas; (2008)
Frobenius and the Symbolical Algebra of Matrices (/isis/citation/CBB000773887/)

Article Carla Bromberg; Ana M. Alfonso-Goldfarb; (2016)
Music and Mathematics: A Case Study in the History of Science (/isis/citation/CBB854514897/)

Article Boniface, Jacqueline; Schappacher, Norbert; (2001)
“Sur le concept de nombre en mathématique”: Cours inédit de Leopold Kronecker à Berlin (1891) (/isis/citation/CBB000770907/)

Article Xing, Ying-rui; (2011)
Husserl's Early Philosophy of Arithmetic (/isis/citation/CBB001250699/)

Book Marchisotto, Elena; Smith, James T.; (2007)
The Legacy of Mario Pieri in Geometry and Arithmetic (/isis/citation/CBB000831265/)

Book Weiner, Joan; (2004)
Frege Explained: From Arithmetic to Analytic Philosophy (/isis/citation/CBB000772767/)

Article Lambert, Kevin; (2013)
A Natural History of Mathematics: George Peacock and the Making of English Algebra (/isis/citation/CBB001320192/)

Authors & Contributors
Boucard, Jenny
Boniface, Jacqueline
Vergnerie, Cédric
Tazzioli, R.
Archibald, T.
Xing, Ying-rui
Concepts
Mathematics
Arithmetic
Algebra
Number theory; number concept
Linear algebra
Logic
Time Periods
19th century
20th century, early
20th century
18th century
16th century
Places
France
Turkey
Italy
Germany
Great Britain
Institutions
University of Chicago
Comments

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment