  Throughout the whole year of 1874, C. Jordan and L. Kronecker were
quarrelling over two theorems. On the one hand, Jordan had stated in 1870 a
canonical form theorem for substitutions of linear groups; on the other hand,
Karl Weierstrass had introduced in 1868 the elementary divisors of non singular
pairs of bilinear forms (P,Q) in stating a key theorem of the theory of
bilinear and quadratic forms. Although they would be considered equivalent as
regard to modern mathematics, not only had these two theorems been stated
independently and for different purposes, they had also been lying within the
distinct frameworks of two theories until some connections came to light in
1872-1873, breeding the 1874 quarrel and hence revealing an opposition over two
practices relating to distinctive cultural features. As we will be looking into
the 1874 quarrel, our purpose will be to show how the complex identities of
practices such as Jordan s canonical reduction and Kronecker s invariant
computation highlight some cultural issues such as tacit knowledge and
perceptions of history peculiar to individuals or communities as well as some
local ways of thinking such as disciplinary ideals and internal philosophies of
generality and simplicity.
