The decline of Cayley's invariant theory (1863–1895)

Different Motivations and Goals in the Historical Development of the Theory of Systems of Linear Inequalities

“…Stiemke handed in his doctoral thesis "Über unendliche algebraische Zahlkörper" [Stiemke, 1925] in the summer of 1914 but he died in the First World War and the thesis 53 For the "race" between the English invariant theorists and the German ones in proving this theorem, which in the literature often is referred to as Gordan's Theorem, see [Crilly, 1986[Crilly, , 1988 and [Parshall, 1989]. 54 In [Parshall, 1989] there is a discussion of the problems involved.…”

“…54 In [Parshall, 1989] there is a discussion of the problems involved. 55 See [Parshall, 1989] and [Crilly, 1986[Crilly, , 1988 for a discussion of the history of invariant theory, especially the differences between the English and the German approach.…”

Minimal Integrity Bases of Invariants of Second Order Tensors in a Flat Riemannian Space

“…It was initiated by Gauss [11]. Cayley [2,3] and Hilbert [8] made fundamental contributions to this development. In the twentieth century, tensor function representation theory was further developed, and found important applications in theoretical and applied mechanics.…”

About Gordan’s Algorithm for Binary Forms

“…About forty years later, Boole [11] established the main purpose of what has become today classical invariant theory. Cayley [23,24] deeply investigated this field of research and developed important tools still in use nowadays, such as the Cayley Omega operator. During about fifteen years (until Cayley's seventh memoir [20] in 1861) the English school of invariant theory, mainly led by Cayley and Sylvester, developed important tools to compute explicit invariant generators of binary forms.…”