Sketched history: VC combinatorics, 1826 up to 1975

Abstract

The earliest published instance found of combinatorial quantities later occurring in the work of Vapnik and Chervonenkis was in a paper of Jakob Steiner in 1826. The next, still more pertinent occurrence foundwas inwork of Ludwig Schläfli done around 1850 but not published until 1901, after his death. The nineteenth century work was on subsets of Euclidean spaces cut by intersections of finitely many half-spaces. Then there is another long gap until a paper of T.M. Cover, who cited Schläfli, in 1965, preceding by a few years the landmark announcement by Vapnik and Chervonenkis in 1968 and longer paper of 1971. Further history is given about Steiner, Schläfli, and some of their contemporary mathematicians and about the initial reception of the Vapnik and Chervonenkis work.