Wed Sep 20, 2017
234 Moses Hall, 6–7:30 PM
|Working Group in the History and Philosophy of Logic, Mathematics, and Science
Douglas Marshall (Carleton College)
Impurity of Methods: Finite Geometry in the Early Twentieth Century
My talk aims to assess the reasonableness of various demands for purity of methods in mathematics by means of a historical case study of finite geometry in the early twentieth century. Work done in the foundations of algebra from 1900-1910 paved the way for corresponding advances in finite geometry. In particular, a geometric theorem on finite projective planes (Veblen and Bussey, 1906) was proved only with the help of an algebraic theorem on finite division rings (Wedderburn, 1905; Dickson 1905). In later years, several attempts were made to find a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem, none of them entirely successful (Segre, 1958; Tecklenberg 1987). Given that it has already been proved, what exactly would be accomplished by the discovery of a “pure” or “purely geometric” proof of Veblen and Bussey’s theorem? What considerations favor or disfavor the devotion of research effort to a purely geometric development of finite geometry?