Social Science and Modernism : the Case of Karl Menger

ions”(Ibid). In his work in various kinds of abstract geometries, concerned with the properties of abstract structures involving lines and planes, curves and point-sets, Menger fell squarely in the development of what Jeremy Gray has described as the “modernist transformation” of mathematics over the period 1890-1930. This evolution marked the emergence in that discipline, as in painting and literature, of “an autonomous body of ideas, having little or no outward reference, placing considerable emphasis on formal aspects of the work and maintaining a complicated – indeed, anxious – rather than a naïve relationship with the day-to-day world” (2008, p.1). At the beginning of the century, says Gray, in line with the increased professionalization and autonomy of the discipline, mathematics underwent a decisive shift. This found expression in both ontology, with the emergence of new autonomous fields of mathematics, and epistemology, with an emphasis on formal proof and a distrust of naive intuition, especially in geometry. “The changes in mathematics