Epistemological aspects of modern painting

The aim of the paper is to analyse the geometrical aspects of a series of m odern paintings and to show the parallel between them and the development o f modern geometry. It starts with El Greco, offering a geometrical explanat ion of his painting the figures in a prolonged manner. Further the analogy between the impressionist way of creating space (in works of Turner, Monet and Seurat) and the geometrical idea of Cayley to use projective space as a basis for non-Euclidean geometry is reconstructed. Next the paper describe s the parallel between the creation of space in the paintings of Cezanne an d Picasso and the concept of space in algebraic topology. In conclusion, th e paper deals with the analogy between Kandinski's abstract paintings and t he set-theoretical foundations of geometry.