Von Neumann and lattice theory

Introduction. John von Neumann's brilliant mind blazed over lattice theory like a meteor, during a brief period centering around 1935-1937. With the aim of interesting him in lattices, I had called his attention, in 1933-1934, to the fact that the sublattice generated by three subspaces of Hubert space (or any other vector space) contained 28 subspaces in general, to the analogy between dimension and measure, and to the characterization of projective geometries as irreducible, finite-dimensional, complemented modular lattices.