Topology

“Presentday topology consists of two distinct parts: point set topology and algebraic topology. The first has mainly been the prerogative of Poland plus a strong American component: the school of R. L. Moore (of Austin, Texas).”

“If geometry is dressed in a suit coat, topology dons jeans and a T-shirt.”

“Topologists are interested not only in finite-dimensional spaces (for example, subspaces of R), but also in infinite-dimensional ones, such as the spaces occurring in quantum field theory.”

“In these days the angel of topology and the devil of abstract algebra fight for the soul of each individual mathematical domain.”