"We now come to a decisive step of mathematical abstraction: we forget about what the symbols stand for... need not be idle; there are many operations which he may carry out with these symbols, without ever having to look at the things they stand for."

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

“This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind.”

“The rapid development of science... has, as it were, burst its old shell, now become too narrow.”

“We cannot hope to give here a final clarification of the essence of fact, judgement, object, property; this task leads into metaphysical abysses; about these one has to seek advice from men whose name cannot be stated without earning a compassionate smile—e.g. Fichte.”

“After Riemann had made known his discoveries, mathematicians busied themselves with working out his system of geometrical ideas formally; chief among these were Christoffel, Ricci, and Levi-Civita. Riemann... clearly left the real development of his ideas in the hands of some subsequent scientist whose genius as a physicist could rise to equal flights with his own as a mathematician. After a lapse of seventy years this mission has been fulfilled by Einstein.”

“The scene of action of reality is not a three-dimensional Euclidean space but rather a four-dimensional world, in which space and time are linked together indissolubly. However deep the chasm may be that separates the intuitive nature of space from that of time in our experience, nothing of this qualitative difference enters into the objective world which physics endeavors to crystallize out of direct experience. It is a four-dimensional continuum, which is neither "time" nor "space". Only the consciousness that passes on in one portion of this world experiences the detached piece which comes to meet it and passes behind it as history, that is, as a process that is going forward in time and takes place in space.”