Abstraction (mathematics)

“Geometry can in no way be viewed... as a branch of mathematics, instead, geometry relates to something already given in nature, namely, space. I... realized that there must be a branch of mathematics which yields in a purely abstract way laws similar to those of geometry.”

“The word element is a term which frequently occurs in philosophy. It signifies any of those parts of an object into which it is or may be separated by analysis; and which, therefore, may be separately considered by abstraction. ...A notion of a thing may be formed by the composition of mathematical parts, and such a composition in its relation to parts, and such a composition in relation to the object might be spoken of as mathematical conception.”

“Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.”