The propositions of mathematics are devoid of all factual content; they convey no information whatever on any empirical subject matter..

The propositions of mathematics have, therefore, the same unquestionable certainty which is typical of such propositions as "All bachelors are unmarr….

...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometri….

The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame ….

A geometrical theory in physical interpretation can never be validated with mathematical certainty ... ; like any other theory of empirical science, ….