Reprinted from "various scientific, literary, and philsophical journals." cf. Pref The human worth of rigorous thinking.--The human significance of mathematics.--The humanization of the teaching of mathematics.--The walls of the world; or, Concerning the figure and the dimensions of the universe of space.--Mathematical emancipations: dimensionality and hyperspace.--The universe and beyond: the existence of the hypercosmic.--The axiom of infinity: a new presupposition of thought.--The permanent basis of a liberal education.--Graduate mathematical instruction for graduate students not intending to become mathematicians.--The source and functions of a university.--Research in American universities.--Principia mathematica.--Concerning multiple interpretations of postulate systems and the "existence" of hyperspace.--Mathematical productivity in the United States.--Mathematics