The study of mathematics is apt to commence in disappointment.

A man really writes for an audience of about ten persons. Of course if others like it, that is clear gain. But if those ten are satisfied, he is content.

Rightness of limitation is essential for growth of reality.

Inventive genius requires pleasurable mental activity as a condition for its vigorous exercise. "Necessity is the mother of invention" is a silly proverb. "Necessity is the mother of futile dodges" is much closer to the truth. The basis of growth of modern invention is science, and science is almost wholly the outgrowth of pleasurable intellectual curiosity.

...the self-satisfied dogmatism with which mankind at each period of its history cherishes the delusion of the finality of existing modes of knowledge.

Life is complex in its expression, involving more than percipience, namely desire, emotion, will, and feeling.

The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.