Algebra reverses the relative importance of the factors in ordinary language. It is essentially a written language, and it endeavors to exemplify in its written structures the patterns which it is its purpose to convey. The pattern of the marks on paper is a particular instance of the pattern to be conveyed to thought. The algebraic method is our best approach to the expression of necessity, by reason of its reduction of accident to the ghostlike character of the real variable.

Culture is activity of thought, and receptiveness to beauty and humane feeling. Scraps of information have nothing to do with it. A merely well informed man is the most useless bore on God's earth.

In the history of the world the prize has not gone to those species which specialized in methods of violence, or even in defensive armor. In fact, nature began with producing animals encased in hard shells for defense against the ill of life. But smaller animals, without external armor, warm-blooded, sensitive, alert, have cleared those monsters off the face of the earth.

It is natural to think that an abstract science cannot be of much importance in affairs of human life, because it has omitted from its consideration everything of real interest.

It requires a very unusual mind to undertake the analysis of the obvious.

It must be admitted that there is a degree of instability which is inconsistent with civilization. But, on the whole, the great ages have been unstable ages.

The great achievements of the past were the adventures of the past. Only the adventurous can understand the greatness of the past.