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.

Algebra is the intellectual instrument which has been created for rendering clear the quantitative aspects of the world.

The consequences of a plethora of half-digested theoretical knowledge are deplorable.

Mathematics, in its widest significance, is the development of all types of formal, necessary, deductive reasoning.

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

A great society is a society in which its men of business think greatly of their functions.

If a dog jumps into your lap, it is because he is fond of you; but if a cat does the same thing, it is because your lap is warmer.