WHAT I wish to say to you today is a general reflection on the subject of high school algebra. As a layman both in mathematics and in secondary school teaching, I can speak only from two lay points of view—that of the pupil, which meets you at one end of your activity, and that of the philosopher, which you encounter at the other. Consequently, I shall begin by talking about the futility and barrenness of algebra, and end, I hope, by reviewing with you its importance, interest, and charm. For it is a peculiarity of the subject that an uninitiate mind can usually see nothing in it but a dry, lifeless discipline, whereas the adept sees in it the apotheosis of human reason.