Chapter 4, Partial Solutions and the Provisional Elimination of Elements of Complexity, part 2

If she forgot again, the teacher might say,—I think I should be inclined to say:—“If you cannot remember not to distract the class by talking about what is irrelevant to the business on hand, I shall have to request you to keep outside my class-room till you can.” In an orderly school the teachers have time to be polite, and it is their business to set the example of being so. In history, especially such history as that of half-civilised countries 3000 years ago, teachers were under too much strain to cultivate either a polite manner of saying things, or, what is of far more consequence, that genuine intellectual courtesy which is the absolutely necessary condition for the development of any really perfect mathematical system. The great Hebrew Algebra, therefore, never became quite perfect. It was only rough hewn, so to speak; and its manners and customs were rough too. The teachers had ways of saying, “Hold your tongue, or else go out of my class-room,” which perhaps we should now call bigoted and brutal. But what I want you to notice is that “Hold your tongue, or get out of my class-room,” is not the same thing as “My hypothesis is right, and yours ought not to be tried anywhere.”

This latter is contrary to the essential basis of Algebra, viz., a recognition of one's own ignorance. The other, a rough way of saying “Get out of my class-room,” is only contrary to that fine intellectual courtesy which is essential to the perfection of mathematical method.