I have sometimes been laughed at when I have ventured the opinion that University students of mathematics ought to do original work in mathematics as part (and an important part) of their degree work. But this will not prevent me from maintaining that original work should be done by every scholar in a junior class of geometry. Of course in one sense this is a mere platitude, for every “problem” and “rider” requires for its solution original work on the part of the scholar. He or she that would solve a geometrical problem must “intend the mind continually” on it, like Sir Isaac Newton, and acquire the faculty of trying different points of view till the right one is found. For him or her, at any rate, the Pragmatists' test of truth is appropriate. He asks of every hypothesis “will it work?” and finds the answer by actual trial.