I had often surprised our friend sitting, in the evening, by the light of a candle, with his elbows on the table and his head between his hands, meditating at great length in front of a big exercise-book crammed with cabalistic signs. From time to time, when an idea came to him, he would take his pen and hastily put down a line of writing wherein letters, large and small, were grouped without any grammatical sense. The letters x and y often recurred, intermingled with figures. Every row ended with the sign of equality and a naught. Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a naught. Page after page was filled in this queer fashion, each line winding up with 0. “What are you doing with all those rows of figures amounting to zero?” I asked him one day. The mathematician gave me a leery look, picked up in barracks. A sarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many naughts did not, however, take an unfair advantage of his superiority. He told me that he was working at analytical geometry. The phrase had a strange effect upon me. I ruminated silently to this purpose: there was a higher geometry, which you learnt more particularly with combinations of letters in which x and y played a prominent part. How would the alphabetical signs, arranged first in one and then in another manner, give an image of actual things, an image visible to the eyes of the mind alone? It beat me. “I shall have to learn analytical geometry some day,” I said. “Will you help me?” “I’m quite willing,” he replied, with a smile in which I read his lack of confidence in my determination. No matter: we struck a bargain that same evening. We would together break up the stubble of algebra and analytical geometry, the foundation of the mathematical degree; we would make common stock: he would bring long hours of calculation, I my youthful ardour. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.