At that time, the college in which, two years before, I had made my first appearance as a teacher, had just halved the size of its classes and largely increased its staff. The newcomers all lived in the building, like myself, and we had our meals in common at the principal's table. We formed a hive where, in our leisure time, some of us, in our respective cells, worked up the honey of algebra and geometry, history and physics, Greek and Latin most of all, sometimes with a view to the class above, sometimes and oftener with a view to acquiring a degree. The university titles lacked variety. All my colleagues were bachelors of letters, but nothing more. They must, if possible, arm themselves a little better to make their way in the world. We all worked hard and steadily. Iwas the youngest of the industrious community and no less eager than the rest to increase my modest equipment.
Visits between the different rooms were frequent. We would come to consult one another about a difficulty, or simply to pass the time of day. I had as a neighbor, in the next cell to mine, a retired quartermaster who, weary of barrack life, had taken refuge in education. When in charge of the books of his company he had become more or less familiar with figures; and it became his ambition to take a mathematical degree. His cerebrum appears to have hardened while he was with his regiment. According to my dear colleagues, those amiable retailers of the misfortunes of others, he had already twice been plucked. Stubbornly, he returned to his books and exercises, refusing to be daunted by two reverses.
It was not that he was allured by the beauties of mathematics, far from it; but the step to which he aspired favored his plans. He hoped to have his own boarders and dispense butter and vegetables to lucrative purpose. The lover of study for its own sake and the persistent trapper hunting a diploma as he would something to put in his mouth were not made to understand or to see much of each other. Chance, however, brought us together.
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 nought. Next came more reflection, with closed eyes, and a fresh row of letters arranged in a different order and likewise followed by a nought. 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. Asarcastic droop in the corner of his eye showed how he pitied my ignorance. My colleague of the many noughts 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. When my next-door neighbor reflected so long, clutching his forehead between his hands, he was trying to discover the hidden meaning of his own hieroglyphics; he saw the ghostly translation of his sums dancing in space. What did he perceive?
How would the alphabetical signs, arranged first in one and then in another manner, give an image of the 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 ardor. We would begin as soon as I had finished with my arts degree, which was my main preoccupation for the moment.
