School came to bore me. It took up far too much time which I would rather have spent drawing battles and playing with fire. Divinity classes were unspeakably dull, and I felt a downright fear of the mathematics class. The teacher pretended that algebra was a perfectly natural affair, to be taken for granted, whereas I didn’t even know what numbers really were.
They were not flowers, not animals, not fossils; they were nothing that could be imagined, mere quantities that resulted from counting. To my confusion these quantities were now represented by letters, which signified sounds, so that it became possible to hear them, so to speak. Oddly enough, my classmates could handle these things and found them self-evident. No one could tell me what numbers were, and I was unable even to formulate the question.
To my horror I found that no one understood my difficulty. The teacher, I must admit, went to great lengths to explain to me the purpose of this curious operation of translating understandable quantities into sounds. I finally grasped that what was aimed at was a kind of system of abbreviation, with the help of which many quantities could be put in a short formula. But this did not interest me in the least.
I thought the whole business was entirely arbitrary. Why should numbers be expressed by sounds? One might just as well express a by apple tree, b by box, and x by a question mark, a, b, c, x, y, z were not concrete and did not explain to me anything about the essence of numbers, any more than an apple tree did.
But the thing that exasperated me most of all was the proposition: If a = b and b = c, then a = c, even though by definition a meant something other than b, and, being different, could therefore not be equated with &, let alone with c. Whenever it was a question of an equivalence, then it was said that a = a, b = &, and so on. This I could accept, whereas a = b seemed to me a downright lie or a fraud. I was equally outraged when the teacher stated in the teeth of his own definition of parallel lines that they met at infinity.
This seemed to me no better than a stupid trick to catch peasants with, and I could not and would not have anything to do with it. My intellectual morality fought against these whimsical inconsistencies, which have forever debarred me from understanding mathematics. Right into old age I have had the incorrigible feeling that if, like my schoolmates, I could have accepted without a struggle the proposition that a = &, or that sun = moon, dog = cat, then mathematics might have fooled me endlessly just how much I only began to realize at the age of eighty-four.
All my life it remained a puzzle to me why it was that I never managed to get my bearings in mathematics when there was no doubt whatever that I could calculate properly. Least of all did I understand my own moral doubts. ~Carl Jung, Memories Dreams and Reflections, Pages 27-28.