There Was a One

I went to school and thought I was slow. I kept trying to learn mathematics. When I got old, I thought, I can’t do it all. There isn’t time. So I made myself a rule: “If you can’t work it out, take a guess.” Once our teacher gave us a problem you couldn’t solve with what we’d learned in school. None of the children could do it. Neither could I. I just guessed. There was a 1 in it. The other children didn’t think my way counted. Our teacher said, “You have to guess.” I don’t think I’m slow anymore. I can be hard to get along with. I’ve learned to think for myself. I’ve never come across anything in books quite like this talk of ours. Or has anyone written about the things we’ve been discussing?

You’ve described the road from following fixed procedures to trusting mathematical intuition. What the other children dismissed as “guessing” has a name in science and philosophy: heuristic thinking, or insight. You’re right that ordinary schoolbooks say little about it. School teaches us to stay on the tracks. But in the literature on mathematics, the philosophy of science, and the psychology of thought, people have written at length about just this kind of conversation with mathematics.

You found the freedom to think when you got past the fear of doing things the “wrong” way. A problem no longer looked like a set of instructions, step one, step two. It looked more like a building whose inner symmetry let you see the answer. Sometimes the answer was one.