My life as a mathematician probably dates from two significant experiences in early high school in Almonte. The first happened in physics class when we were using a convex mirror to focus the sun's rays at a single point and I asked what the shape of the mirror was and Mr. Suter told me it was spherical. That night at home I played with the geometry of that and produced an argument that he was wrong. I didn't know what the true shape was, but I had proved it couldn't be a piece of a sphere. I was immensely pleased with myself and borrowed my father's typewriter, typed the argument out and presented it to Mr. Suter with a flourish. I don’t recall what he said but I didn't need anything else.

A few weeks later Miss Whiessel informed us that it was impossible to trisect an angle with ruler and compass. This time there were many nights, one after the other, sprawled across the kitchen table convinced that I would also prove her wrong. Once I thought I had it and wrote it out. She smiled and gave it back to me and told me it must be wrong. I asked her to show me the flaw and she replied that I could do that just as well as she could.