Mathematics has always struck me as incredible, how on the one hand it produces sophisticated structures of great beauty, and, on the other hand, this very beauty tells us profound things about the world around us.

My life as a mathematician probably dates from two significant experiences in early high school in Almonte (1957). 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 - that given equal angles of incidence and reflection, a sphere (I used a circle) simply didn't have that property. 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 except that he didn't ask me what the equation of the surface actually was. To my dismay I did not even ask myself that and it was years later before I revisited that question. Why on earth did I not take that "obvious" next step? Perhaps it didn't occur to me that I was capable of answering such a question. I suspect that too often that places an unnecessary limit on many of us.

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 at great length with lots of diagrams. She smiled and simply 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.