It so happens that one df
the greatest mathematical
discoveries of all times
was guided by physical
intuition.
—George Polya, on
Archimedes' discovery of
integral calculus
Back in the Soviet Union in the early 1970s, our undergraduate class—about forty mathematics and physics sophomores—was drafted for a summer job in the countryside. Our job included mixing concrete and constructing silos on one of the collective farms. My friend Anatole and I were detailed to shovel gravel. the finals were just behind us and we felt free (as free as one could feel in the circumstances). Anatole's major was physics; mine was mathematics. Like the fans of two rival teams, each of us tried to convince the other that his field was superior. Anatole said bluntly that mathematics is a servant of physics. I countered that mathematics can exist without physics and not the other way around. Theorems, I added, are permanent. Physical theories come and go. Although I did not volunteer this information to Anatole, my own reason for majoring in mathematics was to learn the main tool of physics—the field which I had planned to eventually pursue. in fact, the summer between high school and college I had bumped into my high school physics teacher, who asked me about my plans for the Fall. “Starting on my math major,” I said. “What? Mathematics? You are nuts!” was his reply. I took it as a compliment (perhaps proving his point).