Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you'll never notice the flaws; if you doubt too much you won't get started. It requires a lovely balance.

A parable: A man was examining the construction of a cathedral. He asked a stone mason what he was doing chipping the stones, and the mason replied, "I am making stones." He asked a stone carver what he was doing. "I am carving a gargoyle." And so it went, each person said in detail what they were doing. Finally he came to an old woman who was sweeping the ground. She said. "I am helping build a cathedral." ...Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture.

I have tried, with little success, to get some of my friends to understand my amazement that the abstraction of integers for counting is both possible and useful. Is it not remarkable that 6 sheep plus 7 sheep makes 13 sheep; that 6 stones plus 7 stones make 13 stones? Is it not a miracle that the universe is so constructed that such a simple abstraction as a number is possible? To me this is one of the strongest examples of the unreasonable effectiveness of mathematics. Indeed, I find it both strange and unexplainable.

What are the important problems of your field?

Good teachers deserve apples; great teachers deserve chocolate. A favorite quotation, written in calligraphy on his office door.

Does anyone believe that the difference between the Lebesgue and Riemann integrals can have physical significance, and that whether say, an airplane would or would not fly could depend on this difference? If such were claimed, I should not care to fly in that plane.

Most of the time each person is immersed in the details of one special part of the whole and does not think of how what they are doing relates to the larger picture. For example, in education, a teacher might say in the next class he was going to "explain Young's modulus and how to measure it," rather than, "I am going to educate the students and prepare them for their future careers".