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

One of the characteristics of successful scientists is having courage. Once you get your courage up and believe that you can do important problems, then you can. If you think you can't, almost surely you are not going to.

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.

In mathematics we do not appeal to authority, but rather you are responsible for what you believe.

If you don't work on important problems, it's not likely that you'll do important work.

Computer scientists stand on each other's feet.

It may be said "In research, if you know what you are doing, then you shouldn't be doing it." In a sense, if the answer turns out to be exactly what you expected, then you have learned nothing new, although you may have had your confidence increased somewhat.