Knowledge and productivity are like compound interest. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity. I don`t want to give you a rate, but it is a very high rate. Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.

It is better to do the right problem the wrong way than the wrong problem the right way.

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".

Given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.

If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you dont quite know what problems are worth working on.

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.

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