"Raise your quality standards as high as you can live with, avoid wasting your time on routine problems, and always try to work as closely as possible at the boundary of your abilities. Do this, because it is the only way of discovering how that boundary should be moved forward."
"Never tackle a problem of which you can be pretty sure that (now or in the near future) it will be tackled by others who are, in relation to that problem, at least as competent and well-equipped as you."
Before embarking on an ambitious project, try to kill it.
Avoid involvement in projects so vague that their failure could remain invisible: such involvement tends to corrupt one's scientific integrity.
Striving for perfection is ultimately the only justification for the academic enterprise; if you don't feel comfortable with this goal --e.g. because you think it too presumptuous--, stay out!
"Knowledge and productivity are like compound interest." Given two people of approximately the same ability and one person who works ten percent more than the other, the latter will more than twice out-produce the former. 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 it is very much like compound interest. 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."
Along those lines at some urging from John Tukey and others, I finally adopted what I called "Great Thoughts Time." When I went to lunch Friday noon, I would only discuss great thoughts after that. By great thoughts I mean ones like, "What will be the role of computers in all of AT&T?", "How will computers change science?".
"I used to have this conversation with the head of HP Labs, saying that if we are not failing in two-thirds of the things we try, then we are not taking enough risks."