I think I may not remember all the advice I've received since I generally either take it or dismiss it immediately. Here are four I actually took to heart and pass on.
  1. Marry up. [My Dad]
  2. If you want to teach college mathematics, study mathematics. You can learn how to teach it only after you really know the subject. [paraphrase of advice from Dr. Phil Almes when I was contemplating my graduate program]
  3. You can't talk your way out of a problem you behaved your way into. [Dr. Herb Grover]
  4. First rate people hire first rate people; second rate people hire third rate people. [Dr. Herb Grover]