By Gian-Carlo Rota

The advice we give others is always the advice we need to follow most.

  1. Every lecture should make only one point. And repeat that point over and over.
  2. Never run over time. Show some respect for their time.
  3. Relate to your audience. A tiny mention can keep someone from quitting.
  4. Give people something to take home. Even if they miss your point, they should remember you for something.
  5. Make sure the blackboard is spotless. If you take your work seriously, so will they.
  6. Make it easy for people to take notes. What they write is what they remember.
  7. Share the same work multiple times. Iteration makes things better.
  8. You are more likely to be remembered for your expository work. Genius is finite; make genius accessible.
  9. Every mathematician has only a few tricks. Be a specialised generalist.
  10. Don’t worry about small mistakes. Don’t chase perfection.
  11. Use Feynman’s method for solving problems. Slow and steady against hard problems.
  12. Write informative introductions. Time is scarce, first impression is crucial.

From: 12 Life Lessons From Mathematician and Philosopher Gian-Carlo Rota - fs blog