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10 Lessons I Wish I Had Been Taught

By Gian-Carlo Rota at MIT, April 20 , 1996 on the occasion of the Rotafest. sourcecached (pdf)

The talk was delivered on the occasion of the Rotafest at MIT in April, 1996. However, this applies to life in general and holds key to some of the best lessons one can learn for a more meaningful life.

Here is the summarized version;

  1. Lecturing -- Be as direct as possible.
  2. Blackboard Technique -- Be clear and conscise.
  3. Publish the same result several times -- Most successful endeavors are iterations upon your previous work, keep iterating.
  4. You are more likely to be remembered by your expository work -- Try to be an expert in one specialization first. You can become a generalist once you master one masterpeice.
  5. Every mathematician has only a few tricks -- Everyone has specialized skills, there's fame in using them to their fullest potential to explore many areas.
  6. Do not worry about your mistakes -- There are two kinds of mistakes - (i) fatal mistakes that destroy a theory, (ii) but there are also contingent ones, which are useful in testing the stability of a theory.
  7. Use the Feynman method -- -- Keep a dozen of your favorite problems constantly present in your mind. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps.
  8. Give lavish acknowledgments -- Be generous with Credit To Others no matter how small.
  9. Write informative introductions -- Summarize everything clearly and as long as is necessary: show your work second.
  10. Be prepared for old age -- Your position as an authority will change abruptly. Someonoe will come along that is faster, better, stronger than you. Do not try to compare, compete, and validate against others.