Ten Lessons I wish I had been Taught
Gian-Carlo Rota
MIT, April 20 , 1996 on the occasion of the Rotafest
Allow me to begin by allaying one of your worries. I will not spend the next half hour thanking you for participating in this conference, or for your taking time away from work to travel to Cambridge.
And to allay another of your probable worries, let me add that you are not about to be subjected to a recollection of past events similar to the ones I've been publishing for some years, with a straight face and an occasional embellishment of reality.
Having discarded these two choices for this talk, I was left without a title. Luckily I remembered an MIT colloquium that took place in the late fifties; it was one of the first I attended at MIT. The speaker was Eugenio Calabi. Sitting in the front row of the audience were Norbert Wiener, asleep as usual until the time came to applaud, and Dirk Struik who had been one of Calabi's teachers when Calabi was an undergraduate at MIT in the forties. The subject of the lecture was beyond my competence. After the first five minutes I was completely lost. At the end of the lecture, an arcane dialogue took place between the speaker and some members of the audience, Ambrose and Singer if I remember correctly. There followed a period of tense silence. Professor Struik broke the ice. He raised his hand and said: "Give us something to take home!" Calabi obliged, and in the next five minutes he explained in beautiful simple terms the gist of his lecture. Everybody filed out with a feeling of satisfaction.
Dirk Struik was right: a speaker should try to give his audience something they can take home. But what? I have been collecting some random bits of advice that I keep repeating to myself, do's and don'ts of which I have been and will always be guilty. Some of you have been exposed to one or more of these tidbits. Collecting these items and presenting them in one speech may be one of the less obnoxious among options of equal presumptuousness. The advice we give others is the advice that we ourselves need. Since it is too late for me to learn these lessons, I will discharge my unfulfilled duty by dishing them out to you. They will be stated in order of increasing controversiality.
Lecturing
Blackboard Technique
Publish the same results several times.
You are more likely to be remembered by your expository work.
Every mathematician has only a few tricks.
Do not worry about your mistakes.
Use the Feynmann method.
Give lavish acknowledgments.
Write informative introductions
Be prepared for old age.
https://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html