12 Life Lessons From Mathematician and Philosopher Gian-Carlo Rota

10 Lessons of an MIT Education: Gian-Carlo Rota

• Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of cows, moving slowly in the direction they are being driven towards.

• Never run over time → After fifty minutes (one microcentury as von Neumann used to say), everybody’s attention will turn elsewhere even if we are trying to prove the Riemann hypothesis. One minute over time can destroy the best of lectures.

• Relate to your audience → As you enter the lecture hall, try to spot someone in the audience whose work you have some familiarity with. Quickly rearrange your presentation so as to manage to mention some of that person’s work. “everyone in the audience has come to listen to your lecture with the secret hope of hearing their work mentioned.”

  I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else. One day I tried an experiment. After writing a rather long paper, I began to draft a thorough bibliography. On the spur of the moment I decided to cite a few papers which had nothing whatsoever to do with the content of my paper to see what might happen.

  Somewhat to my surprise, I received letters from two of the authors whose papers I believed were irrelevant to my article. Both letters were written in an emotionally charged tone. Each of the authors warmly congratulated me for being the first to acknowledge their contribution to the field.

• Give people something to take home →

  When we have a conversation, read a book, or listen to a talk, the sad fact is that we are unlikely to remember much of it even a few hours later, let alone years after the event. Even if we enjoyed and valued it, only a small part will stick in our memory.

  So when you’re communicating with people, try to be conscious about giving them something to take home. Choose a memorable line or idea, create a visual image, or use humor in your work.

• Make sure the blackboard is spotless → “By starting with a spotless blackboard, you will subtly convey the impression that the lecture they are about to hear is equally spotless.” Presentation matters. The way our work looks influences how people perceive it. Taking the time to clean our equivalent of a blackboard signals that we care about what we’re doing and consider it important.

• Make it easy for people to take notes → What we write on the blackboard should correspond to what we want an attentive listener to take down in his notebook. It is preferable to write slowly and in a large handwriting, with no abbreviations. Those members of the audience who are taking notes are doing us a favor, and it is up to us to help them with their copying.

• Share the same work multiple times → Explaining the same subject again and again for years allowed him to keep improving it until he was ready to publish. Rota notes, “No wonder the final version was perfect.”

• The mathematical community is split into small groups, each one with its own customs, notation, and terminology. It may soon be indispensable to present the same result in several versions, each one accessible to a specific group; the price one might have to pay otherwise is to have our work rediscovered by someone who uses a different language and notation, and who will rightly claim it as his own.

• You are more likely to be remembered for your expository work → Rota realized that many of the mathematicians he admired the most were known more for their work explaining and building upon existing knowledge, as opposed to their entirely original work. Their extensive knowledge of their domain meant they could expand a little beyond their core specialization and synthesize charted territory.

• Don’t worry about small mistakes → There are two kinds of mistakes. There are fatal mistakes that destroy a theory; but there are also contingent ones, which are useful in testing the stability of a theory.

• Use Feynman’s method for solving problems → Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. 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. Every once in a while there will be a hit, and people will say: ‘How did he do it? He must be a genius!

• Write informative introductions →

• The world and your career are unpredictable, so you are better off learning subjects of permanent value.

• What matters most is the ambiance in which the course is taught

• By and large, “knowing how” matters more than “knowing what.”