Two suggestions by Rota and Feynman on how to do science and math

Giancarlo Rota (1932-1999) was an Italian-born, then naturalized American, mathematician and philosopher. As happens to outstanding thinkers, in his late years he was often invited to give a speech on more or less everything he wanted. At the Rotafest organized in his honour at MIT he spelled out a list of suggestions for scientists1:

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. […] The advice we give others is the advice that we ourselves need.

There would be a lot to say on both the content of those suggestions and wheter the same pieces of advice that are valid for masters are also of great interest for all scientists. But for a change, let me cut this short and just present the two among them that I found the most interesting (one of which is in fact by the physicist Richard Feynman), leaving to the readers all extra-thinking.

5. Every mathematician has only a few tricks. A long time ago an older and well known number theorist made some disparaging remarks about Paul Erdös’ work. You admire Erdös contributions to mathematics as much as I do, and I felt annoyed when  the older mathematician flatly and definitively stated that all of Erdös work could be “reduced” to a few tricks which Erdös repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten.  But on reading the proofs of Hilbert’s striking and deep theorems in  invariant theory, it was surprising to verify that Hilbert’s proofs relied  on the same few tricks. Even Hilbert had only a few tricks!

7. Use the Feynman method. 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!”


Notes

1. This and following citations are taken from: Ten lessons I wish I had been thaught (presented at MIT on April 20, 1996, on the occasion of the Rotafest), in Giancarlo Rota, Indiscrete Thoughts,  Modern Birkhäuser Classics (1997), pages 195–203.

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