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Regarding a few skills, Rota interestingly has similar advice for mathematicians: https://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html https:

Regarding a few skills, Rota interestingly has similar advice for mathematicians: https://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-lessons.html https://alumni.media.mit.edu/~cahn/life/gian-carlo-rota-10-l... "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 Erdos' work. You admire contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdos' work could be reduced to a few tricks which Erdos 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!"

parenthesis 5y ago
In that same article you quote there is also a bit about Feynman, that "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!" " I've come across this before, but it got reversed in my mind to: every time you come across an unsolved problem, try using all your standard tricks on it. Probably none will help. But perhaps eventually one will and you'll seem like a genius for thinking of applying that trick to that problem.

parenthesis 5y ago

In that same article you quote there is also a bit about Feynman, that "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!" " I've come across this before, but it got reversed in my mind to: every time you come across an unsolved problem, try using all your standard tricks on it. Probably none will help. But perhaps eventually one will and you'll seem like a genius for thinking of applying that trick to that problem.