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Replying to @Meaningness @DRMacIver
An interesting justification for silence on these matters -- and, curiously, one more common among the best elder mathematicians -- is that keeping mum prevents talented young people from wasting their time in hero-worship-motivated yet doomed and misguided attempts at imitation.
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Replying to @MathPrinceps @Meaningness
My suspicion is that it is more commonly just vanilla curse of knowledge and people not consciously knowing things that they have very heavily internalised.
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I very rarely find that people are able to articulate most of the heuristics and intuitions they use constantly unless you walk them through it - it requires much more metacognition than most people routinely deploy.
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Replying to @DRMacIver @Meaningness
It requires more motivation than most people usually feel -- and more time and effort that most people are prepared to devote to it. Which is especially odd, when you reflect that, with this particular form of wealth as with all others, you can't take it with you.
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Replying to @MathPrinceps @DRMacIver
OK, here’s the plan. We deploy elite special forces units to capture all the Fields Medalists and take them in black helicopters to a purpose-built underground fortress on Svalbard, and use secret CIA psy-op interrogation techniques to force them to reveal what they know
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Replying to @Meaningness @DRMacIver
Honestly, what impresses me most is how profoundly the attitudes of great masters vary from art to art. Itzhak Perlman, Emanuel Ax, Midori -- all have put a great deal of effort into transmitting their tacit knowledge. The number of great mathematicians who do likewise?
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Replying to @MathPrinceps @DRMacIver
Zero, I think. Rota and Thurston are partial exceptions. Any others?
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Oh, and Terry Tao.
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Polya, surely?
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I propose the following crude estimate of the success of a mathematician-mentor: Take the total number of his/her known descendants, divide it by the number of his/her PhD students, and divide that by the number of years since the first of these completed his/her PhD.
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Replying to @MathPrinceps @pozorvlak and
By this estimate, Lefschetz far outstrips Polya.
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Replying to @MathPrinceps @pozorvlak and
Of course the problem here is that there should be a correction for the eminence/influence of a mathematician-mentor immediate PhD students, as well as for the overall quality of his/her descendants. Not easy to get all this right. Might be fun to think about, though.
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End of conversation
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