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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I agree with what
@DRMacIver is saying here. Decompiling internal representations is a different (and arguably more difficult!) skill from developing and using them, a given skilled mathematician is not necessarily that good at it, and may believe it to be pointless.5 replies 1 retweet 15 likes -
David Chapman Retweeted Laurens Gunnarsen
Yes, although, why are mathematicians so much less willing to do this than masters in other fields with tacit knowledge?https://twitter.com/MathPrinceps/status/1189946692889534464 …
David Chapman added,
Laurens Gunnarsen @MathPrincepsReplying to @Meaningness @DRMacIverHonestly, 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?2 replies 1 retweet 2 likes -
I'm not sure how true that is, but stipulating it: a) There are a surprising number of mathematical cranks lurking around math departments/the internet who will happily waste your time without understanding a thing.
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Replying to @St_Rev @Meaningness and
b) Internal representations don't necessarily transfer. If I mostly do homological algebra with kinesthetic representations, and you think syntactically, I'm not sure what I can tell you. "uh so this is like a string of p-1 red beads and...wait the _string_ is red, and..."
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Ineffability, too, is a convenient excuse. People have found ways to communicate the subtlest of ideas and experiences, when sufficiently determined to do so. Perhaps not perfectly, perhaps not without loss -- but in ways that vastly simplify the learning process.
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It is also crucially important to remember that more can be learned than can be taught. This is perhaps the key truth of tacit knowledge transmission: the project is, for perhaps somewhat mysterious reasons, often more successful than it has any right to be. Patience is key.
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