What is true is that few mathematics professors are willing to confess publicly their private heuristics and intuitions; as Grothendieck once famously lamented, a perverse taboo among them seems to seal their lips on these matters, which, as Leibniz correctly argued, matter most.
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2 replies 1 retweet 17 likes -
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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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 -
Replying to @St_Rev @Meaningness and
A comparison can be made here with improvising on a musical instrument – from personal experience of both. My experience is that the focussed state of mind achieved is very similar.
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Of course there are irreducibly personal aspects of any artistic practice, which stubbornly elude direct communication to others. But just because you can't teach these things doesn't mean that no one can learn them. Apprentices routinely learn things their masters can't teach.
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Replying to @MathPrinceps @bitswrangler and
Nota bene:http://bit.ly/1X1QmZy
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