Many fascinating reply threads! “How to actually do math” is taboo for some reason; there’s almost nothing written about it. You have to get the secret oral transmission. Can we use the interwebs to break that code of silence?https://twitter.com/Meaningness/status/1190039312794079234 …
So… yes, communicating tacit knowledge is hard, and best done one-on-one through apprenticeship. (As it happens I’ve written a lot about that in other contexts here and there on the web!)
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But the fact that so many people find the explanations of Rota, Thurston, and Tao massively helpful suggests that it’s possible and worth attempting. Those guys are all exceptional but they can’t be the only ones capable of communicating SOME of it.
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I did a graduate seminar with Rota and mostly he just taught stuff straight, but the rare times he’d take five minutes to go meta and explain principles and how to think about things were SO valuable. All obvious in retrospect and not esoteric. Would be easy to put in writing.
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