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 …
I may be overgeneralizing from my personal experience. I wish I had had you as a mentor instead! I’m confident that your students’ experience is very different. That said, whenever I gripe about this, many people say “yes that’s how it is” and nearly never “not my experience!”
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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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