This is also important (needs a separate thread). Deep proofs are often found in the shower (specifically—and what is it about showers that do the job?). The mode seems to be kinesthetic, approximately—also a long-evolved vertebrate function.https://twitter.com/St_Rev/status/1149775529802960898 …
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You might like this Terry Tao post about pre-rigorous, rigorous, and post-rigorous mathematics. https://terrytao.wordpress.com/career-advice/theres-more-to-mathematics-than-rigour-and-proofs/ … He makes an explicit comparison with Kohlberg’s stages. This is the familiar pre-systematic, systematic, meta-systematic trichotomy that I keep referring to.
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Yeah, I also came across this post in college and enjoyed it a lot. Good times. I never got to meet Rota but I did take a few classes from Richard Stanley, one of his students, who later wrote one of my grad school rec letters.
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