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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Here’s Terry Tao (Fields Medalist and outstanding math communicator) on that: https://mathoverflow.net/questions/38639/thinking-and-explaining/38882#38882 …pic.twitter.com/DJeWYn76i6
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Replying to @Meaningness
I remember reading something like this from Einstein as a 14- or 15 year old, & thinking "wow, maybe math isn't for me". By 24... it seemed totally obvious that of course this is how things work when you're seriously into something.
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Replying to @michael_nielsen @Meaningness
The strange thing is: this isn't really discussed publicly very often. Yet when I've talked to people who do creative work, especially with mathematics, a considerable fraction seem to have similarly unusual experiences, though the sensory modality may be different.
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Replying to @Meaningness @michael_nielsen
You studied under Rota? That's amazing! I came across a bunch of his writing as a freshman in college during the phase where I was heavily into combinatorics and really loved it.
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Replying to @QiaochuYuan @michael_nielsen
Yes I did graduate seminars in category theory and universal algebra with him. Those are dubious topics but I learned a ton about math at the informal meta level from him.
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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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