(Answer only if you’ve ever derived a mathematical proof.) Have you ever “seen” a proof of a theorem in an intuitive flash of insight?
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Replying to @michael_nielsen
It happened to me for the first time last week (turned out to be d. though) and it kind of freaked me out at the time since I assumed only geniuses could do that; hence trying to find out roughly how common it is.
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Replying to @s_r_constantin
Oh, that's interesting! What was the theorem?
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Replying to @michael_nielsen @s_r_constantin
(Upon reflection, I'm not sure there's much different between b and d. If you're far more comfortable with a subject than your peers, then you'll see in flash things which seem trivial to you, but which quite reasonably seem very insightful to them.)
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Replying to @michael_nielsen @s_r_constantin
I took “see in a flash” to be “you’ve been working on this thing for ages and not solving it and then you have some nonordinary experience where you get the proof more or less instantly for no obvious reason” in which case not trivial (at least not for you!).
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Replying to @Meaningness @s_r_constantin
The breakdown between "yes, after a prolonged period of work" and "yes, almost immediately I understood the problem" is interesting. The latter is usually, IME, a special case of the former, where you luckily happened to do most of the work beforehand.
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Replying to @michael_nielsen @Meaningness
I meant “trivial” in the sense of “you may have found it quite difficult but it’s a well known fact that your colleagues/supervisors/teachers think is obvious”
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Replying to @s_r_constantin @Meaningness
This discussion is reminding/emphasizing (to) me that the word "trivial" is rather interesting and nuanced (and maybe even quite deep???) in mathematics!
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I tried to explain this to my spouse (who is self-teaching undergrad math) about a week ago. It’s highly contextual, at least…
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