(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
A friend was talking about digital physics and talking about stationary objects (like, you’re evolving a cellular-automata discretization of the Schrodinger equation & some regions stay constant over time)
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Replying to @s_r_constantin @michael_nielsen
And I said “you’d need boundary conditions for that, there wouldn’t be any stationary objects like that in Euclidean space”, mostly from just visualizing what you’d need to have a standing wave in a pool or something
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Replying to @s_r_constantin @michael_nielsen
But I think where this applies it depends on how you discretize the differential equation & in the case where it’s definitely true it’s a direct consequence of Liouville’s theorem, so not that cool.
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Replying to @s_r_constantin
That doesn't sound trivial to me! But I guess I can imagine a harmonic analyst going "of course!" Your PhD was harmonic analysis, or something close, right? It's a fun observation!
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Replying to @michael_nielsen @s_r_constantin
I love Thurston's MathOverflow bio:pic.twitter.com/omDhJ0Pxis
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Replying to @michael_nielsen
Thurston had such a kind & creative attitude. (My first real encouragement in math came from one of his former students, who was also “sparkly” and enthusiastic and made topology accessible.)
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Speaking of visual proofs! I still don’t know how Thurston could do proof-by-picture in four dimensions. If there’s anyone in math I suspect of having a bit of chemical aid...
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