This is really slick, but it was a bit of a puzzle for me trying to turn it into a paper proof! After a few minutes, I realized that you can do it by induction on the number of vertices: it's trivial for n = 3, and if it holds for n - 1, slice off a corner and see what happens.https://twitter.com/ThingsWork/status/1121857148068065280 …
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I think his argument goes way too far but it's certainly true that I took years of graduate algebraic geometry without any damn idea what it was for.
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I do sometimes pick up Ravi Vakil's algebraic geometry notes. They're great. But they get really hard fast even if it's probably the friendliest intro to real alg geometry.
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I'm an algebraist and I have a decent handle on group theory, representation theory, algebraic topology etc. But I self-studied Hartshorne before my PhD program and took a lot of courses in algebraic geometry during, and never understood the point.
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Years after all that I picked up https://homepages.warwick.ac.uk/staff/Miles.Reid/MA4A5/UAG.pdf … and finally got an inkling of what it was actually for.
End of conversation
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.