i love how so many maths problems are like

"how many polygons can you draw, without lifting your pen, on the surface of a sphere?": trivial, proven by hand
"...of any 3-dimensional shape?" trivial, proven by hand
"...of any 4-dimensional shape?" trivial, proven by hand
"...of any 5-dimensional shape?" extremely complex, proven by computer search using a novel method in 2011
"...of any 6-dimensional shape?" moderately complex, proven by computer search in 1996
"...of any 7-dimensional shape?" unproven and likely beyond the limits of present day mathematics. it is trivially provable by hand that you can draw any triangle, however

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