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Tom_Breton comments on The Crackpot Offer - Less Wrong
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It seems to be a common childhood experience on this list to have tried to disprove famous mathematical theorems.
Me, I tried to disprove the four-color map conjecture when I was 10 or 11. At that point it was a conjecture, not a theorem. I came up with a nice moderate size map that, after a apparently free initial labelling and a sequence of apparently forced moves, required a fifth color.
Fortunately the first thing that occured to me was to double-check my result, and of course I found a 4-color coloring.
I did exactly the same thing.
I also discovered shortly thereafter that I could force an n-coloring if I allowed discontinuous regions, which might seem trivial... except that real nations on real maps are sometimes discontinuous (Alaska, anyone?).