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benelliott comments on The Crackpot Offer - Less Wrong
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Demonstrated satisfactorily =/= 100% proven
Most things outside mathematics can never be proven, but many can easily be demonstrated satisfactorily.
The 4-colour theorem is not outside mathematics. I think I sort of understand what you mean by 'demonstrated satisfactorily' but in my experience such demonstrations aren't worth much, not only can they be wrong in principle, they are often wrong in practice. Mathematics is nothing if not counter-intuitive.