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I am intrigues by mathematical facts that are very easy to know to be true instinctually or with a verbal explanation but are very difficult to write proofs for.
A good example of this is the four color theorem.
@zevahs Its axiomatic not provable. We choose that particular convention simply because it is useful and ensures consistency with other patterns. See the exponent is a defined operator in principle we could define its behavior however we like, it just wont be too useful if we do.
@shibaprasad
I was wrong though in aaying it isnt provable. Only that it is provable from the axioms
@zevahs
