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I watched this the other day. I was left wondering one big question. Why does this need to be solved? Would that even change anything?
It's so someone can use it as a coding challenge in a technical interview, of course.
Earlier quoted context omitted.
I didn't think that anyone believed that number theory was consistent and complete. [0] https://en.wikipedia.org/wiki/Peano_axioms
That's nitpicky and missing the point. If the only problem with a theory is that it's been reduced Goedel-style to an axiomatic base, then most people would argue we "understand it". Needless to say 3x+1 does not follow in any kind of obvious way from Peano. It's emergent behavior that flies in the face of axiomatic understanding. And that's why it's interesting.