[alexmlamb]

I don't think it's necessarily like that. The error could make the theorem wrong in all cases.

I think it's more that the mathematician has a top-down way of reasoning, where they can see things like "I want to get from New York City to Los Angeles, so I have to board the bus, take a flight, and then take the bus from the airport at LA". There are certain parts where you basically know that a proof will be possible, because it seems true, like "I can get to LA's airport with public transit", so usually a specific hiccup, like a bus being delayed, won't prevent you from getting there.

[blt]

Right, it's possible to get to LA's airport with public transit, but the amount of time it takes cannot be upper bounded using currently known techniques.