And I think the average person would have an extremely difficult time discerning between things that are the former - boring erudite truths - and the latter - simple statements a large chunk of mathematicians disagree with!
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Because for the most part, like with software engineering, whether or not code is formally verified or some biologist's method of integration is proved to converge often has little bearing on whether either method is used. What ground truth is there?
AFAICT your statement and your question are non sequiturs. I'm not sure where to go from here, because I seem to be saying "squares are rectangles" and you seem to be saying "plenty of rectangles aren't squares" — in order to defend the claim that squares aren't a real thing
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Is integration that isn't proven correct integration? Even if they don't know what it is and lack the tools to know why it converges?
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A child doesn't have to know what "weight" *is* — that it's a function (and measure) of gravity — in order to put it to use deciding whether they'll be able to pick something up. It's useful because of facts about the world unknown to the child. The map is not the territory.
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