I think we have to be very careful that we don't perpetuate the myth that all mathematical discoveries were made by white men. It's much harder work to find the examples from other cultures and from women, and we are less likely to be familiar with these histories, so we must actively seek them out.
Because math teachers lie a lot: "you can't take the square root of a negative number", "you can't subtract a big number from a small number", "it's continuous if you can draw it without lifting your pencil" and so on....
Hah! Those lies serve a purpose. It's almost a defining characteristic of math that it can be boundlessly complex. (See what I did there?)
By hiding that complexity, we make math more accessible. I don't think we do permanent harm with those lies. But we do need to admit it's a thing we do.
I'm not sure it's lying in either of the first two examples, but rather as we become more sophisticated, and extend our number systems. If we allow only positive quantities it's true that we can't subtract a bigger number from a smaller one.
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This one is probably too wordy, I try to be more concise.
By hiding that complexity, we make math more accessible. I don't think we do permanent harm with those lies. But we do need to admit it's a thing we do.
If you're lucky, you may be taught this in your high school geometry or algebra II class, but I don't think most people get it until college, if ever.