I think you're engaging in deepities here. It is clearly true that all of mathematics historically descends from thoughts about the real world. It is clearly false that all of mathematics is directly about the real world. Using the same words for both claims, "mathematics is about the real world", is the deepity.

So continuity, as a mathematical construct, started out trying to describe the world, and was later found to have more interesting implications even when it was also found to be physically wrong.

That is news to me. Physicists, even fundamental physicists, still talk about differential geometry and Hilbert spaces and so on. There are speculations about an underlying discrete structure on the Planck scale or below, but did anyone refound physics on that basis yet? Stephen Wolfram made some gestures in that direction in his magnum opus; but I read a physicist writing a review of it saying that Wolfram's idea of explaining quantum entanglement that way was already known not to work.

Ok, so you would say inaccessible cardinals, versions of the continuum hypothesis etc. are "about the real world."

At this point, I am bowing out of this conversation as we aren't using words in the same way.

What was the point of writing that? Do you think I was talking about "3"?