I would even say that black holes started out as "mathematically valid, but so bizarre that there's no way they could exist in nature". Now we know that they are
common.
It's a great example of the theory getting something right before we had good hard evidence for it.
In this sense dark matter is kind of the opposite. We didn't have a theory predicting it. But over the last several decades we've been steadily accumulating observational evidence indicating that this stuff is out there. This evidence is now so hard to ignore that it has become a key part of our current theory of cosmology: the concordance model, or ΛCDM, which literally stands for "Dark Energy + Cold Dark Matter".
It might instead be that our understanding of gravity is wrong, but I think that ship has been nearly sunk. If evidence of dark matter is instead evidence of a flaw in our understanding of gravity, then that flaw is not at all trivial. Modified gravity can explain some of the observations, but not all of them, and not all of them by using the same correction.
Work begins on a vast Dark-Matter mapping project, showing galaxies clustering where the matter is at its densest, though as to whether that is cause or effect of galaxy clustering I do not know, possibly both.
To some extent it is both, but much more the former than the latter.
Galactic clusters are not evenly distributed, but instead lie along these great filaments and sheets, or the "
cosmic web".
Simulations of the evolution of the universe show that it is mainly the gravitational collapse of the dark matter that produces this cosmic web, which then "seeds" the formation of galaxies as gas is also drawn in to the high density regions. Intuitively, you can think of the dark matter playing the dominant role in structure formation just because there's a lot more of it -- it outweighs "regular" matter by about a factor of five. But the growth also works both ways, as there is still more gas and dark matter falling into the galactic clusters from afar. The high density regions of the cosmic web are still growing as their gravitational field pulls in more material.
