Now, the mathematics of quantum mechanics are abstract and hard to visualize.
I think people need to take a step back and just look at what they're actually doing. The issue is that we often try to construct visualizations that are not the same as what is actually being done in practice. This can only go so far. A person who has been blind since birth can never even conceive of what it is like to see color. You have to have observed something before in order to conceive of it. For a visualization to work, it has to be based on something we have observed before, or else we cannot conceive of it. Once they get too exotic, you just can't conceive of it anymore.
Trying to conceive of Hilbert space as a physical space things move through, which is very common in a lot of attempts to visualize QM I've seen, is just a pointless endeavor. It would be nothing like anything we have ever observed before or could ever observe, so any visualization you are thinking of in your head would have to be lying to yourself. Indeed, I've seen several videos that try to create visualizations by showing things turning into waves and moving through 3D space, you cannot do this without leaving a lot of information out.
Really, this is kind of a self-imposed problem, because why are we inventing visualizations based on things we haven't actually observed? It makes sense in Newtonian mechanics to try and visualize a cannonball flying from point A to to point B. Even if you never saw it in between those points, you can still visualize it being there because in principle you could have observed it there. It makes no sense when we get to quantum mechanics to try and visualize a photon in between point A and point B when you didn't see it there, to visualize it as some sort of physical wave spreading out in Hilbert space. That visualization has no connection to what you actually observed.
The issue here is that the visualizations just become entirely detached from reality. It's effectively making things up. If we just stick to what we actually observe in experiment then it is much easier to visualize, because you are visualizing things you can actually go out and observe. Don't visualize the photon as literally spreading out as a wave. Nobody in human history has observed that. Visualize the photon as being at the laser, then later being at the screen at a random position, but if you have millions of them, their overall behavior will converge to wave-like patterns. Visualize
that because that's actually what we see. Everything else is just a nice fiction, really. If that fiction actually helps you solve problems, you can defend it in terms of utility, but if it is just confusing you, then just stop it.
It is better to regard a particle not as a permanent entity but as an instantaneous event. Sometimes these events form chains that give the illusion of permanent beings — but only in particular circumstances and only for an extremely short period of time in every single case.
— Erwin Schrodinger, “Nature and the Greeks and Science and Humanism”