Painius wrote,

...we must keep in mind that these are
no more, no less, mathematical
constructs for us to use to better
understand what's happening out in the
"real" world, the world of "physical
reality".

That's very true in the world of pragmatic "applied sciences".
But there is an interesting case study on the 'Primacy
of Math' axiom going on over in that "Tunnel through the center of the
Earth" thread. The premise is based on 'gravity-as-geometry'. So "The
Math" is calculating acceleration rates of an object dropped down the
hole based on 'gravity-as-geometry'. It shows the object under constant
acceleration all the way to center.
But what if gravity is really caused by Flowing Space?
Would there be a difference in the acceleration curve? Well, let's look
at a column of spaceflow as it enters the Earth's surface (or surface
datum as it were) at 11.2 km/sec or 7 miles a second. As it descends,
velocity drops off and continues dropping with increasing depth (due to
the increasing amount of gravitating mass "above/behind" and abeam). And
the acceleration component of the spaceflow drops concomitantly with
velocity. Velocity (and its acceleration component) will drop to zero at
center. To an object freefalling in the spaceflow, maximum velocity
('terminal velocity') will be reached 'waaay before center. And it will
be some fraction of the peak 11.2 km/s surface velocity. The object
will "coast" on conserved momentum on through center at this reduced
velocity, whereupon it will begin encountering spaceflow coming head-on
from the opposite direction.
So the FSP presents a considerably different picture
than the 'gravity-as-geometry' paradigm and the pefectly good Math
describing it.