Well, here's my take:
Reality's real. The stories we tell ourselves about reality
color our experience of reality. The stories may be called
"beliefs". The stories may be called 'reason". The stories may
be called "Science' or "math" or "God" or whatever. But since
they all are languages, they're all "after the fact" stories.
The stories both make up our subjective realities yet do not
directly modify reality "as it is", if one is limiting to
physical reality.
Other realities which are somewhat more abstracted can equally
be real but are more modifiable than physical reality.
The way we DESCRIBE physical reality can happen in many ways.
Some better than others. Math isn't the reality but it's
superimposed upon it as a map and a way for us to compress
knowledge into a form we can consume.
BUT, the names we give the things isn't what they are. It's what
they are FOR OUR USE.
Something exists where the thing we call Rock is.
But is there such a thing as a "rock"?
There is and yet there isn't. Our desire (or biological need
more likely) to compress reality into simplified forms that can
be compressed within our brains seems to be necessary because:
Our brains are too small.
We can't hold reality "as it is" in all of its uniqueness and
transience within our small brains.
So, we simplify.
A lot.
Data gets lost in simplification.
But poor data doesn't make a poor reality.
I believe we're CAPABLE of experiencing/knowing reality as it
is.. but not necessarily describing it properly, not entirely.