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.