Sorry if I put my words in your mouth. It is MY opinion
that what mathematical models miss is anything that is indivisible within its functions, and that that indivisibility represents a more general principle. If we "back out" so we can mathematically represent the more general principle's presence in a more general system, and there is still something unrepresentable mathematically, then again we've run into yet a more general principle. Is there an absolute bottom line, where indivisibility may be absolute?
I think in terms of ontologically backing out of manifest reality toward more and more basic systems (i.e. toward raw existence), one might run into consciousness at a pretty basic level, but I suspect that an absolute most basic level of existence is beneath that and not conscious at all. Why?
If the absolute most basic level is conscious, then how do we explain learning, development, conscious evolution? Assuming we humans are specific manifestations of something more generally conscious, then the fact that we can learn demonstrates the more general thing learns. But if it is now learned more than it used to be, then we can assume earlier it was less learned. Tracing that back we come to a stage that is unlearned, which suggests consciousness has a begining.
For that reason I suspect there is a level of existence more basic than consciousness. A raw poteniality which has the potential
for consciousness, as well as for everything else that is manifest. In the past I've postulated this raw poteniality is an infinite continuum of non-quantumized
"ground state" light. If so, obviously it would be too subtle to be detected by our machinery.