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Why do you say that? Math is a tool for conceptual modeling of an “external process”. Therein lies the connection. Geometry is a means to study shapes in 3-dimension before committing money to building them. Am I wrong?

Maybe I should have made more clear that by “connection” I meant a material link, an interdependency, lest one succumb to reification.

The geometric model is not true in that the actual external object deviates from your model.  If I think of the model, then die, the object remains ans is unaffected by my death.  If 10 people think about the object, draw diagrams, and write equations about the object then that object is not altered at all.

It is easy to confuse the abstraction for the reality, called reification, a fallacy, which I am as susceptible to as anybody else.  The great practical success of mathematics enabling technology enhances our innate tendency to confuse our abstraction with an external reality.

This problem of reification becomes acute for the theist and others who suffer from a variety of delusions, thinking their dreams, fantasies, and abstractions are themselves external realizations.

At this time we have no true models of reality available to us, none whatsoever.  The best models of physics are, however, considered valid approximations for very good reasons, namely that experiment confirms they are highly accurate over a very wide range of conditions.