Modelling is not the same thing as reference. Arguably, a mathematical model refers to mathematical objects--which are non-physical and causally inefficacious--and draws a comparison between them and physical objects. Of course, this is a simplification. The success of a model doesn't...
It seems like a lot of people in this thread are conflating the metaphysical theory of mathematical platonism and its epistemic implications.
The metaphysical version is simple to define. It says that mathematical objects exist, they are abstract (i.e. causally inefficacious), and they exist...