I think the biggest problem with the “objective reality is mathematical” point of view is that there are many non-equivalent ways of interpreting the mathematic

I think the biggest problem with the “objective reality is mathematical” point of view is that there are many non-equivalent ways of interpreting the mathematics (e.g. wavefunction collapse vs. many worlds). It’s also the case that two non-equivalent mathematical formalisms can describe the same phenomenon. I’m not a physicist, but I think classical vs. Hamiltonian mechanics fits the bill there. Also possibly quantum vs. Bohmian mechanics (but I’m far too naïve in physics to be able to judge that one properly).