Let's assume your philosophy is correct - that mathematics is used as a tool, this would imply that the universe can be described independent of mathematics and it leads to two kinds of experiments, the qualitative kind and the quantitative kind, the latter being important for mathematical analysis. In your comment, you made mention of experimental data which i believe is quantitative in nature, remember that the quantum world unlike the classical world houses entities that cannot be observed directly because of their size - that is if they actually have, and other factors. If i may ask, does the experiment tell about the shape of an electron or quark or photon ?
Different theories can give the same predictions that can conform numerically with quantitative experimental data but give different qualitative predictions, an example can be seen in Einstein's and Newton's theories of gravitation.
Also remember that there are issues yet to be resolved by the standard model of particle physics. If another theory exists that would predict what the standard model predicts and also resolve these other issues, then there's possibility that there might be another definition for a particle, it could be something we may not have imagined at all - the universe is full of surprises.
Well, this is not "my" philosophy. It has, as a matter of fact, nothing to do with philosophy. It is instead the mere definition of physics as the science that studies the properties of matter (and the laws governing all associated phenomena). Mathematics are useful. That's clear. But they are not the purpose, and I don't see how this implies that the universe can be described independently of mathematics. I have never made this implication and I disagree with it.
In addition, quantum theories are predictive (which is why they are called "theories") and these predictions can be compared with data. Moreover, many quantum phenomena have been observed and some are even at the source of technological applications.
To discuss the last point of your reply, it is clear that they are issues with the Standard Model. No one will say the contrary. However, the Standard Model works super well for many things as a quantum field theory. Any theory that may supersede it in years from now (and I hope I will live enough to see this happening, which is not guaranteed), will just be as the Standard Model in the appropriate limit (exactly as for relativity and classical mechanics). Therefore, I maintain my statement. We have here a predictive quantum field theory, whose predictions are in excellent agreement with data. In other words, we have an example of a quantum field theory that works (despite of being imperfect).
You seem to have a very strong bias mind. Well, it is a free world and we are free to believe whatever we like.
If you say so....
Let me just finish by reminding that this "bias" is motivated by 100 years of data and discoveries (i.e. facts), and there is currently no other framework capable to do as good. This is the reason why this framework is acknowledged as the standard paradigm by physicists from all over the world.
This being said, yes we can believe in whatever we want as individuals.