Math doesn't really justify the claim: we have plenty of math to justify classic mechanics, yet it's not how the nature works. At some point you need to stop calculating and start thinking.

You make a good point and I agree with the "start thinking" part. But I think philosophizing about everything without actually being able to give concrete, substantive results is as useless as trying to use mathematics blindly and w/o "thinking".

Actually yes, that's how nature "works", at certains scales and regimes of applicability. Likewise quantum mechanics also tells us something fundamental about how nature works, again at certain regimes of applicability. It's still not a theory of everything, but that doesn't mean it's wrong.

Newtonian physics is only coincidentally correct. It’s not “wrong” in the sense that the math isn’t sound or that experiments aren’t reproducible within earth, but it’s not the correct model for what really happens in physical phenomenon regardless of scale.

What? It's not "coincidentally" correct, and yes, it absolutely is a correct model for phenomena at a certain scale (in fact, for the vast majority of phenomena in engineering disciplines for instance).

It's really not a correct model even at the scale of the phenomena for which it is correct, that's why it can't explain what's beyond its scale, nor can anyone draw a line to clearly define the boundaries of the scale in which it is correct. I'm afraid I don't have a more profound argument than that. The math of Newtonian physics merely coincides with what's actually going on in reality, but what's actually going on in reality is as explained by Einsteinian physics. We're only keeping Newtonian physics around because it's close enough as an approximation of natural phenomenon and therefore it is pragmatic, but pragmatic does not mean correct and it remains an estimation nonetheless. It's not the correct model of what's actually going on.

What scale? Quantum mechanics has no limit on scale, e.g. delayed choice experiment has galactic scale.

It certainly has. It's no theory of everything, therefore it has limits. For example not explaining gravity.

Exactly! Without the math to back it up, the additional rationalizing is not a foundational study. It cannot be built upon, and that is why it isn't a great idea.

Einstein would apparently disagree with you.

I find this to be a very narrow minded perspective.

Without the philosophy to back it up how can you justify your belief in the mathematics?

Do I really need to know the history of science and philosophy in order to come up with Lorentz Transformation? No, I need solid understanding of physics and the mathematical models that are already available in that framework, and then build upon those.

Sure, these articles could be fun to read, but one does not really expect to have more practical knowledge after reading them. How would you use Hume’s arguments to help you learn the theory of relativity better?

And it’s not just in physics. I can make the same claim in almost any field of science that values results over cheap talk. In game theory for example, does philosophy help you come up with something as magnificent as Nash Equilibrium? No, but Kakutani’s theorem does. Learn the math and practical knowledge, the rest is a waste of time.

It depends on your goals and where your interests align. The domain of philosophy is fundamental and all encompassing, and you have philosophical opinions that you can choose to examine or not. From a career perspective you are almost certainly right that time is better spent extending your skills in the empirical domain but others have a different temperament and have use for philosophy. And for some of those people, their contributions are long lasting and impactful.

See this link titled “The Purpose of Philosophy”: http://assets.press.princeton.edu/chapters/s10113.pdf

Well, the very idea of the scientific method is a philosophical innovation. I think you're not even aware of the history of how we got here.

Saying that physics has a “mathematical framework” is a philosophical stance.